diff --git "a/raw/mathlib-v4.33.0/declarations-51.jsonl" "b/raw/mathlib-v4.33.0/declarations-51.jsonl"
new file mode 100644--- /dev/null
+++ "b/raw/mathlib-v4.33.0/declarations-51.jsonl"
@@ -0,0 +1,10000 @@
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+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_le_valuationSubring.match_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_le_valuationSubring","reducibility":"abbrev","statement_dag_size":278,"type_refs":["CommRing.toNonAssocCommRing","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toSupSet","Field","Field.toCommRing","LocalSubring","LocalSubring.toSubring","Membership.mem","NonAssocCommRing.toNonAssocRing","Set","Set.Elem","Set.instMembership","SetLike.instMembership","Subring","Subring.instCompleteLattice","Subring.instSetLike","Subtype","Subtype.mk","Subtype.val","iSup"],"value_dag_size":339,"value_refs":["CommRing.toNonAssocCommRing","CompleteLattice.toConditionallyCompleteLattice","ConditionallyCompleteLattice.toConditionallyCompletePartialOrder","ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup","ConditionallyCompletePartialOrderSup.toSupSet","Field","Field.toCommRing","LocalSubring","LocalSubring.toSubring","Membership.mem","NonAssocCommRing.toNonAssocRing","Set","Set.Elem","Set.instMembership","SetLike.instMembership","Subring","Subring.instCompleteLattice","Subring.instSetLike","Subtype","Subtype.casesOn","Subtype.mk","Subtype.val","iSup"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedIn.match_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedIn","reducibility":"abbrev","statement_dag_size":1297,"type_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","AlgHom","AlgHom.funLike","Algebra.id","Algebra.ofSubsemiring","And","And.intro","CommGroupWithZero.toDivisionCommMonoid","CommRing.toCommSemiring","CommRing.toNonAssocCommRing","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Exists","Exists.intro","Field","Field.toCommRing","Field.toSemifield","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HSub.hSub","Ideal","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","Invertible","Invertible.invOf","IsLocalRing.maximalIdeal","LocalSubring","LocalSubring.isLocalRing","LocalSubring.toSubring","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NonAssocCommRing.toNonAssocRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.aeval","Polynomial.algebraOfAlgebra","Polynomial.leadingCoeff","Polynomial.semiring","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","SubNegMonoid.toSub","Submodule.setLike","Subring","Subring.instSetLike","Subring.instSubringClass","Subring.toCommRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Zero.toOfNat0","instDistribOfSemiring","instHSub","instMulZeroClassOfSemiring","invertibleInv"],"value_dag_size":1622,"value_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","AlgHom","AlgHom.funLike","Algebra.id","Algebra.ofSubsemiring","And","And.casesOn","And.intro","CommGroupWithZero.toDivisionCommMonoid","CommRing.toCommSemiring","CommRing.toNonAssocCommRing","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Exists","Exists.casesOn","Exists.intro","Field","Field.toCommRing","Field.toSemifield","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HSub.hSub","Ideal","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","Invertible","Invertible.invOf","IsLocalRing.maximalIdeal","LocalSubring","LocalSubring.isLocalRing","LocalSubring.toSubring","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NonAssocCommRing.toNonAssocRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.aeval","Polynomial.algebraOfAlgebra","Polynomial.leadingCoeff","Polynomial.semiring","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","SubNegMonoid.toSub","Submodule.setLike","Subring","Subring.instSetLike","Subring.instSubringClass","Subring.toCommRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Zero.toOfNat0","instDistribOfSemiring","instHSub","instMulZeroClassOfSemiring","invertibleInv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedIn.match_1_3","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedIn","reducibility":"abbrev","statement_dag_size":1487,"type_refs":["Algebra.adjoin","Algebra.algebraMap","Algebra.id","Algebra.ofSubsemiring","And","