Datasets:
CloKTech
/
MesoMathematics

Dataset card Data Studio Files
xet
 Community
1
definition_height
int64
0
59
⌀
is_auto_or_private
bool
2 classes
is_internal_name
bool
2 classes
kind
stringclasses
7 values
module
stringlengths
12
90
name
stringlengths
2
347
namespace
stringlengths
0
235
reducibility
stringclasses
3 values
statement_dag_size
int64
1
13.9k
type_refs
listlengths
0
229
value_dag_size
int64
1
95.1k
⌀
value_refs
listlengths
0
699
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_replace
AList
null
50
[ "AList", "AList.instMembership", "AList.replace", "DecidableEq", "Iff", "Membership.mem" ]
172
[ "AList", "AList.instMembership", "AList.keys", "AList.keys_replace", "AList.mem_keys", "AList.replace", "DecidableEq", "Eq", "Eq.mpr", "Eq.symm", "Iff", "Iff.rfl", "List", "List.instMembership", "Membership.mem", "congrArg", "id", "propext" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.mem_replace._simp_1
AList.mem_replace
null
52
[ "AList", "AList.instMembership", "AList.replace", "DecidableEq", "Eq", "Membership.mem" ]
59
[ "AList", "AList.instMembership", "AList.mem_replace", "AList.replace", "DecidableEq", "Membership.mem", "propext" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mem_union
AList
null
52
[ "AList", "AList.instMembership", "AList.instUnion", "DecidableEq", "Iff", "Membership.mem", "Or", "Union.union" ]
34
[ "AList", "AList.entries", "DecidableEq", "List.mem_keys_kunion" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.mem_union._simp_1
AList.mem_union
null
54
[ "AList", "AList.instMembership", "AList.instUnion", "DecidableEq", "Eq", "Membership.mem", "Or", "Union.union" ]
60
[ "AList", "AList.instMembership", "AList.instUnion", "AList.mem_union", "DecidableEq", "Membership.mem", "Or", "Union.union", "propext" ]
null
false
false
constructor
Mathlib.Data.List.AList
AList.mk
AList
null
23
[ "AList", "List", "List.NodupKeys", "Sigma" ]
null
[]
null
true
true
abbrev
Mathlib.Data.List.AList
AList.mk._flat_ctor
AList.mk
abbrev
23
[ "AList", "List", "List.NodupKeys", "Sigma" ]
25
[ "AList.mk", "List", "List.NodupKeys", "Sigma" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.mk.congr_simp
AList.mk
null
63
[ "AList", "AList.mk", "Eq", "Eq.ndrec", "List", "List.NodupKeys", "Sigma" ]
96
[ "AList", "AList.mk", "Eq", "Eq.ndrec", "Eq.rec", "Eq.refl", "List", "List.NodupKeys", "Sigma" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.mk.inj
AList.mk
null
53
[ "AList", "AList.mk", "Eq", "List", "List.NodupKeys", "Sigma" ]
78
[ "AList", "AList.mk", "AList.mk.noConfusion", "Eq", "HEq", "List", "List.NodupKeys", "Sigma", "eq_of_heq" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.mk.injEq
AList.mk
null
56
[ "AList", "AList.mk", "Eq", "List", "List.NodupKeys", "Sigma" ]
107
[ "AList", "AList.mk", "AList.mk.inj", "Eq", "Eq.ndrec", "Eq.propIntro", "Eq.refl", "List", "List.NodupKeys", "Sigma" ]
null
true
false
abbrev
Mathlib.Data.List.AList
AList.mk.noConfusion
AList.mk
abbrev
59
[ "AList", "AList.mk", "Eq", "HEq", "List", "List.NodupKeys", "Sigma" ]
95
[ "AList", "AList.mk", "AList.noConfusion", "Eq", "Eq.refl", "HEq", "HEq.refl", "List", "List.NodupKeys", "Sigma", "heq_of_eq", "id" ]
null
true
false
theorem
Mathlib.Data.List.AList
AList.mk.sizeOf_spec
AList.mk
null
96
[ "AList", "AList._sizeOf_inst", "AList.mk", "Eq", "HAdd.hAdd", "List", "List.NodupKeys", "List._sizeOf_inst", "Nat", "OfNat.ofNat", "Sigma", "Sigma._sizeOf_inst", "SizeOf", "SizeOf.sizeOf", "instAddNat", "instHAdd", "instOfNatNat", "instSizeOfDefault" ]
78
[ "Eq.refl", "HAdd.hAdd", "List", "List.NodupKeys", "List._sizeOf_inst", "Nat", "OfNat.ofNat", "Sigma", "Sigma._sizeOf_inst", "SizeOf", "SizeOf.sizeOf", "instAddNat", "instHAdd", "instOfNatNat", "instSizeOfDefault" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.mk_cons_eq_insert
AList
null
74
[ "AList", "AList.insert", "AList.mk", "DecidableEq", "Eq", "List", "List.NodupKeys", "List.cons", "List.nodupKeys_of_nodupKeys_cons", "Sigma", "Sigma.fst", "Sigma.snd" ]
267
[ "AList", "AList.entries", "AList.insert", "AList.insert._proof_1", "AList.mk", "AList.mk.congr_simp", "AList.mk.injEq", "And", "DecidableEq", "Eq", "Eq.mpr", "Eq.ndrec", "Eq.symm", "Eq.trans", "List", "List.NodupKeys", "List.cons", "List.cons.injEq", "List.kerase", "List.kerase...
