name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
TensorProduct.AlgebraTensorModule.rightComm._proof_31 | Mathlib.LinearAlgebra.TensorProduct.Tower | [
"TensorProduct.leftHasSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"IsScalarTower.to_sm... | false |
Tactic.MfldSetTac._aux_Mathlib_Logic_Equiv_PartialEquiv___elabRules_Tactic_MfldSetTac_mfldSetTac_1 | Mathlib.Logic.Equiv.PartialEquiv | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.instantiateMVars",
"Lean.TSyntax",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.instMonadMCtxOfMonadLift",
"Lean.Elab.Term.instMon... | false |
Subgroup.instInhabitedLeftTransversal.eq_1 | Mathlib.GroupTheory.Complement | [
"Group",
"QuotientGroup.leftRel",
"Quotient.out",
"Subgroup",
"Subgroup.instInhabitedLeftTransversal._proof_1",
"Subtype.mk",
"Subgroup.LeftTransversal",
"SetLike.coe",
"Quotient",
"Subgroup.instInhabitedLeftTransversal",
"Inhabited",
"Eq.refl",
"Set.range",
"Subgroup.IsComplement",
"Eq"... | true |
_private.Mathlib.RingTheory.Polynomial.HilbertPoly.0.Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_lt._simp_1_9 | Mathlib.RingTheory.Polynomial.HilbertPoly | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"Nat.cast",
"CharZero",
"AddZero.toZero",
"Nat.cast_eq_zero",
"Nat",
"propext",
"Zero.toOfNat0",
"AddMonoidWithOne.toAddMonoid",
"OfNat.ofNat",
"Eq",
"AddMonoidWithOne"
] | false |
CovBy.unique_right | Mathlib.Order.Cover | [
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"LE.le.antisymm'",
"CovBy",
"LinearOrder",
"PartialOrder.toPreorder",
"DistribLattice.toLattice",
"CovBy.ge_of_gt",
"CovBy.lt",
"SemilatticeSup.toPartialOrder",
"Eq",
"instDistribLatticeOfLinearOrder"
] | true |
Lean.Parser.checkNoImmediateColon | Lean.Parser.Basic | [
"Lean.Parser.ParserInfo.mk",
"Lean.Parser.FirstTokens.unknown",
"Lean.Parser.Parser",
"Lean.Parser.ParserState.stxStack",
"String",
"Lean.Parser.ParserState.mkUnexpectedError",
"Lean.Parser.Parser.mk",
"Lean.Parser.ParserContext.toParserContextCore",
"Lean.Parser.Token",
"Lean.Syntax",
"id",
"... | true |
LinearMap.codRestrictOfInjective | Mathlib.Algebra.Module.Submodule.Equiv | [
"Submodule",
"RingHomSurjective.ids",
"LinearEquiv.symm",
"CommSemiring.toSemiring",
"Submodule.addCommMonoid",
"LinearMap.instFunLike",
"Membership.mem",
"LinearMap.range",
"Subtype",
"Submodule.module",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"LinearMap.comp",
"LinearEquiv.toLine... | true |
Function.Semiconj.mapsTo_range | Mathlib.Data.Set.Function | [
"_private.Mathlib.Data.Set.Function.0.Function.Semiconj.mapsTo_range.match_1_1",
"Membership.mem",
"Eq.rec",
"Set.MapsTo",
"Exists.intro",
"Function.Semiconj",
"Set.range",
"Eq",
"Set.instMembership",
"Set"
] | true |
CategoryTheory.Presheaf.imageSieve_whisker_forget | Mathlib.CategoryTheory.Sites.LocallySurjective | [
"CategoryTheory.Presheaf.imageSieve",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"TypeCat.instFunLikeFun",
"CategoryTheory.Sieve",
"CategoryTheory.ConcreteCategory",
"CategoryTheo... | true |
List.iterateTR_loop_eq | Mathlib.Data.List.Defs | [
"List.iterate",
"Nat.recAux",
"List.append_assoc",
"congrArg",
"instOfNatNat",
"List.append_nil",
"List.cons",
"List.reverse_cons",
"instHAppendOfAppend",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"List.reverse",
"of_eq_true",
"instAddNat",
"congrFun'",
"List.i... | true |
TwoSidedIdeal.instPartialOrder | Mathlib.RingTheory.TwoSidedIdeal.Basic | [
"PartialOrder.ofSetLike",
"NonUnitalNonAssocRing",
"TwoSidedIdeal",
"PartialOrder",
"TwoSidedIdeal.setLike"
] | true |
instCoeTCOrderAddMonoidHomOfOrderHomClassOfAddMonoidHomClass.eq_1 | Mathlib.Algebra.Order.Hom.Monoid | [
"instCoeTCOrderAddMonoidHomOfOrderHomClassOfAddMonoidHomClass",
"CoeTC",
"OrderMonoidHomClass.toOrderAddMonoidHom",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"AddZeroClass",
