name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Batteries.UnionFind.parent_push | Batteries.Data.UnionFind.Lemmas | [
"Batteries.UnionFind.push",
"congrArg",
"Batteries.UnionFind.parentD",
"Batteries.UnionFind.arr",
"Nat",
"True",
"eq_self",
"Batteries.UnionFind.parentD_push",
"of_eq_true",
"Batteries.UnionFind",
"congrFun'",
"Eq",
"Eq.trans",
"Batteries.UnionFind.parent"
] | true |
Lean.Parser.Term.valueOf | Lean.Parser.Term | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"instHAndThenOfAndThen",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.withAntiquot",
"Bool.true",
"Unit",
"Nat",
"Lean.Parser.withCache",
"Lean.Parser.Term.ident",
"OfNat.ofNat",
"Lean.Parser.mkAntiquot",
"Bool.f... | true |
Std.DTreeMap.Internal.Impl.maxKey!_eq_maxKey! | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Ord",
"congrArg",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.maxKey?",
"Std.DTreeMap.Internal.Impl.Ordered",
"Std.DTreeMap.Internal.Impl.maxKey!",
"Option.get!",
"Std.Internal.List.maxKey!",
"Std.DTreeMap.Internal.Impl.maxKey!_eq_get!_maxKey?",
"congr",
"True",
"eq_self",
"Std.Internal.Lis... | true |
Ideal.span_iUnion | Mathlib.RingTheory.Ideal.Span | [
"Semiring.toModule",
"iSup",
"Submodule.completeLattice",
"CompleteLattice.toConditionallyCompleteLattice",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Submodule.span_iUnion",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"Ideal.span",
"ConditionallyCompleteLattice.toCon... | true |
CategoryTheory.CosimplicialObject.Augmented.toArrow_obj_right | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.Comma.right",
"CategoryTheory.CosimplicialObject.instCategoryAugmented",
"CategoryTheory.CosimplicialObject",
"CategoryTheory.CosimplicialObject.Augmented",
"CategoryTheory.Functor.id",
"instOfNatNat",
"CategoryTheory.instCategoryArrow",
"CategoryTheory.CosimplicialObject.const",
"Ca... | true |
Lean.Parser.Command.recommended_spelling._regBuiltin.Lean.Parser.Command.recommended_spelling.docString_3 | Lean.Parser.Command | [
"Lean.addBuiltinDocString",
"IO",
"Unit",
"Lean.Name.mkStr4"
] | false |
ContinuousMap.coeFnAlgHom | Mathlib.Topology.ContinuousMap.Algebra | [
"ContinuousMap.instNonAssocSemiringOfIsTopologicalSemiring",
"IsTopologicalSemiring",
"AlgHom",
"ContinuousMap",
"Algebra",
"RingHom",
"ContinuousMap.instSemiringOfIsTopologicalSemiring",
"CommSemiring",
"TopologicalSpace",
"Pi.semiring",
"Function.algebra",
"NonAssocSemiring.toNonUnitalNonAss... | true |
op_smul_eq_mul | Mathlib.Algebra.Group.Action.Defs | [
"instHSMul",
"HMul.hMul",
"Mul.toSMulMulOpposite",
"MulOpposite",
"Mul",
"HSMul.hSMul",
"Eq",
"rfl",
"MulOpposite.op",
"instHMul"
] | true |
CategoryTheory.OverClass.asOverHom_comp | Mathlib.CategoryTheory.Comma.Over.OverClass | [
"CategoryTheory.Over",
"CategoryTheory.instHomIsOverComp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.instCategoryOver",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.OverClass.asOver",
"CategoryTheory.OverClass",
"CategoryTheory.OverClass.asOverHom",
"Category... | true |
Aesop.BaseM.instMonadHashMapCacheAdapterExprEntry | Aesop.BaseM | [
"Pure.pure",
"Aesop.BaseM",
"StateRefT'.instAlternativeOfMonad",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"modify",