null
true
false
abbrev
Mathlib.Data.List.AList
AList.noConfusion
AList
abbrev
55
[ "AList", "AList.noConfusionType", "Eq", "HEq" ]
208
[ "AList", "AList.casesOn", "AList.noConfusionType", "Eq", "Eq.ndrec", "HEq", "HEq.refl", "List", "List.NodupKeys", "Sigma", "eq_of_heq" ]
null
true
false
abbrev
Mathlib.Data.List.AList
AList.noConfusionType
AList
abbrev
16
[ "AList" ]
73
[ "AList", "AList.casesOn", "HEq", "List", "List.NodupKeys", "Sigma" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.nodupKeys
AList
null
20
[ "AList", "AList.entries", "List.NodupKeys" ]
12
[ "AList" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.notMem_empty
AList
null
29
[ "AList", "AList.instEmptyCollection", "AList.instMembership", "EmptyCollection.emptyCollection", "Membership.mem", "Not" ]
12
[ "List.not_mem_nil" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.notMem_empty._simp_1
AList.notMem_empty
null
33
[ "AList", "AList.instEmptyCollection", "AList.instMembership", "EmptyCollection.emptyCollection", "Eq", "False", "Membership.mem" ]
34
[ "AList", "AList.instEmptyCollection", "AList.instMembership", "AList.notMem_empty", "EmptyCollection.emptyCollection", "Membership.mem", "eq_false" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.perm_erase
AList
null
52
[ "AList", "AList.entries", "AList.erase", "DecidableEq", "List.Perm", "Sigma" ]
39
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.Perm.kerase" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.perm_insert
AList
null
56
[ "AList", "AList.entries", "AList.insert", "DecidableEq", "List.Perm", "Sigma" ]
75
[ "AList", "AList.entries", "AList.insert", "AList.nodupKeys", "DecidableEq", "List.Perm", "List.Perm.kinsert", "Sigma", "id" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.perm_lookup
AList
null
50
[ "AList", "AList.entries", "AList.lookup", "DecidableEq", "Eq", "List.Perm", "Option", "Sigma" ]
53
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.Perm", "List.perm_dlookup", "Sigma" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.perm_replace
AList
null
56
[ "AList", "AList.entries", "AList.replace", "DecidableEq", "List.Perm", "Sigma" ]
43
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.Perm.kreplace" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.perm_union
AList
null
75
[ "AList", "AList.entries", "AList.instUnion", "DecidableEq", "List.Perm", "Sigma", "Union.union" ]
74
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.Perm", "List.Perm.kunion", "Sigma" ]
null
false
false
recursor
Mathlib.Data.List.AList
AList.rec
AList
null
38
[ "AList", "AList.mk", "List", "List.NodupKeys", "Sigma" ]
null
[]
null
true
false
abbrev
Mathlib.Data.List.AList
AList.recOn
AList
abbrev
39
[ "AList", "AList.mk", "List", "List.NodupKeys", "Sigma" ]
44
[ "AList", "AList.mk", "AList.rec", "List", "List.NodupKeys", "Sigma" ]
6
false
false
definition
Mathlib.Data.List.AList
AList.replace
AList
regular
23
[ "AList", "DecidableEq" ]
44
[ "AList", "AList.entries", "AList.mk", "AList.replace._proof_1", "DecidableEq", "List.kreplace" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.replace._proof_1
AList.replace
null
36
[ "AList", "AList.entries", "DecidableEq", "List.NodupKeys", "List.kreplace" ]
53
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "Iff.mpr", "List.NodupKeys", "List.kreplace", "List.kreplace_nodupKeys" ]
1
false
false
definition
Mathlib.Data.List.AList
AList.singleton
AList
regular
15
[ "AList" ]
36
[ "AList.mk", "AList.singleton._proof_1", "List.cons", "List.nil", "Sigma", "Sigma.mk" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.singleton._proof_1
AList.singleton
null
30
[ "List.NodupKeys", "List.cons", "List.nil", "Sigma", "Sigma.mk" ]
21
[ "List.nodupKeys_singleton", "Sigma.mk" ]
null
true
false
theorem
Mathlib.Data.Finmap
AList.singleton.eq_1
AList.singleton
null
48
[ "AList", "AList.mk", "AList.singleton", "AList.singleton._proof_1", "Eq", "List.cons", "List.nil", "Sigma", "Sigma.mk" ]
23
[ "AList", "AList.singleton", "Eq.refl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.singleton_entries
AList
null
41
[ "AList.entries", "AList.singleton", "Eq", "List", "List.cons", "List.nil", "Sigma", "Sigma.mk" ]
29
[ "AList.entries", "AList.singleton", "List", "Sigma", "rfl" ]
null
false
false
theorem
Mathlib.Data.Finsupp.AList
AList.singleton_lookupFinsupp
AList
null
39
[ "AList.lookupFinsupp", "AList.singleton", "Eq", "Finsupp", "Finsupp.single", "Zero" ]
98
[ "AList", "AList.insert_lookupFinsupp", "AList.instEmptyCollection", "AList.lookupFinsupp", "AList.singleton", "Classical.propDecidable", "EmptyCollection.emptyCollection", "Eq", "Eq.trans", "Finsupp", "Finsupp.single", "True", "Zero", "congrArg", "congrFun'", "eq_self", "of_eq_true" ...