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonAssocCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DFunLike.coe","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toSemiring","Exists","Exists.intro","Field","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","HAdd.hAdd","Ideal","Ideal.map","Ideal.span","Inv.inv","InvOneClass.toInv","IsLocalRing.maximalIdeal","LE.le","LocalSubring","LocalSubring.isLocalRing","LocalSubring.toSubring","Membership.mem","NonAssocCommRing.toNonAssocRing","NonAssocRing.toNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalSubring","NonUnitalSubring.instSetLike","PartialOrder.toPreorder","Preorder.toLE","Ring.toNonAssocRing","RingHom","RingHom.instFunLike","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.image","Set.instLE","Set.instSingletonSet","SetLike.coe","SetLike.instMembership","Singleton.singleton","Subalgebra","Subalgebra.algebra","Subalgebra.instSetLike","Subalgebra.toSemiring","Subalgebra.toSubring","Submodule.pointwiseAdd","Submodule.setLike","Subring","Subring.instPartialOrder","Subring.instSetLike","Subring.instSubringClass","Subring.subtype","Subring.toCommRing","SubringClass.toNonAssocRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","ValuationSubring","ValuationSubring.nonunits","ValuationSubring.toSubring","instHAdd"],"value_dag_size":1703,"value_refs":["Algebra.adjoin","Algebra.algebraMap","Algebra.id","Algebra.ofSubsemiring","And","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonAssocCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DFunLike.coe","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toSemiring","Exists","Exists.casesOn","Exists.intro","Field","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","HAdd.hAdd","Ideal","Ideal.map","Ideal.span","Inv.inv","InvOneClass.toInv","IsLocalRing.maximalIdeal","LE.le","LocalSubring","LocalSubring.isLocalRing","LocalSubring.toSubring","Membership.mem","NonAssocCommRing.toNonAssocRing","NonAssocRing.toNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalSubring","NonUnitalSubring.instSetLike","PartialOrder.toPreorder","Preorder.toLE","Ring.toNonAssocRing","RingHom","RingHom.instFunLike","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Semiring.toNonAssocSemiring","Set","Set.image","Set.instLE","Set.instSingletonSet","SetLike.coe","SetLike.instMembership","Singleton.singleton","Subalgebra","Subalgebra.algebra","Subalgebra.instSetLike","Subalgebra.toSemiring","Subalgebra.toSubring","Submodule.pointwiseAdd","Submodule.setLike","Subring","Subring.instPartialOrder","Subring.instSetLike","Subring.instSubringClass","Subring.subtype","Subring.toCommRing","SubringClass.toNonAssocRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","ValuationSubring","ValuationSubring.nonunits","ValuationSubring.toSubring","instHAdd"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_valuationRing_of_isMax.match_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_valuationRing_of_isMax","reducibility":"abbrev","statement_dag_size":1186,"type_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","AlgHom","AlgHom.funLike","Algebra.id","Algebra.ofSubsemiring","And","And.intro","CommRing.toCommSemiring","CommRing.toNonAssocCommRing","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Exists","Exists.intro","Field","Field.toCommRing","Field.toSemifield","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HSub.hSub","Ideal","InvOneClass.toOne","Invertible","Invertible.invOf","IsLocalRing.maximalIdeal","LocalSubring","LocalSubring.isLocalRing","LocalSubring.toSubring","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NonAssocCommRing.toNonAssocRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.aeval","Polynomial.algebraOfAlgebra","Polynomial.leadingCoeff","Polynomial.semiring","Ring.toAddGroupWithOne","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","SubNegMonoid.toSub","Submodule.setLike","Subring","Subring.instSetLike","Subring.instSubringClass","Subring.toCommRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Zero.toOfNat0","instDistribOfSemiring","instHSub","instMulZeroClassOfSemiring"],"value_dag_size":1490,"value_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","AlgHom","AlgHom.funLike","Algebra.id","Algebra.ofSubsemiring","And