"Lean.Expr.instBEq",
"Lean.Meta.State",
"instMonadLiftT",
"MonadState.get",
"IO",
"StateRefT'.instMonadStateOfOfMonadLiftTST",
"Lean.Expr",
"Lea... | true |
FourierInvModule.mk.inj | Mathlib.Analysis.Fourier.Notation | [
"FourierInvModule.mk.noConfusion",
"instHSMul",
"outParam",
"SMul",
"FourierInvModule.mk",
"instHAdd",
"FourierTransformInv.fourierInv",
"HAdd.hAdd",
"FourierInvModule",
"eq_of_heq",
"HEq",
"HSMul.hSMul",
"Eq",
"FourierTransformInv",
"Add"
] | true |
BigOperators.delabFinsetExpect | Mathlib.Algebra.BigOperators.Expect | [
"guard",
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.PrettyPrinter.Delaborator.SubExpr.withAppArg",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.PrettyPrinter.Delaborator.withBindingBodyUnusedName",
"_private.Mathlib.Algebra.BigOperators.Expect.0.BigOperators.delabFinsetExpect.match_1",
"Lean.... | true |
Std.TreeMap.getElem!_alter | Std.Data.TreeMap.Lemmas | [
"instDecidableEqOrdering",
"Std.TreeMap.alter",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Std.DTreeMap.Const.get!_alter",
"Option.get!",
"Std.TransCmp",
"Std.TreeMap.instMembership",
"Std.TreeMap.instGetElem?Mem",
"Inhabited",
"GetElem?.getElem?",
"Eq",
"GetElem?... | true |
_private.Mathlib.Data.Vector3.0.Vector3.eq_nil.match_1_1 | Mathlib.Data.Vector3 | [
"False",
"HEq.refl",
"False.elim",
"Fin2.fz",
"noConfusion_of_Nat",
"Fin2.casesOn",
"instOfNatNat",
"Fin2.fs",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Nat.ctorIdx",
"instAddNat",
"Eq.refl",
"HEq",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Nat.add",
"Fin2"
] | false |
AddMonoidAlgebra.lift_mapRangeRingHom_algebraMap | Mathlib.Algebra.MonoidAlgebra.Basic | [
"AddMonoidAlgebra.semiring",
"Equiv.instEquivLike",
"Algebra.algebraMap",
"MonoidHom",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"AddMonoidAlgebra.mapRingHom",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.algebra",
"Algebra",
"RingHom",
"Algebra.toSMul",
"A... | true |
MvPowerSeries.nat_le_weightedOrder | Mathlib.RingTheory.MvPowerSeries.Order | [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"Nat.instMulZeroClass",
"Preorder.toLT",
"Semiring.toModule",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ENat.instNatCast",
"instTopENat",
"instLinearOrderENat",
"Finsupp.weight",
"congrArg",
... | true |
CategoryTheory.CategoryOfElements.instHasInitialElementsOppositeOfIsRepresentable | Mathlib.CategoryTheory.Limits.Elements | [
"CategoryTheory.categoryOfElements",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.Elements.initialOfRepresentableBy",
"CategoryTheory.Limits.IsInitial.hasInitial",
"CategoryTheory.Functor.Elements.isInitialOfRepresentableBy",
"CategoryTheory.types",
... | true |
SzemerediRegularity.card_eq_of_mem_parts_chunk | Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | [
"SzemerediRegularity.stepBound",
"Real",
"instHDiv",
"HMul.hMul",
"Finset.univ",
"congrArg",
"Finset",
"Nat.instMonoid",
"SimpleGraph.Adj",
"DecidableRel",
"HSub.hSub",
"Membership.mem",
"Eq.mp",
"dif_pos",
"Fintype.card",
"HDiv.hDiv",
"Finpartition.equitabilise",
"instSubNat",
"... | true |