"Eq.refl",
"OrderAddMonoidHom",
"Eq",
"OrderHomClass",
"Preorder",
"FunLike",
"CoeTC.mk"
] | true |
List.SortedGT.sortedGE | Mathlib.Data.List.Sort | [
"List.get",
"List.SortedGT.strictAnti_get",
"List.SortedGT",
"List",
"Antitone.sortedGE",
"Fin.instPartialOrder",
"List.SortedGE",
"Fin",
"List.length",
"Preorder",
"StrictAnti.antitone"
] | true |
isClopen_discrete._simp_1 | Mathlib.Topology.Clopen | [
"DiscreteTopology",
"isClopen_discrete",
"TopologicalSpace",
"True",
"eq_true",
"IsClopen",
"Eq",
"Set"
] | false |
GoToModuleLinkProps._sizeOf_1 | ImportGraph.Tools.FindHome | [
"GoToModuleLinkProps",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Name",
"GoToModuleLinkProps.rec",
"OfNat.ofNat"
] | false |
FintypeCat.toProfinite._proof_4 | Mathlib.Topology.Category.Profinite.Basic | [
"Finite.compactSpace",
"Finite",
"FintypeCat",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"FintypeCat.botTopology",
"CompactSpace",
"CategoryTheory.types",
"FintypeCat.instFiniteObj"
] | false |
FirstOrder.Language.Formula.realize_iff._simp_1 | Mathlib.ModelTheory.Semantics | [
"FirstOrder.Language.Formula.realize_iff",
"FirstOrder.Language.Formula.iff",
"FirstOrder.Language.Structure",
"Iff",
"FirstOrder.Language.Formula",
"propext",
"FirstOrder.Language",
"Eq",
"FirstOrder.Language.Formula.Realize"
] | false |
ONote.brecOn.go | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.rec",
"ONote.below",
"PProd.mk",
"ONote.oadd",
"ONote.zero",
"PProd",
"PUnit",
"PUnit.unit",
"ONote",
"PNat"
] | true |
Mathlib.Meta.NormNum.isNNRat_lt_false | Mathlib.Tactic.NormNum.Ineq | [
"Preorder.toLT",
"HMul.hMul",
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"instMulNat",
"LE.le",
"instLENat",
"Mathlib.Meta.NormNum.isNNRat_le_true",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Semiring",
"De... | true |
Lean.Elab.Level.Context.mk.noConfusion | Lean.Elab.Level | [
"Lean.Syntax",
"id",
"Lean.Elab.Level.Context.mk",
"Lean.Elab.Level.Context.noConfusion",
"Lean.Elab.Level.Context",
"Bool",
"Lean.Options",
"Eq"
] | false |
_private.Init.Data.Array.QSort.Basic.0.Array.qpartition.loop._unsafe_rec | Init.Data.Array.QSort.Basic | [
"_private.Init.Data.Array.QSort.Basic.0.Array.qpartition.loop._unsafe_rec",
"_private.Init.Data.Array.QSort.Basic.0.Array.qpartition._proof_12",
"Vector",
"_private.Init.Data.Array.QSort.Basic.0.Array.qpartition._proof_14",
"Vector.instGetElemNatLt",
"_private.Init.Data.Array.QSort.Basic.0.Array.qpartitio... | false |
basisOfLinearIndependentOfCardEqFinrank.congr_simp | Mathlib.LinearAlgebra.FiniteDimensional.Lemmas | [
"basisOfLinearIndependentOfCardEqFinrank",
"AddCommGroup.toAddCommMonoid",
"Eq.rec",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"Fintype.card",
"Module.Basis",
"Fintype",
"Nat",
"LinearIndependent",
"DivisionSemiring.toSemiring",
"Eq.ndrec",
"Nonempty",
"Eq.refl",
"DivisionRing",... | true |
_private.Mathlib.Algebra.Polynomial.Eval.Defs.0.Polynomial.eval₂_mul_C'._simp_1_1 | Mathlib.Algebra.Polynomial.Eval.Defs | [
"MulZeroClass.toMul",
"Commute.zero_left",
"Commute",
"MulZeroClass",
"True",
"eq_true",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero"
] | false |
CategoryTheory.MorphismProperty.respectsIso_of_isStableUnderComposition | Mathlib.CategoryTheory.MorphismProperty.Composition | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"PartialOrder.toPreorder",
"CategoryTheory.MorphismProperty.IsStableUnderComposition",
"Preorder.toLE",
"CategoryTheory.Iso",
"CategoryTheory.Morph... | true |
LightCondensed.lanPresheafExt_inv | Mathlib.Condensed.Discrete.Colimit | [
"CategoryTheory.Functor.op",
"Eq.mpr",
"CategoryTheory.Functor.costructuredArrowMapCocone",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"Opposite",
"CategoryTheory.Functor.pointwiseLeftKanExtensionUnit",