","And.casesOn","And.intro","CommRing.toCommSemiring","CommRing.toNonAssocCommRing","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Exists","Exists.casesOn","Exists.intro","Field","Field.toCommRing","Field.toSemifield","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HSub.hSub","Ideal","InvOneClass.toOne","Invertible","Invertible.invOf","IsLocalRing.maximalIdeal","LocalSubring","LocalSubring.isLocalRing","LocalSubring.toSubring","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NonAssocCommRing.toNonAssocRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.aeval","Polynomial.algebraOfAlgebra","Polynomial.leadingCoeff","Polynomial.semiring","Ring.toAddGroupWithOne","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","SubNegMonoid.toSub","Submodule.setLike","Subring","Subring.instSetLike","Subring.instSubringClass","Subring.toCommRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Zero.toOfNat0","instDistribOfSemiring","instHSub","instMulZeroClassOfSemiring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.isMax_iff.match_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.isMax_iff","reducibility":"abbrev","statement_dag_size":93,"type_refs":["Eq","Exists","Exists.intro","Field","Field.toCommRing","LocalSubring","ValuationSubring","ValuationSubring.toLocalSubring"],"value_dag_size":119,"value_refs":["Eq","Exists","Exists.casesOn","Exists.intro","Field","Field.toCommRing","LocalSubring","ValuationSubring","ValuationSubring.toLocalSubring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.Subring.eq_iInf_of_isIntegrallyClosedIn.match_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.Subring.eq_iInf_of_isIntegrallyClosedIn","reducibility":"abbrev","statement_dag_size":209,"type_refs":["And","CommRing.toNonAssocCommRing","Exists","Exists.intro","Field","Field.toCommRing","LE.le","Membership.mem","NonAssocCommRing.toNonAssocRing","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subring","Subring.instPartialOrder","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.toSubring"],"value_dag_size":257,"value_refs":["And","CommRing.toNonAssocCommRing","Exists","Exists.casesOn","Exists.intro","Field","Field.toCommRing","LE.le","Membership.mem","NonAssocCommRing.toNonAssocRing","Not","PartialOrder.toPreorder","Preorder.toLE","SetLike.instMembership","Subring","Subring.instPartialOrder","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.toSubring"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn._simp_1_3","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn","reducibility":null,"statement_dag_size":58,"type_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","Eq","HSub.hSub","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub"],"value_dag_size":62,"value_refs":["AddGroup","AddGroup.toSubNegMonoid","AddGroup.toSubtractionMonoid","Eq","HSub.hSub","NegZeroClass.toZero","OfNat.ofNat","SubNegMonoid.toSub","SubNegZeroMonoid.toNegZeroClass","SubtractionMonoid.toSubNegZeroMonoid","Zero.toOfNat0","instHSub","propext","sub_eq_zero"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn.match_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn","reducibility":"abbrev","statement_dag_size":1300,"type_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","AlgHom","AlgHom.funLike","Algebra.id","Algebra.ofSubsemiring","And","And.intro","Bot.bot","CommGroupWithZero.toDivisionCommMonoid","CommRing.toCommSemiring","CommRing.toNonAssocCommRing","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Exists","Exists.intro","Field","Field.toCommRing","Field.toSemifield","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HSub.hSub","Ideal","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","Invertible","Invertible.invOf","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NonAssocCommRing.toNonAssocRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.aeval","Polynomial.algebraOfAlgebra","Polynomial.leadingCoeff","Polynomial.semiring","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","SubNegMonoid.toSub","Submodule.instBot","Submodule.setLike","Subring","Subring.instSetLike","Subring.instSubringClass","Subring.toCommRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Zero.toOfNat0","instDistribOfSemiring","instHSub","instMulZeroClassOfSemiring