CategoryTheory.CosimplicialObject.Augmented.const_obj_hom | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.CosimplicialObject.instCategoryAugmented",
"CategoryTheory.CosimplicialObject",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CosimplicialObject.Augmented",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Comma.hom",
"Categor... | true |
_private.Init.Control.State.0.ForM.forIn.match_3 | Init.Control.State | [
"Except.ok",
"Except.error",
"PUnit",
"Except.casesOn",
"Except",
"Prod"
] | false |
sSetTopAdj_unit_app_app_down | Mathlib.AlgebraicTopology.SingularSet | [
"SSet.yonedaEquiv",
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"SSet.toTop",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.toSSet",
"TopCat.instCategory",
"CategoryTheory.Functor.category",
... | true |
instAddCommGroupTangentSpace._proof_11 | Mathlib.Geometry.Manifold.IsManifold.Basic | [
"NormedSpace",
"AddCommGroup.toAddGroup",
"instOfNatNat",
"instAddCommGroupTangentSpace._aux_8",
"AddSemigroup.mk",
"autoParam",
"TopologicalSpace",
"ModelWithCorners",
"instHAdd",
"AddSemigroup.toAdd",
"instAddCommGroupTangentSpace._proof_3",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"AddMo... | false |
IsHomeomorph.toEquiv_homeomorph | Mathlib.Topology.Homeomorph.Lemmas | [
"IsHomeomorph.homeomorph",
"Homeomorph.toEquiv",
"Equiv",
"TopologicalSpace",
"Equiv.ofBijective",
"IsHomeomorph.bijective",
"Eq.refl",
"Eq",
"IsHomeomorph"
] | true |
Num.decidablePrime | Mathlib.Data.Num.Prime | [
"Decidable",
"Num.Prime",
"Num",
"Unit",
"Nat.not_prime_zero",
"instZeroNum",
"DecidablePred",
"Zero.toOfNat0",
"Num.minFac.match_1",
"PosNum",
"Decidable.isFalse",
"OfNat.ofNat",
"PosNum.decidablePrime"
] | true |
Prod.toSigma_inj._simp_1 | Mathlib.Data.Sigma.Basic | [
"Prod.toSigma",
"Prod.toSigma_inj",
"propext",
"Prod",
"Eq",
"Sigma"
] | false |
SeminormedRing.mk._flat_ctor | Mathlib.Analysis.Normed.Ring.Basic | [
"Monoid.npow_zero._autoParam",
"AddGroupWithOne.intCast_negSucc._autoParam",
"Ring.mk",
"AddMonoidWithOne.natCast_zero._autoParam",
"UniformSpace",
"Mul.mk",
"Real.instLE",
"Real",
"iInf",
"PseudoMetricSpace.uniformity_dist._autoParam",
"One.mk",
"HMul.hMul",
"AddGroupWithOne.intCast_ofNat._... | false |
StandardSubspace.toClosedSubmodule_inj._simp_1 | Mathlib.Analysis.InnerProductSpace.StandardSubspace | [
"InnerProductSpace.toNormedSpace",
"Real",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"StandardSubspace.toClosedSubmodule_inj",
"PseudoMetricSpace.toUniformSpace",
"Real.semiring",
"StandardSubspace",
"Complex.instRCLike",
"StandardSubspace.toClosedSubmodule",
"ClosedSubmodule",
"... | false |
CategoryTheory.Over.iteratedSliceBackward | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.Over.iteratedSliceBackward._proof_4",
"CategoryTheory.Over.iteratedSliceBackward._proof_2",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Over.mk",
... | true |
CategoryTheory.Functor.PushoutObjObj.ι.eq_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Functor.PushoutObjObj",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.PushoutObjObj.ι._proof_1",
"CategoryTheory.Functor.PushoutObjObj.ι",
"CategoryTheory.Functor.PushoutObjObj.isPushout",
... | true |