null
false
false
theorem
Mathlib.Data.List.AList
AList.toAList_cons
AList
null
54
[ "AList", "AList.insert", "DecidableEq", "Eq", "List", "List.cons", "List.toAList", "Sigma", "Sigma.mk" ]
45
[ "AList", "DecidableEq", "List", "List.cons", "List.toAList", "Sigma", "Sigma.mk", "rfl" ]
3
false
false
definition
Mathlib.Data.Finmap
AList.toFinmap
AList
regular
15
[ "AList", "Finmap" ]
31
[ "AList", "AList.entries", "AList.nodupKeys", "Finmap.mk", "Multiset.ofList", "Sigma" ]
null
true
false
theorem
Mathlib.Data.Finmap
AList.toFinmap.eq_1
AList.toFinmap
null
42
[ "AList", "AList.entries", "AList.nodupKeys", "AList.toFinmap", "Eq", "Finmap", "Finmap.mk", "Multiset.ofList", "Sigma" ]
22
[ "AList", "AList.toFinmap", "Eq.refl", "Finmap" ]
null
false
false
theorem
Mathlib.Data.Finmap
AList.toFinmap_entries
AList
null
36
[ "AList", "AList.entries", "AList.toFinmap", "Eq", "Finmap.entries", "Multiset", "Multiset.ofList", "Sigma" ]
28
[ "AList", "AList.toFinmap", "Finmap.entries", "Multiset", "Sigma", "rfl" ]
null
false
false
theorem
Mathlib.Data.Finmap
AList.toFinmap_eq
AList
null
43
[ "AList", "AList.entries", "AList.toFinmap", "Eq", "Finmap", "Iff", "List.Perm", "Sigma" ]
316
[ "AList", "AList.casesOn", "AList.entries", "AList.mk", "AList.nodupKeys", "AList.toFinmap", "Eq", "Eq.ndrec", "Eq.refl", "Eq.symm", "Eq.trans", "Finmap", "Finmap.mk", "Finmap.mk.injEq", "Iff", "List", "List.NodupKeys", "List.Perm", "Multiset", "Multiset.coe_eq_coe._simp_1", "...
5
false
false
definition
Mathlib.Data.List.AList
AList.union
AList
regular
22
[ "AList", "DecidableEq" ]
42
[ "AList", "AList.entries", "AList.mk", "AList.union._proof_1", "DecidableEq", "List.kunion" ]
null
true
true
theorem
Mathlib.Data.List.AList
AList.union._proof_1
AList.union
null
35
[ "AList", "AList.entries", "DecidableEq", "List.NodupKeys", "List.kunion" ]
38
[ "AList", "AList.entries", "AList.nodupKeys", "DecidableEq", "List.NodupKeys.kunion" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.union_assoc
AList
null
52
[ "AList", "AList.entries", "AList.instUnion", "DecidableEq", "List.Perm", "Sigma", "Union.union" ]
381
[ "AList", "AList.entries", "AList.instUnion", "AList.nodupKeys", "And", "DecidableEq", "Eq", "Eq.trans", "Iff", "List", "List.dlookup", "List.dlookup_kunion_eq_some._simp_1", "List.instMembership", "List.keys", "List.kunion", "List.lookup_ext", "List.mem_keys_kunion._simp_1", "Membe...
null
false
false
theorem
Mathlib.Data.List.AList
AList.union_comm_of_disjoint
AList
null
52
[ "AList", "AList.Disjoint", "AList.entries", "AList.instUnion", "DecidableEq", "List.Perm", "Sigma", "Union.union" ]
596
[ "AList", "AList.Disjoint", "AList.entries", "AList.instUnion", "AList.keys", "AList.keys.eq_1", "AList.nodupKeys", "And", "And.intro", "And.right", "Bool", "Bool.true", "DecidableEq", "Eq", "Eq.mpr", "Eq.refl", "Eq.symm", "Eq.trans", "Iff", "Iff.intro", "List", "List.dlooku...