","invertibleInv"],"value_dag_size":1632,"value_refs":["AddGroup.toSubNegMonoid","AddGroupWithOne.toAddGroup","AddGroupWithOne.toAddMonoidWithOne","AddMonoidWithOne.toOne","AlgHom","AlgHom.funLike","Algebra.id","Algebra.ofSubsemiring","And","And.casesOn","And.intro","Bot.bot","CommGroupWithZero.toDivisionCommMonoid","CommRing.toCommSemiring","CommRing.toNonAssocCommRing","CommRing.toRing","CommSemiring.toSemiring","DFunLike.coe","Distrib.toMul","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionSemiring.toGroupWithZero","DivisionSemiring.toSemiring","Eq","Exists","Exists.casesOn","Exists.intro","Field","Field.toCommRing","Field.toSemifield","GroupWithZero.toDivisionMonoid","GroupWithZero.toMonoidWithZero","HSub.hSub","Ideal","Inv.inv","InvOneClass.toInv","InvOneClass.toOne","Invertible","Invertible.invOf","Membership.mem","MonoidWithZero.toMulZeroOneClass","MulZeroClass.toMul","MulZeroClass.toZero","MulZeroOneClass.toMulZeroClass","NonAssocCommRing.toNonAssocRing","OfNat.ofNat","One.toOfNat1","Polynomial","Polynomial.aeval","Polynomial.algebraOfAlgebra","Polynomial.leadingCoeff","Polynomial.semiring","Ring.toAddGroupWithOne","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","SubNegMonoid.toSub","Submodule.instBot","Submodule.setLike","Subring","Subring.instSetLike","Subring.instSubringClass","Subring.toCommRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Zero.toOfNat0","instDistribOfSemiring","instHSub","instMulZeroClassOfSemiring","invertibleInv"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.LocalSubring","name":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn.match_1_4","namespace":"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.Subring.exists_le_valuationSubring_of_isIntegrallyClosedIn","reducibility":"abbrev","statement_dag_size":1151,"type_refs":["Algebra.adjoin","Algebra.id","Algebra.ofSubsemiring","And","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonAssocCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DFunLike.coe","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toSemiring","Exists","Exists.intro","Field","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Ideal","Ideal.span","Inv.inv","InvOneClass.toInv","LE.le","Membership.mem","NonAssocCommRing.toNonAssocRing","NonAssocRing.toNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalSubring","NonUnitalSubring.instSetLike","PartialOrder.toPreorder","Preorder.toLE","Ring.toNonAssocRing","RingHom","RingHom.instFunLike","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Set","Set.image","Set.instLE","Set.instSingletonSet","SetLike.coe","SetLike.instMembership","Singleton.singleton","Subalgebra","Subalgebra.toSubring","Submodule.setLike","Subring","Subring.instPartialOrder","Subring.instSetLike","Subring.instSubringClass","Subring.subtype","Subring.toCommRing","SubringClass.toNonAssocRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","ValuationSubring","ValuationSubring.nonunits","ValuationSubring.toSubring"],"value_dag_size":1295,"value_refs":["Algebra.adjoin","Algebra.id","Algebra.ofSubsemiring","And","CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonAssocCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","DFunLike.coe","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","DivisionRing.toRing","DivisionSemiring.toSemiring","Exists","Exists.casesOn","Exists.intro","Field","Field.toCommRing","Field.toDivisionRing","Field.toSemifield","Ideal","Ideal.span","Inv.inv","InvOneClass.toInv","LE.le","Membership.mem","NonAssocCommRing.toNonAssocRing","NonAssocRing.toNonAssocSemiring","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalSubring","NonUnitalSubring.instSetLike","PartialOrder.toPreorder","Preorder.toLE","Ring.toNonAssocRing","RingHom","RingHom.instFunLike","Semifield.toCommGroupWithZero","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toAddCommMonoid","Semiring.toModule","Set","Set.image","Set.instLE","Set.instSingletonSet","SetLike.coe","SetLike.instMembership","Singleton.singleton","Subalgebra","Subalgebra.toSubring","Submodule.setLike","Subring","Subring.instPartialOrder","Subring.instSetLike","Subring.instSubringClass","Subring.subtype","Subring.toCommRing","SubringClass.toNonAssocRing","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","ValuationSubring","ValuationSubring.nonunits","ValuationSubring.toSubring"]}