"CategoryTheory.CategoryS... | true |
Ideal.Quotient.field._proof_13 | Mathlib.RingTheory.Ideal.Quotient.Basic | [
"Submodule.Quotient.instZeroQuotient",
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toSemiring",
"Ideal.Quotient.exists_inv",
"Exists",
"Ideal",
"instDistribOfSemiring",
"HasQuotient.Quotient",
"Ideal.Quotient.ring",
"Ideal.instIsTwoSided_1",
"CommRing.toCommSemiring",
"Dist... | false |
String.Slice.Pattern.ToBackwardSearcher.noConfusion | Init.Data.String.Pattern.Basic | [
"String.Slice.Pattern.ToBackwardSearcher.noConfusionType",
"HEq.refl",
"String.Slice.Pattern.ToBackwardSearcher.casesOn",
"String.Slice.Pattern.SearchStep",
"String.Slice",
"Std.Iter",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq",
"String.Slice.Pattern.ToBackwardSearcher"
] | false |
_private.Mathlib.GroupTheory.FreeGroup.Basic.0.FreeGroup.Red.sizeof_of_step._proof_1_3 | Mathlib.GroupTheory.FreeGroup.Basic | [
"Lean.RArray.leaf",
"False",
"Bool.not",
"congrArg",
"Classical.byContradiction",
"instSizeOfDefault",
"Nat.Linear.ExprCnstr.eq_true_of_isValid",
"Lean.Grind.Nat.lt_eq",
"Lean.RArray.branch",
"id",
"False.casesOn",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Linear.Expr.num",
"Bool.true... | false |
CategoryTheory.Limits.HasWidePullback | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.HasLimit",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.WidePullbackShape.wideCospan",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Cat... | true |
CompletableTopField | Mathlib.Topology.Algebra.UniformField | [
"UniformSpace",
"CompletableTopField.mk",
"Field"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Regularity.Increment.0.SzemerediRegularity.distinctPairs | Mathlib.Combinatorics.SimpleGraph.Regularity.Increment | [
"Real",
"Finset.univ",
"SProd.sprod",
"Finset",
"SimpleGraph.Adj",
"DecidableRel",
"Membership.mem",
"Subtype",
"SzemerediRegularity.chunk",
"Finpartition.parts",
"Finset.offDiag",
"Prod.fst",
"SimpleGraph",
"Finset.instSProd",
"Fintype",
"Finset.instSetLike",
"Finset.instLattice",
... | true |
Lean.Grind.CommRing.Poly.combine.go.match_1.congr_eq_2 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.add",
"id",
"Int",
"heq_of_eq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Lean.Grind.CommRing.Poly.casesOn",
"Lean.Grind.CommRing.Poly.combine.go.match_1",
"Eq.symm",
"Eq",
"Lean.Grind.CommRing.Mon",
"Lean.Grind.CommRing.Poly.num"
] | true |
AlgebraicGeometry.Scheme.Hom.appLE_map'_assoc | Mathlib.AlgebraicGeometry.Scheme | [
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"congrArg",
... | true |
Std.Tactic.BVDecide.BVExpr.bitblast.mkFullAdderOut.eq_1 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Add | [
"Std.Sat.AIG.Ref.cast",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Tactic.BVDecide.BVExpr.bitblast.mkFullAdderOut",
"Std.Tactic.BVDecide.BVExpr.bitblast.mkFullAdderOut._proof_1",
"Std.Sat.AIG.BinaryInput.mk",
"Std.Sat.AIG.Entrypoint",
"Std.Sat.AIG.Entrypoint.ref",
"Std.Tactic.BVDecide.BVExpr.bitblast.FullAdde... | true |
abs.unexpander | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Array.mkArray0",
"Lea... | true |
CentroidHom.comp_apply | Mathlib.Algebra.Ring.CentroidHom | [
"CentroidHom.comp",
"NonUnitalNonAssocSemiring",
"CentroidHom.instFunLike",
"Eq",
"DFunLike.coe",
"CentroidHom",
"rfl"
] | true |
ProofWidgets.instRpcEncodablePanelWidgetProps.dec._@.ProofWidgets.Component.Panel.Basic.2840189264._hygCtx._hyg.1 | ProofWidgets.Component.Panel.Basic | [
"Pure.pure",
"Lean.Json",
"Option.mapM",
"Lean.Lsp.instToJsonPosition",
"ReaderT",
"Monad.toApplicative",
"String",
"Lean.SubExpr.instToJsonGoalsLocation",
"instMonadLiftT",
"ProofWidgets.PanelWidgetProps.mk",
"Lean.FromJson.fromJson?",
"ProofWidgets.instFromJsonRpcEncodablePacket._@.ProofWidg... | false |