null
false
false
theorem
Mathlib.Data.List.AList
AList.union_empty
AList
null
37
[ "AList", "AList.instEmptyCollection", "AList.instUnion", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Union.union" ]
90
[ "AList", "AList.entries", "AList.ext", "AList.instEmptyCollection", "AList.instUnion", "DecidableEq", "EmptyCollection.emptyCollection", "Eq", "Eq.trans", "List", "List.kunion_nil", "Sigma", "True", "Union.union", "congrArg", "congrFun'", "eq_self", "of_eq_true" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.union_entries
AList
null
52
[ "AList", "AList.entries", "AList.instUnion", "DecidableEq", "Eq", "List", "List.kunion", "Sigma", "Union.union" ]
43
[ "AList", "AList.entries", "AList.instUnion", "DecidableEq", "List", "Sigma", "Union.union", "rfl" ]
null
false
false
theorem
Mathlib.Data.List.AList
AList.union_erase
AList
null
50
[ "AList", "AList.erase", "AList.instUnion", "DecidableEq", "Eq", "Union.union" ]
90
[ "AList", "AList.entries", "AList.erase", "AList.ext", "AList.instUnion", "DecidableEq", "Eq.symm", "List", "List.kerase", "List.kunion", "List.kunion_kerase", "Sigma", "Union.union" ]
null
false
false
abbrev
Mathlib.Algebra.Category.Grp.Basic
Ab
abbrev
1
[]
1
[ "AddCommGrpCat" ]
13
false
false
definition
Mathlib.GroupTheory.Abelianization.Defs
Abelianization
regular
6
[ "Group" ]
21
[ "Group", "HasQuotient.Quotient", "QuotientGroup.instHasQuotientSubgroup", "Subgroup", "commutator" ]
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.coe_lift_symm
Abelianization
null
149
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Equiv", "Equiv.instEquivLike", "Equiv.symm", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMul...
121
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Equiv", "Equiv.instEquivLike", "Equiv.symm", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "Mu...
14
false
false
definition
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.commGroup
Abelianization
regular
12
[ "Abelianization", "CommGroup", "Group" ]
42
[ "Abelianization", "Abelianization.commGroup._proof_2", "CommGroup.mk", "Group", "HasQuotient.Quotient", "QuotientGroup.Quotient.group", "QuotientGroup.instHasQuotientSubgroup", "Subgroup", "commutator", "instNormalCommutator" ]
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.commGroup._proof_1
Abelianization.commGroup
null
93
[ "Bracket.bracket", "DivInvMonoid.toMonoid", "DivInvOneMonoid.toInvOneClass", "DivisionMonoid.toDivInvOneMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Group.toDivisionMonoid", "HMul.hMul", "Inv.inv", "InvOneClass.toInv", "Monoid.toMulOneClass", "Monoid.toSemigroup", "MulOne.toMul", "Mu...
264
[ "Bracket.bracket", "DivInvMonoid.toInv", "DivInvMonoid.toMonoid", "DivInvOneMonoid.toInvOneClass", "DivisionMonoid.toDivInvMonoid", "DivisionMonoid.toDivInvOneMonoid", "DivisionMonoid.toInvolutiveInv", "Eq", "Eq.trans", "Group", "Group.toDivInvMonoid", "Group.toDivisionMonoid", "HMul.hMul", ...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.commGroup._proof_2
Abelianization.commGroup
null
68
[ "Abelianization", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "HMul.hMul", "HasQuotient.Quotient", "Monoid.toSemigroup", "QuotientGroup.Quotient.group", "QuotientGroup.instHasQuotientSubgroup", "Semigroup.toMul", "Subgroup", "commutator", "instHMul", "instNormalCommut...
507
[ "Abelianization", "Abelianization.commGroup._proof_1", "And", "And.intro", "Bracket.bracket", "Con.mk", "Con.toSetoid", "DivInvMonoid.toMonoid", "DivInvOneMonoid.toInvOneClass", "DivisionMonoid.toDivInvOneMonoid", "Eq", "Exists", "Exists.intro", "Group", "Group.toDivInvMonoid", "Group....
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.commutator_subset_ker
Abelianization
null
82
[ "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "LE.le", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.ker", "MulOneClass.toMulOne", "PartialOrder.toPreorder", "Preorder.toLE", "Subgroup", "Subgroup.instPartialOrder", "commutator" ]
740
[ "Bracket.bracket", "CommGroup", "CommGroup.toCommMonoid", "CommGroup.toDivisionCommMonoid", "CommGroup.toGroup", "CommMagma.toMul", "CommMonoid.toCommSemigroup", "CommSemigroup.toCommMagma", "DFunLike.coe", "DivInvMonoid.toInv", "DivInvMonoid.toMonoid", "DivisionCommMonoid.toDivisionMonoid", ...