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+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.eq_top_iff._simp_1_2","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.eq_top_iff","reducibility":null,"statement_dag_size":41,"type_refs":["Eq","Iff","Membership.mem","SetLike","SetLike.instMembership"],"value_dag_size":46,"value_refs":["Eq","Iff","Membership.mem","SetLike","SetLike.ext_iff","SetLike.instMembership","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal._simp_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal","reducibility":null,"statement_dag_size":57,"type_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership"],"value_dag_size":62,"value_refs":["And","Eq","Exists","Membership.mem","Set","Set.image","Set.instMembership","Set.mem_image","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal._simp_1_2","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal","reducibility":null,"statement_dag_size":45,"type_refs":["Eq","Membership.mem","Set","Set.instMembership","SetLike","SetLike.coe","SetLike.instMembership"],"value_dag_size":50,"value_refs":["Membership.mem","Set","Set.instMembership","SetLike","SetLike.coe","SetLike.instMembership","SetLike.mem_coe","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal._simp_1_3","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal","reducibility":null,"statement_dag_size":158,"type_refs":["CommRing.toNonAssocCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Eq","Exists","Field","Field.toCommRing","Field.toSemifield","Ideal","IsLocalRing.maximalIdeal","Membership.mem","NonAssocCommRing.toNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalSubring","NonUnitalSubring.instSetLike","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule.setLike","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Subtype.mk","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.instSubringClass","ValuationSubring.isLocalRing","ValuationSubring.nonunits"],"value_dag_size":162,"value_refs":["CommRing.toNonAssocCommRing","CommRing.toNonUnitalCommRing","CommSemiring.toSemiring","Exists","Field","Field.toCommRing","Field.toSemifield","Ideal","IsLocalRing.maximalIdeal","Membership.mem","NonAssocCommRing.toNonAssocRing","NonUnitalCommRing.toNonUnitalNonAssocCommRing","NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing","NonUnitalSubring","NonUnitalSubring.instSetLike","Semifield.toCommSemiring","Semiring.toAddCommMonoid","Semiring.toModule","SetLike.instMembership","Submodule.setLike","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Subtype.mk","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.instSubringClass","ValuationSubring.isLocalRing","ValuationSubring.mem_nonunits_iff_exists_mem_maximalIdeal","ValuationSubring.nonunits","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal._simp_1_4","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.image_maximalIdeal","reducibility":null,"statement_dag_size":25,"type_refs":["And","Eq","Exists"],"value_dag_size":29,"value_refs":["And","Exists","exists_and_right","propext"]}
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+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.instIsDomainSubtypeMem._proof_1","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.instIsDomainSubtypeMem","reducibility":null,"statement_dag_size":73,"type_refs":["CommRing.toNonAssocCommRing","CommSemiring.toSemiring","Field","Field.toCommRing","Field.toSemifield","IsDomain","Membership.mem","NonAssocCommRing.toNonAssocRing","Semifield.toCommSemiring","SetLike.instMembership","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.instSubringClass"],"value_dag_size":33,"value_refs":["CommRing.toRing","Field","Field.toCommRing","Field.toSemifield","Subring.instIsDomainSubtypeMem","ValuationSubring","ValuationSubring.toSubring","instIsDomain"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.instIsFractionRingSubtypeMem.match_1","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.instIsFractionRingSubtypeMem","reducibility":"abbrev","statement_dag_size":337,"type_refs":["CommMonoid.toMonoid","CommRing.toNonAssocCommRing","CommSemiring.toCommMonoid","CommSemiring.toSemiring","Field","