CategoryTheory.Functor.RepresentableBy.casesOn | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"Quiver.Hom.op",
"CategoryTheory.Functor.RepresentableBy.rec",
"TypeCat.instFunLikeFun",
"Equiv",
"CategoryTheory.Functor.RepresentableBy",
... | false |
AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion.stalk_iso | Mathlib.Geometry.RingedSpace.OpenImmersion | [
"AlgebraicGeometry.PresheafedSpace.IsOpenImmersion.stalk_iso",
"CategoryTheory.IsIso",
"AlgebraicGeometry.PresheafedSpace.carrier",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
"AlgebraicGeometry.LocallyRingedSpace.instQuiver",
"Algebr... | true |
CategoryTheory.Limits.biprod.opIso_hom_fst_assoc | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.biprod.opIso",
"Eq.mp",
"CategoryTheory.Limits.HasBinaryBip... | true |
_private.Lean.Data.Iterators.Producers.PersistentHashMap.0.Lean.PersistentHashMap.Node.measure.measureEntries._unsafe_rec | Lean.Data.Iterators.Producers.PersistentHashMap | [
"Lean.PersistentHashMap.Entry.entry",
"Lean.PersistentHashMap.Entry",
"congrArg",
"_private.Lean.Data.Iterators.Producers.PersistentHashMap.0.Lean.PersistentHashMap.Node.measure.measureEntries._unsafe_rec",
"Lean.PersistentHashMap.Entry.ref",
"Lean.PersistentHashMap.Node",
"instSizeOfDefault",
"Lean.P... | false |
SzemerediRegularity.mul_sq_le_sum_sq | Mathlib.Combinatorics.SimpleGraph.Regularity.Bound | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Trans.trans",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"sum_div_card_sq_le_sum_sq_div_card",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"AddGroupWithOne.toAddGroup",
"Even.pow_nonneg",
"Finset",
"Li... | true |
instMonoidUniformOnFun._proof_3 | Mathlib.Topology.Algebra.UniformConvergence | [
"Monoid",
"MulOne.toOne",
"Semigroup.toMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"instOneUniformOnFun",
"Semigroup.mk",
"Pi.monoid._proof_4",
"MulOne.toMul",
"instMonoidUniformOnFun._proof_1",
"MulOneClass.toMulOne",
"instMulUniformOnFun",
"One.toOfNat1",
"UniformOnFun",
"OfNat.ofNat",
... | false |
Equiv.Perm.disjoint_noncommProd_right | Mathlib.GroupTheory.Perm.Support | [
"Finset",
"Commute",
"Membership.mem",
"Finset.noncommProd_induction",
"DivInvMonoid.toMonoid",
"Set.Pairwise",
"Finset.noncommProd",
"Group.toDivInvMonoid",
"Equiv.Perm.permGroup",
"SetLike.coe",
"Finset.instSetLike",
"Equiv.Perm",
"Equiv.Perm.instMul",
"Equiv.Perm.disjoint_one_right",
... | true |
Filter.HasBasis.recOn | Mathlib.Order.Filter.Bases.Basic | [
"Filter.instMembership",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"And",
"Filter.HasBasis",
"Iff",
"Filter.HasBasis.rec",
"Filter.HasBasis.mk",
"Filter",
"Set.instHasSubset",
"Set"
] | false |
_private.Mathlib.Probability.Kernel.RadonNikodym.0.ProbabilityTheory.Kernel.rnDeriv_eq_top_iff._simp_1_5 | Mathlib.Probability.Kernel.RadonNikodym | [
"False",
"Real",
"eq_false",
"ENNReal.ofReal",
"ENNReal",
"ENNReal.instTop",
"ENNReal.ofReal_ne_top",
"Top.top",
"Eq"
] | false |
Acc.ndrecOnC.eq_1 | Init.WFComputable | [
"Acc.recC",
"Acc",
"Eq.refl",
"Acc.ndrecOnC",
"Eq"
] | true |
Std.TreeMap.inter | Std.Data.TreeMap.Basic | [
"Std.TreeMap.inner",
"Std.TreeMap.mk",
"Ordering",
"Std.DTreeMap.inter",
"Std.TreeMap"
] | true |
ProbabilityTheory.Kernel.IsFiniteKernel.comapRight | Mathlib.Probability.Kernel.Basic | [
"Eq.mpr",
"ProbabilityTheory.IsFiniteKernel",
"MeasureTheory.Measure",
"Preorder.toLT",
"ProbabilityTheory.Kernel.comapRight",
"congrArg",
"Set.univ",
"ProbabilityTheory.IsFiniteKernel.mk",
"PartialOrder.toPreorder",
"ProbabilityTheory.Kernel.instFunLike",
"id",
"LE.le",
"MeasurableSpace",
... | true |
Ideal.Quotient.algebraMap_mk_of_liesOver | Mathlib.RingTheory.Ideal.Over | [
"Ideal.Quotient.commSemiring",
"Ideal.Quotient.algebraOfLiesOver",
"CommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"Algebra",
"RingHom",
"Ideal.LiesOver",