17
false
false
definition
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.equivOfComm
Abelianization
regular
48
[ "Abelianization", "Abelianization.commGroup", "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MulEquiv", "MulOne.toMul", "MulOneClass.toMulOne" ]
190
[ "Abelianization", "Abelianization.commGroup", "Abelianization.equivOfComm._proof_1", "Abelianization.equivOfComm._proof_2", "Abelianization.equivOfComm._proof_3", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Equiv", "...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.equivOfComm._proof_1
Abelianization.equivOfComm
null
135
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Function.LeftInverse", "Group.toDivInvMonoid", "Monoid.toMulOneClass"...
137
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq.refl", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHo...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.equivOfComm._proof_2
Abelianization.equivOfComm
null
135
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Function.RightInverse", "Group.toDivInvMonoid", "Monoid.toMulOneClass...
181
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Eq.refl", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.equivOfComm._proof_3
Abelianization.equivOfComm
null
92
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Eq", "Group.toDivInvMonoid", "HMul.hMul", "Monoid.toMulOneClass", "MonoidHom.toOneHom", "MulOne.toMul", "MulOne.toOne", "MulOneClass.toMulOne", "OneHom.toFun", ...
47
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom.map_mul'", "MulOneClass.toMulOne" ]
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.equivOfComm_apply
Abelianization
null
99
[ "Abelianization", "Abelianization.commGroup", "Abelianization.equivOfComm", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "EquivLike.toFunLike", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.instFunLike", "...
79
[ "Abelianization", "Abelianization.commGroup", "Abelianization.equivOfComm", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq.refl", "EquivLike.toFunLike", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MulEquiv", "MulEquiv.instEquivLike", "MulOne.toMul", "...
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.equivOfComm_symm_apply
Abelianization
null
159
[ "Abelianization", "Abelianization.commGroup", "Abelianization.equivOfComm", "Abelianization.lift", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "Mono...
85
[ "Abelianization", "Abelianization.commGroup", "Abelianization.equivOfComm", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq.refl", "EquivLike.toFunLike", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MulEquiv", "MulEquiv.instEquivLike", "MulEquiv.symm", ...
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.hom_ext
Abelianization
null
147
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MulOneClass.toMulOne" ]
258
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of", "CommGroup.toGroup", "DFunLike.coe", "DFunLike.congr_fun", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MonoidHom.ext", "MonoidHom.ins...
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.hom_ext_iff
Abelianization
null
130
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Iff", "Monoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MulOneClass.toMulOne" ]
383
[ "Abelianization", "Abelianization.commGroup", "Abelianization.hom_ext", "Abelianization.of", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Eq", "Eq.casesOn", "Eq.ndrec", "Eq.refl", "Eq.symm", "Group", "Group.toDivInvMonoid", "HEq", "HEq.refl", "Iff.intro", "Monoid", "Monoid.toMulO...
15
false
false
definition
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.instInhabited
Abelianization
regular
12
[ "Abelianization", "Group", "Inhabited" ]
39
[ "Abelianization", "Abelianization.commGroup", "CommGroup.toDivisionCommMonoid", "DivInvOneMonoid.toInvOneClass", "DivisionCommMonoid.toDivisionMonoid", "DivisionMonoid.toDivInvOneMonoid", "Group", "Inhabited.mk", "InvOneClass.toOne", "OfNat.ofNat", "One.toOfNat1" ]
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.ker_of
Abelianization
null
44
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom.ker", "Subgroup", "commutator" ]
18
[ "Group", "QuotientGroup.ker_mk'", "commutator", "instNormalCommutator" ]
16
false
false
definition
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift
Abelianization
regular
70
[ "Abelianization", "Abelianization.commGroup", "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Equiv", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MulOneClass.toMulOne" ]
152
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift._proof_1", "Abelianization.lift._proof_2", "Abelianization.lift._proof_4", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Equiv.mk", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", ...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift._proof_1
Abelianization.lift
null
244
[ "Abelianization", "Abelianization.commGroup", "Abelianization.commutator_subset_ker", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Function.LeftInverse", "Group", "Group.toDivInvMonoid", "Iff.mpr", "Membership.mem", "Monoid.toMulO...
268
[ "Abelianization", "Abelianization.commGroup", "Abelianization.commutator_subset_ker", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Eq.refl", "Group", "Group.toDivInvMonoid", "Iff.mpr", "Membership.mem", "Monoid.toMulOneClass", "...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift._proof_2
Abelianization.lift
null
97
[ "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Membership.mem", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.ker", "MulOneClass.toMulOne", "SetLike.instMembership", "Subgroup", "Subgroup.instSetLike", "commutator" ]
159
[ "Abelianization.commutator_subset_ker", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Iff.mpr", "Membership.mem", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.instFunLike", "MonoidHom.ker", "MonoidHom.mem_ker", "Mu...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift._proof_3
Abelianization.lift
null
142
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Membership.mem", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MonoidHom.ker", "MulOneClass.toMulOne", "SetLike.instMe...
194
[ "Abelianization", "Abelianization.commGroup", "Abelianization.commutator_subset_ker", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Iff.mpr", "Membership.mem", "Monoid.toMulOneClass", "MonoidHom", ...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift._proof_4
Abelianization.lift
null
154
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift._proof_3", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "HasQuotient.Quotient", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MulOneClass...