CategoryTheory.Functor.IsLocallyFull.recOn | Mathlib.CategoryTheory.Sites.LocallyFullyFaithful | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Membership.mem",
"CategoryTheory.Sieve",
"CategoryTheory.Functor.IsLocallyFull",
"CategoryTheory.Functor.IsLocallyFull.mk",
"CategoryTheory.Sieve.functorPushforward",
"CategoryTheory.GrothendieckTopology",
"Category... | false |
HomologicalComplex.IsStrictlySupportedOutside.mk._flat_ctor | Mathlib.Algebra.Homology.Embedding.IsSupported | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex",
"HomologicalComplex.IsStrictlySupportedOutside",
"ComplexShape",
"HomologicalComplex.IsStrictlySupportedOutside.mk",
"ComplexShape.Embedding.f",
"ComplexShape.Embedding",
"CategoryTheory.Limits.IsZero",
"HomologicalComplex.X",
"Catego... | false |
Std.DTreeMap.Internal.Impl.getKeyD_minKey | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.getKeyD",
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.getKeyD_eq_getKeyD",
"Std.DTreeMap.Internal.Impl.isEmpty_eq_isEmpty",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"Std.Internal.List.getKeyD",
"beqOfOrd",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",... | true |
Codisjoint.sup_right | Mathlib.Order.Disjoint | [
"Codisjoint",
"le_sup_left",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"OrderTop",
"Max.max",
"Codisjoint.mono_right",
"SemilatticeSup.toPartialOrder",
"SemilatticeSup"
] | true |
_private.Mathlib.Combinatorics.Enumerative.Schroder.0.Nat.smallSchroder.match_1.eq_1 | Mathlib.Combinatorics.Enumerative.Schroder | [
"Unit.unit",
"Nat.smallSchroder.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
Std.IsPartialOrder.of_le | Init.Data.Order.Factories | [
"Std.Antisymm.antisymm",
"Std.Antisymm",
"Std.IsPartialOrder",
"Std.IsPreorder.of_le",
"inferInstance",
"Std.IsPartialOrder.mk",
"Std.Refl",
"LE.le",
"autoParam",
"LE",
"Trans",
"Std.IsPreorder",
"Std.IsPartialOrder.of_le._auto_3",
"Std.IsPartialOrder.of_le._auto_1",
"Std.IsPartialOrder.... | true |
Lean.SubExpr.Pos | Lean.SubExpr | [
"Nat"
] | true |
padicNorm_two_harmonic | Mathlib.NumberTheory.Harmonic.Int | [
"zpow_natCast",
"Rat.instOfNat",
"Norm.norm",
"Nat.cast_ofNat",
"Eq.mpr",
"Padic.eq_padicNorm",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"DivisionRing.toRatCast",
"congrArg",
"Real.instRatCast",
"Rat",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"... | true |
List.length_take_le' | Init.Data.List.Nat.TakeDrop | [
"_private.Init.Data.List.Nat.TakeDrop.0.List.length_take_le'._simp_1_1",
"congrArg",
"LE.le",
"instLENat",
"List.length_take",
"List",
"Nat",
"True",
"of_eq_true",
"congrFun'",
"List.take",
"List.length",
"Min.min",
"instMinNat",
"Eq.trans"
] | true |
WithZero.coe_expEquiv_apply | Mathlib.Algebra.GroupWithZero.WithZero | [
"Units.val",
"Multiplicative.monoid",
"Equiv.instEquivLike",
"WithZero.instMonoidWithZero",
"Units",
"Equiv",
"Multiplicative",
"AddGroup",
"AddGroup.toSubNegMonoid",
"WithZero",
"WithZero.exp",
"SubNegMonoid.toAddMonoid",
"Eq",
"DFunLike.coe",
"MonoidWithZero.toMonoid",
"rfl",
"With... | true |
Function.Embedding.trans_arrowCongrLeft | Mathlib.Logic.Embedding.Basic | [
"Eq.mpr",
"Inhabited.default",
"Function.Embedding.arrowCongrLeft",
"congrArg",
"Function.comp",
"id",
"Function.Embedding",