"Ideal",
"HasQuotient.Quotient",
"Ideal.Quotient.ring",
"Ideal.instIsTwoSided_1",
"CommRing.toCommSem... | true |
Representation.finsuppToCoinvariants._proof_2 | Mathlib.RepresentationTheory.Coinvariants | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomInvPair",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
Std.DTreeMap.Internal.Impl.Balanced.inner | Std.Data.DTreeMap.Internal.Balanced | [
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.Balanced.inner",
"instOfNatNat",
"instHAdd",
"Std.DTreeMap.Internal.Impl.BalancedAtRoot",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq",
"Std.DTre... | true |
ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"LinearIsometryEquiv.instEquivLike",
"NormedCommRing.toSeminormedCommRing",
"SeminormedAddCommGroup",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.addCommGroup... | true |
CategoryTheory.Cat.isoOfEquiv._auto_3 | Mathlib.CategoryTheory.Category.Cat | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
MeasureTheory.AEFinStronglyMeasurable.eq_1 | Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"Exists",
"Filter.EventuallyEq",
"MeasureTheory.AEFinStronglyMeasurable",
"MeasurableSpace",
"TopologicalSpace",
"And",
"MeasureTheory.FinStronglyMeasurable",
"Eq.refl",
"Eq",
"MeasureTheory.Measure.instFunLike",
"Zero",
"MeasureTheory.Measure.i... | true |
MeasureTheory.integral_image_eq_integral_deriv_smul_of_antitoneOn | Mathlib.MeasureTheory.Function.JacobianOneDim | [
"IsModuleTopology.toContinuousSMul",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Real.instIsOrderedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"abs_neg",
"neg_smul",
"Real",
"instHSMul",
"MeasureTheory.M... | true |
_private.Mathlib.Algebra.Homology.DerivedCategory.FullyFaithful.0.DerivedCategory.instFullSingleFunctor.match_1 | Mathlib.Algebra.Homology.DerivedCategory.FullyFaithful | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.singleFunctor",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"CategoryTheory... | false |
_private.Mathlib.CategoryTheory.Limits.FilteredColimitCommutesProduct.0.CategoryTheory.Limits.Types.isIso_colimitPointwiseProductToProductColimit.match_1_1 | Mathlib.CategoryTheory.Limits.FilteredColimitCommutesProduct | [
"CategoryTheory.Discrete.mk",
"CategoryTheory.Discrete.casesOn",
"CategoryTheory.Discrete"
] | false |
Lean.Lsp.HoverParams.mk.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.HoverParams._sizeOf_inst",
"instOfNatNat",
"Lean.Lsp.HoverParams.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.Lsp.TextDocumentPositionParams",
"instAddNat",
"Eq.refl",
"Lean.Lsp.HoverParams",
"OfNat.ofNat",
"Eq",
"Lean.Lsp.TextDocumentPositionParams._sizeOf_inst"
] | true |
NormedAddGroupHom.toNormedAddCommGroup | Mathlib.Analysis.Normed.Group.Hom | [
"NormedAddGroupHom",
"NormedAddGroupHom.toNormedAddCommGroup._proof_3",
"NormedAddGroupHom.toNormedAddCommGroup._proof_1",
"AddCommGroup.toAddGroup",
"NormedAddGroupHom.opNorm",
"NormedAddGroupHom.toNormedAddCommGroup._proof_2",
"NormedAddGroupHom.toNormedAddCommGroup._proof_4",
"NormedAddGroupHom.toA... | true |
ContinuousMap.instSeminormedRing._proof_6 | Mathlib.Topology.ContinuousMap.Compact | [
"Monoid.npow",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"SeminormedRing.toRing",
"inferInstance",
"ContinuousMap.instSeminormedRing._proof_1",
"instOfNatNat",
"Monoid.npow_zero",
"TopologicalSpace",
"Nat",
"Semiring.toMonoid",
"One.toOfNat1",
"Monoid.toOne",
"SeminormedRing.toP... | false |
MvPolynomial.sumAlgEquiv_comp_rename_inl | Mathlib.Algebra.MvPolynomial.Equiv | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"AlgEquiv.toAlgHom",
"congrArg",
"CommSemiring.toSemiring",
"MvPolynomial.ext",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"MvPolynomial.X",
"AddMonoidAlgebra.commSemiring",
"Nat.instAddMonoid",