548
[ "Abelianization", "Abelianization.commGroup", "Abelianization.commutator_subset_ker", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "HasQuotient.Quotient", "Iff.mpr", "Membership.mem", "Monoid.toMulO...
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift_apply_of
Abelianization
null
195
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "Mo...
183
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom"...
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift_of
Abelianization
null
98
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "Mo...
58
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Equiv.apply_symm_apply", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.id", "MulOneClass.toMulOne" ]
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift_of_comp
Abelianization
null
182
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.map", "Abelianization.of", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClas...
175
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom....
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift_symm_apply
Abelianization
null
164
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Equiv", "Equiv.instEquivLike", "Equiv.symm", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMul...
151
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Equiv", "Equiv.instEquivLike", "Equiv.symm", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "Mu...
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.lift_unique
Abelianization
null
284
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "Mo...
298
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "Mo...
17
false
false
definition
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.map
Abelianization
regular
83
[ "Abelianization", "Abelianization.commGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MulOneClass.toMulOne" ]
172
[ "Abelianization", "Abelianization.commGroup", "Abelianization.lift", "Abelianization.of", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Equiv", "Equiv.instEquivLike", "EquivLike.toFunLike", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom....
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.map_comp
Abelianization
null
198
[ "Abelianization", "Abelianization.commGroup", "Abelianization.map", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MulOneClass.toMulOne" ]
217
[ "Abelianization", "Abelianization.commGroup", "Abelianization.hom_ext", "Abelianization.map", "Abelianization.of", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MulOneClass.toMulOne", "rfl" ]
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.map_id
Abelianization
null
56
[ "Abelianization", "Abelianization.commGroup", "Abelianization.map", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.id", "MulOneClass.toMulOne" ]
75
[ "Abelianization", "Abelianization.commGroup", "Abelianization.hom_ext", "Abelianization.map", "Abelianization.of", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MonoidHom.id", "MulOneClass.toMulOne", ...
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.map_map_apply
Abelianization
null
245
[ "Abelianization", "Abelianization.commGroup", "Abelianization.map", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MonoidHom.instFunLike", "MulOneClass.toMulOne" ]
224
[ "Abelianization", "Abelianization.commGroup", "Abelianization.map", "Abelianization.map_comp", "CommGroup.toGroup", "DFunLike.congr_fun", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.comp", "MonoidHom.instFunLike", "MulOneClass.t...
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.map_of
Abelianization
null
186
[ "Abelianization", "Abelianization.commGroup", "Abelianization.map", "Abelianization.of", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.instFunLike", "MulOneClass.toMulOne" ]
141
[ "Abelianization", "Abelianization.commGroup", "Abelianization.map", "Abelianization.of", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.instFunLike", "MulOneClass.toMulOne", "rfl" ]
null
false
false
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.mk_eq_of
Abelianization
null
83
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of", "CommGroup.toGroup", "DFunLike.coe", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MonoidHom.instFunLike", "MulOneClass.toMulOne", "Quot", "Quot.mk", "QuotientGrou...
29
[ "Group", "Quot", "Quot.mk", "QuotientGroup.leftRel", "Setoid.r", "commutator", "rfl" ]
15
false
false
definition
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.of
Abelianization
regular
41
[ "Abelianization", "Abelianization.commGroup", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom", "MulOneClass.toMulOne" ]
68
[ "Abelianization", "Abelianization.commGroup", "Abelianization.of._proof_1", "Abelianization.of._proof_2", "CommGroup.toGroup", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MonoidHom.mk", "MulOne.toOne", "MulOneClass.toMulOne", "OneHom.mk", "QuotientGro...
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.of._proof_1
Abelianization.of
null
45
[ "Abelianization", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MulOne.toOne", "MulOneClass.toMulOne", "OfNat.ofNat", "One.toOfNat1", "QuotientGroup.mk", "commutator" ]
44
[ "Abelianization", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "Monoid.toMulOneClass", "MulOne.toOne", "MulOneClass.toMulOne", "OfNat.ofNat", "One.toOfNat1", "QuotientGroup.mk", "commutator", "rfl" ]
null
true
true
theorem
Mathlib.GroupTheory.Abelianization.Defs
Abelianization.of._proof_2
Abelianization.of
null
51
[ "Abelianization", "DivInvMonoid.toMonoid", "Eq", "Group", "Group.toDivInvMonoid", "HMul.hMul", "Monoid.toMulOneClass", "MulOne.toMul", "MulOneClass.toMulOne", "QuotientGroup.mk", "commutator", "instHMul" ]
50
[ "Abelianization", "DivInvMonoid.toMonoid", "Group", "Group.toDivInvMonoid", "HMul.hMul", "Monoid.toMulOneClass", "MulOne.toMul", "MulOneClass.toMulOne", "QuotientGroup.mk", "commutator", "instHMul", "rfl" ]
7
false
false
definition
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex
regular
24
[ "AddCommMonoid", "PartialOrder", "SMul", "SeminormedRing", "Set" ]
50
[ "AddCommMonoid", "And", "Balanced", "Convex", "PartialOrder", "Ring.toSemiring", "SMul", "SeminormedRing", "SeminormedRing.toRing", "Set" ]
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.absConvexHull_eq
AbsConvex
null
81
[ "AbsConvex", "AddCommMonoid", "ChainCompletePartialOrder.instOfCompleteLattice", "ChainCompletePartialOrder.toPartialOrder", "ClosureOperator", "ClosureOperator.instFunLike", "CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra", "CompleteBooleanAlgebra.toCompleteLattice", "DFunLike.coe", "Eq", ...