"funext",
"Function.comp_def",
"Function.extend",
"Function.Embedding.trans",
"Function.Embedding.injective",
"Function.Embedding.ext",
"Inhabited",
"Eq.refl",
"... | true |
leansearchclient.backend | LeanSearchClient.Basic | [
"Inhabited.default",
"Lean.Option",
"String",
"String.instInhabited",
"Lean.instInhabitedOption"
] | true |
ModelWithCorners._sizeOf_1 | Mathlib.Geometry.Manifold.IsManifold.Basic | [
"Real.partialOrder",
"Real",
"ModelWithCorners.rec",
"Continuous",
"RCLike.toNormedAlgebra",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"PartialEquiv",
"Set.univ",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"instSizeOfDefault",
"PseudoMetricSp... | false |
_private.Mathlib.Data.Finsupp.Basic.0.Finsupp.equivMapDomain._simp_2 | Mathlib.Data.Finsupp.Basic | [
"Finsupp.toFun",
"Finset",
"Finsupp.support",
"Membership.mem",
"Ne",
"Finset.instSetLike",
"propext",
"Zero.toOfNat0",
"Finsupp.mem_support_toFun",
"OfNat.ofNat",
"Eq",
"SetLike.instMembership",
"Finsupp",
"Zero"
] | false |
_private.Init.Data.String.Slice.0.String.Slice.lines.lineMap.match_1 | Init.Data.String.Slice | [
"Option.ctorIdx",
"Option.some",
"String.Slice",
"Nat.hasNotBit",
"_private.Init.Data.String.Slice.0.String.Slice.Pos.skipWhile._sparseCasesOn_1",
"Option"
] | false |
Complex.tan_ofReal_im | Mathlib.Analysis.Complex.Trigonometric | [
"Eq.mpr",
"Real",
"Real.instZero",
"congrArg",
"Complex.im",
"id",
"Complex.ofReal",
"Complex.re",
"Complex.ofReal_tan_ofReal_re",
"Complex.tan",
"Zero.toOfNat0",
"Eq.refl",
"Complex.ofReal_im",
"Complex",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | true |
Aesop.Frontend.Priority.ctorIdx | Aesop.Frontend.RuleExpr | [
"Int",
"Aesop.Frontend.Priority.casesOn",
"Nat",
"Aesop.Frontend.Priority",
"Aesop.Percent"
] | false |
Std.DTreeMap.Internal.Impl.containsThenInsertIfNew!.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Ord",
"Std.DTreeMap.Internal.Impl.insert!",
"instDecidableEqBool",
"Prod.mk",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"Bool",
"Eq.refl",
"Prod",
"Bool.false",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.containsThenInsertIfNew!",
"ite"
] | true |
Nat.b_eq_digitChar | Init.Data.Nat.ToString | [
"Nat.digitChar",
"instOfNatNat",
"eq_comm",
"Iff",
"Nat",
"Nat.digitChar_eq_b",
"Iff.trans",
"Char",
"OfNat.ofNat",
"Eq",
"Char.ofNat"
] | true |
Module.preReflection | Mathlib.LinearAlgebra.Reflection | [
"LinearMap.id",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"HSub.hSub",
"AddCommGroup",
"Module.preReflection._proof_1",
"LinearMap.instSub",
"LinearMap",
"CommRing.toCommSemiring",
"instHSub",
"LinearMap.smulRight",
"Module.End",
"Module"... | true |
Lean.Compiler.LCNF.InferType.Pure.inferAppType._unsafe_rec | Lean.Compiler.LCNF.InferType | [
"Pure.pure",
"Std.Rio.instForIn'InferInstanceMembershipOfLawfulUpwardEnumerableOfLawfulUpwardEnumerableLTOfLawfulUpwardEnumerableLeast?OfMonadOfFiniteIteratorId",
"instForInOfForIn'",
"Std.PRange.instLawfulUpwardEnumerableLeast?Nat",
"Std.Rio.mk",
"Option.some",
"Std.PRange.instLawfulUpwardEnumerableLTN... | false |
instLawfulCommIdentityUInt16HXorOfNat | Init.Data.UInt.Bitwise | [
"Std.Identity.mk",
"instCommutativeUInt16HXor",
"Std.LeftIdentity.mk",