"MvP... | true |
CategoryTheory.Limits.CatCospanTransform.rightUnitor._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.CatCospanTransform | [
"CategoryTheory.CatCommSq.vComp",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CatCommSq.vId_iso_hom_app",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.rightUnitor",
"CategoryTheory.Funct... | false |
VectorField.fderivWithin_pullbackWithin | Mathlib.Analysis.Calculus.VectorField | [
"ContinuousLinearEquiv.symm",
"ContinuousLinearEquiv.apply_symm_apply",
"NormedSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"VectorField.pullbackWithin_eq_of_fderivWithin_eq",
"ContinuousLinearMap.IsInvertible",
"VectorField.pullbackWit... | true |
CategoryTheory.Limits.ColimitPresentation.Total.Hom.recOn | Mathlib.CategoryTheory.Presentable.ColimitPresentation | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.ColimitPresentation.ι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"Sigma.fst",
"CategoryTheory.Functor.map",
"CategoryTheory.Limits.ColimitPresentation.diag",
"CategoryTheory.Limits.ColimitPresentation.... | false |
Lean.Compiler.LCNF.markRecDecls | Lean.Compiler.LCNF.Basic | [
"StateT.run",
"_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.markRecDecls.match_1",
"Lean.Compiler.LCNF.Decl.mk",
"Lean.Compiler.LCNF.Decl.toSignature",
"Lean.NameSet",
"Array.map",
"Lean.Compiler.LCNF.Decl",
"instDecidableEqBool",
"Lean.Compiler.LCNF.Decl.value",
"Lean.Compiler.LCNF.Puri... | true |
_private.Mathlib.MeasureTheory.Covering.Differentiation.0.VitaliFamily.ae_tendsto_lintegral_enorm_sub_div._simp_1_1 | Mathlib.MeasureTheory.Covering.Differentiation | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Module.DualBases.finite._autoParam | Mathlib.LinearAlgebra.Dual.Basis | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.Abelian.SpectralObject.toCycles_cyclesMap._auto_1 | Mathlib.Algebra.Homology.SpectralObject.Cycles | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.Order.CompleteLattice.Basic.0.iSup_prod._simp_1_1 | Mathlib.Order.CompleteLattice.Basic | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
Std.DTreeMap.Internal.Impl.applyPartition._proof_4 | Std.Data.DTreeMap.Internal.Model | [
"False",
"Std.DTreeMap.Internal.Cell.empty",
"Ord",
"congrArg",
"Bool.false_eq_true",
"Ordering",
"Eq.mp",
"id",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains'",
"Std.DTreeMap.Internal.Impl.leaf",
"Bool.not_eq_true",
"True",
"eq_true",
"Bool",
"of_eq_true",
"Eq.refl",
"congrFun... | false |
Lean.Meta.Grind.Arith.Linear.State.mk.sizeOf_spec | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.Meta.Grind.Arith.Linear.State",
"Option._sizeOf_inst",
"Lean.PHashMap",
"Lean.PArray",
"Lean.Meta.Sym.ExprPtr._sizeOf_inst",
"Lean.PersistentArray._sizeOf_inst",
"Lean.Expr",
"instOfNatNat",
"Lean.PHashSet",
"Lean.Meta.Grind.Arith.Linear.Struct",
"Array._sizeOf_inst",
"Array",
"Lean.Pe... | true |
Std.Internal.IO.Async.TCP.Socket.Client.ctorIdx | Std.Internal.Async.TCP | [
"Std.Internal.IO.Async.TCP.Socket.Client",
"Nat"
] | false |
dist_self_sub_left | Mathlib.Analysis.Normed.Group.Uniform | [
"Norm.norm",
"Eq.mpr",
"Real",
"SeminormedAddCommGroup",
"congrArg",
"dist_self_sub_right",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"id",
"dist_comm",
"SubNegMonoid.toSub",
"SeminormedAddCommGroup.toNorm",
"instHSub",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid... | true |
Std.TreeMap.find?_toArray_eq_some_iff_getKey?_eq_some_and_getElem?_eq_some | Std.Data.TreeMap.Lemmas | [
"instDecidableEqOrdering",
"Std.TreeMap.toArray",
"Std.TreeMap.inner",
"Option.some",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Prod.mk",
"Std.TransCmp",
"instBEqOfDecidableEq",
"Prod.fst",
"Std.DTreeMap.Const.find?_toArray_eq_some_iff_getKey?_eq_some_and_get?_eq_some",
"And",
"BEq.beq... | true |