91
[ "AbsConvex", "AddCommMonoid", "ChainCompletePartialOrder.instOfCompleteLattice", "ChainCompletePartialOrder.toPartialOrder", "ClosureOperator", "ClosureOperator.instFunLike", "CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra", "CompleteBooleanAlgebra.toCompleteLattice", "DFunLike.coe", "Eq", ...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.absConvexHull_subset_iff
AbsConvex
null
92
[ "AbsConvex", "AddCommMonoid", "ChainCompletePartialOrder.instOfCompleteLattice", "ChainCompletePartialOrder.toPartialOrder", "ClosureOperator", "ClosureOperator.instFunLike", "CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra", "CompleteBooleanAlgebra.toCompleteLattice", "DFunLike.coe", "Iff",...
78
[ "AbsConvex", "AddCommMonoid", "ChainCompletePartialOrder.instOfCompleteLattice", "ChainCompletePartialOrder.toPartialOrder", "ClosureOperator.IsClosed", "ClosureOperator.IsClosed.closure_le_iff", "CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra", "CompleteBooleanAlgebra.toCompleteLattice", "Pa...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.closure
AbsConvex
null
252
[ "AbsConvex", "AddCommGroup", "AddCommGroup.toAddCommMonoid", "AddCommGroup.toAddGroup", "AddGroup.toSubNegMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "ContinuousSMul", "DistribMulAction.toDistribSMul", "DistribSMul.toSMulZeroClass", "DivisionSemiring.toSemi...
315
[ "AbsConvex", "AddCommGroup", "AddCommGroup.toAddCommMonoid", "AddCommGroup.toAddGroup", "AddGroup.toSubNegMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And.intro", "And.left", "And.right", "Balanced", "Balanced.closure", "ContinuousSMul", "ContinuousSM...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.empty
AbsConvex
null
38
[ "AbsConvex", "AddCommMonoid", "EmptyCollection.emptyCollection", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instEmptyCollection" ]
67
[ "AddCommMonoid", "And.intro", "Balanced", "Convex", "EmptyCollection.emptyCollection", "PartialOrder", "Ring.toSemiring", "SMul", "SeminormedRing", "SeminormedRing.toRing", "Set", "Set.instEmptyCollection", "balanced_empty", "convex_empty" ]
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.iInter
AbsConvex
null
50
[ "AbsConvex", "AddCommMonoid", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.iInter" ]
158
[ "AbsConvex", "AbsConvex.sInter", "AddCommMonoid", "Eq", "Eq.rec", "Iff.mpr", "Membership.mem", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.forall_mem_range", "Set.iInter", "Set.instMembership", "Set.range", "Set.sInter", "Set.sInter_range" ]
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.iInter₂
AbsConvex
null
73
[ "AbsConvex", "AddCommMonoid", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.iInter" ]
84
[ "AbsConvex", "AbsConvex.iInter", "AddCommMonoid", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.iInter" ]
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.inter
AbsConvex
null
63
[ "AbsConvex", "AddCommMonoid", "Inter.inter", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instInter" ]
120
[ "AbsConvex", "AddCommMonoid", "And.intro", "And.left", "And.right", "Balanced", "Balanced.inter", "Convex", "Convex.inter", "Inter.inter", "PartialOrder", "Ring.toSemiring", "SMul", "SeminormedRing", "SeminormedRing.toRing", "Set", "Set.instInter" ]
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.sInter
AbsConvex
null
62
[ "AbsConvex", "AddCommMonoid", "Membership.mem", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instMembership", "Set.sInter" ]
135
[ "AbsConvex", "AddCommMonoid", "And.intro", "And.left", "And.right", "Balanced", "Balanced.sInter", "Convex", "Membership.mem", "PartialOrder", "Ring.toSemiring", "SMul", "SeminormedRing", "SeminormedRing.toRing", "Set", "Set.instMembership", "Set.sInter", "convex_sInter" ]
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvex
AbsConvex.univ
AbsConvex
null
33
[ "AbsConvex", "AddCommMonoid", "PartialOrder", "SMul", "SeminormedRing", "Set.univ" ]
62
[ "AddCommMonoid", "And.intro", "Balanced", "Convex", "PartialOrder", "Ring.toSemiring", "SMul", "SeminormedRing", "SeminormedRing.toRing", "Set.univ", "balanced_univ", "convex_univ" ]
8
false
false
definition
Mathlib.Analysis.LocallyConvex.AbsConvexOpen
AbsConvexOpenSets
regular
26
[ "AddCommMonoid", "PartialOrder", "SMul", "SeminormedRing", "TopologicalSpace" ]
80
[ "AbsConvex", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instMembership", "Subtype", "TopologicalSpace", ...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvexOpen
AbsConvexOpenSets.coe_balanced
AbsConvexOpenSets
null
97
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "Balanced", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instMembership",...