"Std.LawfulCommIdentity.mk",
"UInt16.xor_zero",
"UInt16",
"HXor.hXor",
"Std.LawfulRightIdentity.mk",
"Std.LawfulCommIdentity",
"Std.Commutative.comm",
"instXorOpUInt16",
"OfNat.ofNat",
"Std.LawfulLeftIdentity.mk",
"UInt... | true |
_private.Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree.0.groupHomology.H2π_eq_zero_iff._simp_1_5 | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.leftHomologyMap'",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.leftHomologyMapIso'",
"CategoryTheory.ShortCompl... | false |
FirstOrder.Language.ClosedUnder.sInf | Mathlib.ModelTheory.Substructures | [
"Membership.mem",
"FirstOrder.Language.ClosedUnder",
"FirstOrder.Language.Structure",
"Nat",
"FirstOrder.Language.Functions",
"FirstOrder.Language",
"Set.instInfSet",
"Fin",
"Set.instMembership",
"InfSet.sInf",
"Set"
] | true |
Infinite.of_not_fintype | Mathlib.Data.Fintype.EquivFin | [
"False",
"IsEmpty",
"IsEmpty.mk",
"Fintype",
"Iff.mp",
"Infinite",
"isEmpty_fintype"
] | true |
Lean.Meta.ApplyNewGoals.recOn | Init.Meta.Defs | [
"Lean.Meta.ApplyNewGoals.all",
"Lean.Meta.ApplyNewGoals",
"Lean.Meta.ApplyNewGoals.rec",
"Lean.Meta.ApplyNewGoals.nonDependentFirst",
"Lean.Meta.ApplyNewGoals.nonDependentOnly"
] | false |
Rep.resFunctor._proof_3 | Mathlib.RepresentationTheory.Rep.Res | [
"Monoid",
"Rep.V",
"Representation.IntertwiningMap.instLinearMapClass",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"Rep.resFunctor._proof_1",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Rep.of",
"Module.End.instSemiring",
"Rep.instCategory",
... | false |
TwoSidedIdeal.finsetProd_mem | Mathlib.RingTheory.TwoSidedIdeal.BigOperators | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Multiset.Nodup",
"TwoSidedIdeal",
"Finset",
"Membership.mem",
"Exists",
"Multiset",
"id",
"Finset.val",
"Finset.casesOn",
"Finset.prod",
"And",
"Finset.instSetLike",
"TwoSidedIdeal.setLike",
... | true |
TrivSqZeroExt.inl_neg | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"NegZeroClass.toNeg",
"TrivSqZeroExt",
"TrivSqZeroExt.ext",
"TrivSqZeroExt.inl",
"TrivSqZeroExt.fst",
"Neg",
"TrivSqZeroExt.neg",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass",
"Eq.symm",
"neg_zero",
"NegZeroClass.toZero",
"Eq",
"Neg.neg",
"rfl"
] | true |
CategoryTheory.Limits.IsLimit.binaryFanSwap._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Limits.BinaryFan.swap",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.BinaryFan.fst",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.BinaryFan",
"CategoryTheory.Functor.cate... | false |
NumberField.mixedEmbedding.polarSpaceCoord.eq_1 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.PolarCoord | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"Pi.topologicalSpace",
"NumberField.InfinitePlace.IsComplex",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"NumberField.mixedEmbedding.polarSpace",
"OpenPartialHomeomorph.transHomeomorph",
"Subtype",
"Nu... | true |
_private.Mathlib.RingTheory.Polynomial.UniversalFactorizationRing.0.MvPolynomial.ker_eval₂Hom_universalFactorizationMap._simp_1_4 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"NonUnitalNonAssocRing",
"HMul.hMul",