lp.toNorm | Mathlib.Analysis.Normed.Lp.lpSpace | [
"Norm.norm",
"Real",
"instAddCommGroupPreLp",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Subtype",
"Real.normedAddCommGroup",
"Subtype.mk",
"AddSubgroup",
"lp",
"NormedAddCommGroup.toNorm",
"AddSubgroup.instSetLike",
"ENNReal",
"PreLp",
"Subtype.val",
"SetLike.instMembership",
"No... | true |
_private.Mathlib.GroupTheory.Index.0.Subgroup.index_eq_two_iff_exists_notMem_and'._simp_1_1 | Mathlib.GroupTheory.Index | [
"HMul.hMul",
"Monoid.toMulOneClass",
"Xor",
"Group",
"Membership.mem",
"Exists",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"instOfNatNat",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Nat",
"Subgroup.index",
"Subgroup.index_eq_two_iff'",
"propext",
"OfNat.ofNat",
"Eq... | false |
_private.Mathlib.Order.Filter.NAry.0.Filter.map₂_neBot_iff._simp_1_2 | Mathlib.Order.Filter.NAry | [
"not_or",
"And",
"propext",
"Or",
"Eq",
"Not"
] | false |
exists_isTranscendenceBasis_between | Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis | [
"Subalgebra.instSetLike",
"Nontrivial",
"Iff.mpr",
"IsDomain",
"CommRing",
"IsDomain.to_noZeroDivisors",
"faithfulSMul_iff_algebraMap_injective",
"AlgebraicIndependent.matroid_indep_iff",
"Algebra.algebraMap",
"AlgebraicIndepOn",
"congrArg",
"CommSemiring.toSemiring",
"Subtype.val_injective"... | true |
galGroupBasis.match_1 | Mathlib.FieldTheory.KrullTopology | [
"Monoid.toMulOneClass",
"Submonoid.toSubsemigroup",
"Algebra",
"Membership.mem",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"Field.toSemifield",
"And.casesOn",
"Group.toDivInvMonoid",
"FilterBasis.sets",
"MulOneClass.toMulOne",
"And",
"galBasis",
"Semifield.toDivisionSemiring",... | false |
Language.reverse_mem_reverse | Mathlib.Computability.Language | [
"Eq.mpr",
"congrArg",
"Language.mem_reverse",
"Iff.rfl",
"Membership.mem",
"id",
"Language.reverse",
"List",
"Iff",
"List.reverse_reverse",
"propext",
"List.reverse",
"Language.instMembershipList",
"Language",
"Eq"
] | true |
Finset.strongInduction._unsafe_rec | Mathlib.Data.Finset.Card | [
"Finset",
"HasSSubset.SSubset",
"Finset.card_lt_card",
"Finset.strongInduction._unsafe_rec",
"Nat",
"LT.lt",
"Finset.card",
"Finset.instHasSSubset",
"instLTNat"
] | false |
Subgroup.finiteIndex_of_finite | Mathlib.GroupTheory.Index | [
"QuotientGroup.finite",
"Subgroup.FiniteIndex",
"Finite",
"Group",
"Subgroup",
"Subgroup.finiteIndex_of_finite_quotient"
] | true |
Equiv.prodPUnit._proof_2 | Mathlib.Logic.Equiv.Prod | [
"Prod.mk",
"Prod.fst",
"PUnit",
"Function.RightInverse",
"Eq.refl",
"PUnit.unit",
"Prod"
] | false |
CategoryTheory.Limits.FormalCoproduct.homPullbackEquiv._proof_8 | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.FormalCoproduct.Hom",
"Function.Pullback",
"CategoryTheory.eqToHom",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.PullbackCone.fst",
"Pr... | false |
_private.Init.Data.String.Lemmas.Order.0.String.Slice.Pos.ofSlice_next._simp_1_1 | Init.Data.String.Lemmas.Order | [
"String.Slice.Pos.offset",
"String.Slice",
"String.Pos.Raw",
"propext",
"String.Slice.Pos",
"Eq",
"String.Slice.Pos.ext_iff"
] | false |
Lean.Parser.Term.strictImplicitRightBracket | Lean.Parser.Term.Basic | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"instHAndThenOfAndThen",
"Lean.Parser.group",
"HOrElse.hOrElse",
"Lean.Parser.symbol",
"Unit",
"Lean.Parser.atomic",
"instHOrElseOfOrElse",
"Lean.Parser.instOrElseParser",
"Lean.Parser.instAndThenParser"
] | true |
_private.Mathlib.Data.Analysis.Topology.0.Ctop.mem_nhds_toTopsp.match_1_3 | Mathlib.Data.Analysis.Topology | [
"Membership.mem",
"Exists",
"HasSubset.Subset",
"Ctop",
"Ctop.f",
"And",
"Exists.casesOn",
"Exists.intro",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | false |