Field.toCommRing","Field.toSemifield","Membership.mem","Monoid.toMulOneClass","NonAssocCommRing.toNonAssocRing","Semifield.toCommSemiring","Semiring.toMonoidWithZero","SetLike.instMembership","Submonoid","Submonoid.instSetLike","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Subtype.mk","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.instSubringClass","nonZeroDivisors"],"value_dag_size":398,"value_refs":["CommMonoid.toMonoid","CommRing.toNonAssocCommRing","CommSemiring.toCommMonoid","CommSemiring.toSemiring","Field","Field.toCommRing","Field.toSemifield","Membership.mem","Monoid.toMulOneClass","NonAssocCommRing.toNonAssocRing","Semifield.toCommSemiring","Semiring.toMonoidWithZero","SetLike.instMembership","Submonoid","Submonoid.instSetLike","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Subtype.casesOn","Subtype.mk","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.instSubringClass","nonZeroDivisors"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.instSetLike.match_1","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.instSetLike","reducibility":"abbrev","statement_dag_size":119,"type_refs":["CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonAssocCommRing","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Field","Field.toCommRing","Field.toSemifield","Inv.inv","InvOneClass.toInv","Membership.mem","MulOne.toMul","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NonAssocCommRing.toNonAssocRing","NonAssocRing.toNonAssocSemiring","NonAssocSemiring.toMulZeroOneClass","Or","Semifield.toCommGroupWithZero","Set","Set.instMembership","Submonoid.toSubsemigroup","Subring","Subring.toSubsemiring","Subsemigroup.carrier","Subsemiring.toSubmonoid","ValuationSubring","ValuationSubring.mk"],"value_dag_size":197,"value_refs":["CommGroupWithZero.toDivisionCommMonoid","CommRing.toNonAssocCommRing","DivInvOneMonoid.toInvOneClass","DivisionCommMonoid.toDivisionMonoid","DivisionMonoid.toDivInvOneMonoid","Field","Field.toCommRing","Field.toSemifield","Inv.inv","InvOneClass.toInv","Membership.mem","MulOne.toMul","MulOneClass.toMulOne","MulZeroOneClass.toMulOneClass","NonAssocCommRing.toNonAssocRing","NonAssocRing.toNonAssocSemiring","NonAssocSemiring.toMulZeroOneClass","Or","Semifield.toCommGroupWithZero","Set","Set.instMembership","Submonoid.toSubsemigroup","Subring","Subring.toSubsemiring","Subsemigroup.carrier","Subsemiring.toSubmonoid","ValuationSubring","ValuationSubring.casesOn","ValuationSubring.mk"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.ker_unitGroupToResidueFieldUnits._simp_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.ker_unitGroupToResidueFieldUnits","reducibility":null,"statement_dag_size":128,"type_refs":["DFunLike.coe","DivInvMonoid.toMonoid","Eq","Group","Group.toDivInvMonoid","Membership.mem","Monoid.toMulOneClass","MonoidHom","MonoidHom.instFunLike","MulOneClass.toMulOne","SetLike.instMembership","Subgroup","Subgroup.comap","Subgroup.instSetLike"],"value_dag_size":135,"value_refs":["DFunLike.coe","DivInvMonoid.toMonoid","Group","Group.toDivInvMonoid","Membership.mem","Monoid.toMulOneClass","MonoidHom","MonoidHom.instFunLike","MulOneClass.toMulOne","SetLike.instMembership","Subgroup","Subgroup.comap","Subgroup.instSetLike","Subgroup.mem_comap","propext"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.ker_unitGroupToResidueFieldUnits._simp_1_2","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.ker_unitGroupToResidueFieldUnits","reducibility":null,"statement_dag_size":318,"type_refs":["CommRing.toCommSemiring","CommRing.toNonAssocCommRing","CommSemiring.toSemiring","DFunLike.coe","DivisionSemiring.toSemiring","Eq","EquivLike.toFunLike","Field","Field.toCommRing","Field.toSemifield","IsLocalRing.ResidueField","IsLocalRing.ResidueField.field","IsLocalRing.residue","Membership.mem","MonoidHom.ker","MulEquiv","MulEquiv.instEquivLike","NonAssocCommRing.toNonAssocRing","RingHom.toMonoidHom","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subgroup","Subgroup.instSetLike","Subgroup.mul","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Subtype.val","Units","Units.instGroup","Units.instMul","Units.instMulOneClass","Units.map","ValuationSubring","ValuationSubring.instCommRingSubtypeMem","ValuationSubring.instSetLike","ValuationSubring.instSubringClass","ValuationSubring.isLocalRing","ValuationSubring.principalUnitGroup","ValuationSubring.unitGroup","ValuationSubring.unitGroupMulEquiv"],"value_dag_size":322,"value_refs":["CommRing.toCommSemiring","CommRing.toNonAssocCommRing","CommSemiring.toSemiring","DFunLike.coe","DivisionSemiring.toSemiring","EquivLike.toFunLike","Field","Field.toCommRing","Field.toSemifield","IsLocalRing.ResidueField","IsLocalRing.ResidueField.field","IsLocalRing.residue","Membership.mem","MonoidHom.ker","MulEquiv","MulEquiv.instEquivLike","NonAssocCommRing.toNonAssocRing","RingHom.toMonoidHom","Semifield.toCommSemiring","Semifield.toDivisionSemiring","Semiring.toMonoid","Semiring.toNonAssocSemiring","SetLike.instMembership","Subgroup","Subgroup.instSetLike","Subgroup.mul","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","Subtype.val","Units","Units.instGroup","Units.instMul","Units.instMulOneClass","Units.map","ValuationSubring","ValuationSubring.coe_mem_principalUnitGroup_iff","ValuationSubring.instCommRingSubtypeMem","ValuationSubring.instSetLike","ValuationSubring.instSubringClass","ValuationSubring.isLocalRing","ValuationSubring.principalUnitGroup","ValuationSubring.unitGroup","ValuationSubring.unitGroupMulEquiv","propext"]}
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+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.le_total_ideal.match_1","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.le_total_ideal","reducibility":"abbrev","statement_dag_size":254,"type_refs":["CommRing.toNonAssocCommRing","CommSemiring.toSemiring","Field","Field.toCommRing","Field.toSemifield","Ideal","Ideal.IsPrime","Membership.mem","NonAssocCommRing.toNonAssocRing","PrimeSpectrum","PrimeSpectrum.mk","Semifield.toCommSemiring","SetLike.instMembership","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.instSubringClass"],"value_dag_size":274,"value_refs":["CommRing.toNonAssocCommRing","CommSemiring.toSemiring","Field","Field.toCommRing","Field.toSemifield","Ideal","Ideal.IsPrime","Membership.mem","NonAssocCommRing.toNonAssocRing","PrimeSpectrum","PrimeSpectrum.casesOn","PrimeSpectrum.mk","Semifield.toCommSemiring","SetLike.instMembership","SubringClass.toSubsemiringClass","SubsemiringClass.toCommSemiring","Subtype","ValuationSubring","ValuationSubring.instSetLike","ValuationSubring.instSubringClass"]}
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+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"abbrev","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.mem_of_valuation_le_one.match_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.mem_of_valuation_le_one","reducibility":"abbrev","statement_dag_size":321,"type_refs":["Algebra.algebraMap","CommRing.toCommSemiring","CommSemiring.toSemiring","DFunLike.coe","DivisionSemiring.toSemiring","Eq","Exists","Exists.intro","Field","Field.toSemifield","Membership.mem","RingHom","RingHom.instFunLike","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","ValuationSubring","ValuationSubring.instAlgebraSubtypeMem","ValuationSubring.instCommRingSubtypeMem","ValuationSubring.instSetLike"],"value_dag_size":378,"value_refs":["Algebra.algebraMap","CommRing.toCommSemiring","CommSemiring.toSemiring","DFunLike.coe","DivisionSemiring.toSemiring","Eq","Exists","Exists.casesOn","Exists.intro","Field","Field.toSemifield","Membership.mem","RingHom","RingHom.instFunLike","Semifield.toDivisionSemiring","Semiring.toNonAssocSemiring","SetLike.instMembership","Subtype","ValuationSubring","ValuationSubring.instAlgebraSubtypeMem","ValuationSubring.instCommRingSubtypeMem","ValuationSubring.instSetLike"]}
+{"definition_height":null,"is_auto_or_private":true,"is_internal_name":true,"kind":"theorem","module":"Mathlib.RingTheory.Valuation.ValuationSubring","name":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.nonunits_injective._simp_1_1","namespace":"_private.Mathlib.RingTheory.Valuation.ValuationSubring.0.ValuationSubring.nonunits_injective","reducibility":null,"statement_dag_size":36,"type_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE"],"value_dag_size":40,"value_refs":["And","Eq","LE.le","PartialOrder","PartialOrder.toPreorder","Preorder.toLE","le_antisymm_iff","propext"]}
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