157
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "And.left", "And.right", "Balanced", "Convex", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "Ring.toSemiring", ...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvexOpen
AbsConvexOpenSets.coe_convex
AbsConvexOpenSets
null
105
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "Convex", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "Ring.toSemiring", "SMul", "SeminormedRing", "Seminormed...
156
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "And.right", "Balanced", "Convex", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "Ring.toSemiring", "SMul", "S...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvexOpen
AbsConvexOpenSets.coe_isOpen
AbsConvexOpenSets
null
94
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instMembership", "Subtype.va...
134
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "And.left", "And.right", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.i...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvexOpen
AbsConvexOpenSets.coe_nhds
AbsConvexOpenSets
null
117
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "Filter", "Filter.instMembership", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "SMul", "SeminormedRing", "Set"...
129
[ "AbsConvex", "AbsConvexOpenSets", "AbsConvexOpenSets.coe_isOpen", "AbsConvexOpenSets.coe_zero_mem", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "IsOpen", "IsOpen.mem_nhds", "Membership.mem", "OfNat.ofNat", "...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvexOpen
AbsConvexOpenSets.coe_zero_mem
AbsConvexOpenSets
null
110
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instMembership", "Subtype.va...
130
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "And.left", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instMembership",...
9
false
false
definition
Mathlib.Analysis.LocallyConvex.AbsConvexOpen
AbsConvexOpenSets.instCoeOut
AbsConvexOpenSets
regular
40
[ "AbsConvexOpenSets", "AddCommMonoid", "CoeOut", "PartialOrder", "SMul", "SeminormedRing", "Set", "TopologicalSpace" ]
92
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "CoeOut.mk", "IsOpen", "Membership.mem", "OfNat.ofNat", "PartialOrder", "SMul", "SeminormedRing", "Set", "Set.instMembership"...
null
false
false
theorem
Mathlib.Analysis.LocallyConvex.AbsConvexOpen
AbsConvexOpenSets.instNonempty
AbsConvexOpenSets
null
37
[ "AbsConvexOpenSets", "AddCommMonoid", "Nonempty", "PartialOrder", "SMul", "SeminormedRing", "TopologicalSpace" ]
259
[ "AbsConvex", "AbsConvexOpenSets", "AddCommMonoid", "AddCommMonoid.toAddMonoid", "AddMonoid.toAddZeroClass", "AddZero.toZero", "AddZeroClass.toAddZero", "And", "And.intro", "Balanced", "Convex", "Eq", "Eq.mpr", "Eq.symm", "Exists", "Exists.intro", "IsOpen", "Membership.mem", "None...
null
false
false
inductive
Mathlib.Algebra.Order.AbsoluteValue.Basic
AbsoluteValue
null
16
[ "PartialOrder", "Semiring" ]
null
[]
null
false
false
abbrev
Mathlib.Analysis.Normed.Field.WithAbs
AbsoluteValue.Completion
AbsoluteValue
abbrev
26
[ "AbsoluteValue", "DivisionSemiring.toSemiring", "Field", "Field.toSemifield", "Real", "Real.partialOrder", "Real.semiring", "Semifield.toDivisionSemiring" ]
62
[ "AbsoluteValue", "DivisionSemiring.toSemiring", "Field", "Field.toSemifield", "NormedCommRing.toSeminormedCommRing", "NormedField.toNormedCommRing", "PseudoMetricSpace.toUniformSpace", "Real", "Real.partialOrder", "Real.semiring", "Semifield.toDivisionSemiring", "SeminormedCommRing.toSeminorme...
29
false
false
definition
Mathlib.Analysis.Normed.Field.WithAbs
AbsoluteValue.Completion.instCoe
AbsoluteValue.Completion
regular
34
[ "AbsoluteValue", "AbsoluteValue.Completion", "Coe", "DivisionSemiring.toSemiring", "Field", "Field.toSemifield", "Real", "Real.partialOrder", "Real.semiring", "Semifield.toDivisionSemiring" ]
81
[ "AbsoluteValue", "AbsoluteValue.Completion", "Coe.mk", "DivisionSemiring.toSemiring", "Field", "Field.toSemifield", "NormedCommRing.toSeminormedCommRing", "NormedField.toNormedCommRing", "PseudoMetricSpace.toUniformSpace", "Real", "Real.partialOrder", "Real.semiring", "Semifield.toDivisionSe...