QuadraticMap.restrictScalars | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"QuadraticMap.mk",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"QuadraticMap.instFunLike",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
... | true |
CategoryTheory.bijection_natural | Mathlib.CategoryTheory.Monoidal.Closed.Ideal | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalClosed.uncurry_natural_right",
"Equiv.instEquivLike",
"CategoryTheory.MonoidalClosed.uncurry",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.bijection._proof_1",
"CategoryTheory.unitCompPartialBi... | true |
ConvexCone.Flat | Mathlib.Geometry.Convex.Cone.Basic | [
"NegZeroClass.toNeg",
"AddCommGroup.toAddCommMonoid",
"SMul",
"ConvexCone.instSetLike",
"Membership.mem",
"Exists",
"PartialOrder",
"AddCommGroup",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"And",
"ConvexCo... | true |
_private.Mathlib.NumberTheory.Bernoulli.0.Bernoulli.vonStaudtIndicator | Mathlib.NumberTheory.Bernoulli | [
"Rat.instOfNat",
"Dvd.dvd",
"Nat.decidable_dvd",
"Rat",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"instHSub",
"Nat.instDvd",
"Nat",
"OfNat.ofNat",
"ite"
] | true |
Stream'.Seq.ext_iff | Mathlib.Data.Seq.Defs | [
"Stream'.Seq",
"Stream'.Seq.ext",
"HEq.refl",
"Eq.casesOn",
"Iff",
"Nat",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Stream'.Seq.get?",
"Option"
] | true |
BitVec.ssubOverflow | Init.Data.BitVec.Basic | [
"instPowNat",
"HSub.hSub",
"Int.decLe",
"BitVec",
"GE.ge",
"Int.instNegInt",
"instSubNat",
"instOfNatNat",
"Int",
"Int.instNatPow",
"Int.instLTInt",
"instHSub",
"HPow.hPow",
"instOfNat",
"Nat",
"LT.lt",
"Bool",
"Bool.or",
"Int.instSub",
"BitVec.toInt",
"Int.decLt",
"instHPo... | true |
_private.Init.Data.List.Pairwise.0.List.pairwise_flatten._simp_1_6 | Init.Data.List.Pairwise | [
"List.Pairwise",
"Membership.mem",
"List.cons",
"List.pairwise_cons",
"List",
"And",
"List.instMembership",
"propext",
"Eq"
] | false |
Lean.Grind.Linarith.Poly.denoteExpr | Lean.Meta.Tactic.Grind.Arith.Linear.DenoteExpr | [
"Pure.pure",
"_private.Lean.Meta.Tactic.Grind.Arith.Linear.DenoteExpr.0.Lean.Grind.Linarith.Poly.denoteExpr.denoteTerm",
"Monad.toApplicative",
"Lean.Meta.Grind.Arith.Linear.Struct.zero",
"Lean.Expr",
"Int",
"Lean.Grind.Linarith.Var",
"Applicative.toPure",
"_private.Lean.Meta.Tactic.Grind.Arith.Line... | true |
EisensteinSeries.summand_bound_of_mem_verticalStrip | Mathlib.NumberTheory.ModularForms.EisensteinSeries.Summable | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Real.instIsOrderedRing",
"Norm.norm",
"Int.cast",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Real.instPow",
"Real.partialOrder",
"Real.instLE",
"Real",
"HMul.hMul",
"EisensteinSeries.r_lower_bound... | true |
PontryaginDual.map_apply | Mathlib.Topology.Algebra.PontryaginDual | [
"Monoid",
"PontryaginDual.map",
"PontryaginDual",
"PontryaginDual.instFunLikeCircle",
"DivInvMonoid.toMonoid",
"PontryaginDual.instCommGroup",
"Group.toDivInvMonoid",
"TopologicalSpace",
"ContinuousMonoidHom.instFunLike",
"instTopologicalSpacePontryaginDual",
"Circle",
"ContinuousMonoidHom",
... | true |
SSet.Subcomplex.Pairing.RankFunction.filtration_monotone | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | [
"SSet.S.subcomplex",
"Eq.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Opposite",
"Equiv.instEquivLike",
"SSet.Subcomplex.Pairing.RankFunction.filtration",
"congrArg",
"iSup",
"LinearOrder",
"SSet.Subcomplex.Pairing.RankFunction.subcomplex_le_filtration",
"PartialOrder.toPreorder",
"Mo... | true |
_private.Mathlib.AlgebraicTopology.SimplexCategory.ToMkOne.0.SimplexCategory.toMk₁_surjective._simp_1_5 | Mathlib.AlgebraicTopology.SimplexCategory.ToMkOne | [
"Fin.castSucc_lt_castSucc_iff",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instLTFin",
"propext",
"instAddNat",
"Fin.castSucc",
"OfNat.ofNat",
"Fin",
"Eq"
] | false |
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