"NonUnitalNonAssocRing.toAddCommGroup",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"SubNegMonoid.toSub",
"sub_mul",
"instHSub",
"AddGroup.toSubNegMonoid",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistr... | false |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.0._regBuiltin.UInt16.reduceGE.declare_127._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.1661162788._hygCtx._hyg.211 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | [
"UInt16.reduceGE",
"IO",
"Lean.Meta.DiscrTree.Key.star",
"Lean.Meta.DiscrTree.Key",
"instOfNatNat",
"List.toArray",
"List.cons",
"Unit",
"Nat",
"Lean.Meta.Simp.registerBuiltinSimproc",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.Meta.DiscrTree.Key.const",
"List.nil"
] | false |
_private.Lean.Meta.ExprDefEq.0.Lean.Meta.processAssignmentFOApprox.loop | Lean.Meta.ExprDefEq | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"Lean.Meta.instInhabitedMetaM",
"Bool"
] | true |
Std.DTreeMap.maxKeyD_insert | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.insert",
"Std.DTreeMap.maxKeyD",
"Std.DTreeMap.maxKey?",
"Ord.mk",
"Ordering",
"instDecidableEqBool",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Bool.true",
"Std.DTreeMap.wf",
"Bool",
"Ordering.isLE",
"Option.elim",
"Std.DTreeMap.Internal.Impl.maxKeyD_insert",
... | true |
CategoryTheory.instInhabitedMkId | Mathlib.CategoryTheory.Category.KleisliCat | [
"Inhabited.default",
"CategoryTheory.KleisliCat.mk",
"id",
"Inhabited",
"Inhabited.mk"
] | true |
CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π_assoc | Mathlib.CategoryTheory.Abelian.Projective.Resolution | [
"CategoryTheory.ProjectiveResolution.π",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.assoc",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCa... | true |
ContinuousLinearEquiv.isAddHaarMeasure_map | Mathlib.MeasureTheory.Group.Measure | [
"ContinuousLinearEquiv.symm",
"MeasureTheory.Measure",
"AddEquiv.isAddHaarMeasure_map",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"RingHom",
"BorelSpace",
"AddCommGroup",
"ContinuousLinearEquiv.equivLike",
"AddEquivClass.toAddEquiv",
"IsTopologicalAddGroup.toContinuousAdd",
"R... | true |
SemiRingCat.hom_ext | Mathlib.Algebra.Category.Ring.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SemiRingCat.Hom.ext",
"RingHom",
"SemiRingCat.Hom.hom",
"SemiRingCat.carrier",
"SemiRingCat.semiring",
"SemiRingCat.instCategory",
"CategoryTheory.Category.toCategoryStruct",
"SemiRingCat",
"Semiring.toNonAssocSemiring",
"Eq"
] | true |
Lean.Meta.Tactic.Cbv.CbvSimprocOLeanEntry.keys._default | Lean.Meta.Tactic.Cbv.CbvSimproc | [
"id",
"Lean.Meta.DiscrTree.Key",
"List.toArray",
"Array",
"List.nil"
] | false |
CategoryTheory.Limits.ker._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"congrArg",
"CategoryTheory.Limits.kernel",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.w",
"CategoryTheory.Arrow.hom",
"Cat... | false |
Array.mem_mapFinIdx | Init.Data.Array.MapIdx | [
"List.mem_mapFinIdx._simp_1",
"Iff.mpr",
"Iff.of_eq",
"congrArg",
"List.getElem_toArray._proof_1",
"Array.instMembership",
"Membership.mem",
"Exists",
"Array.casesOn",
"List.mem_toArray._simp_1",
"List.mapFinIdx",
"List.toArray",
"Array",
"GetElem.getElem",
"iff_self",
"funext",
"Arr... | true |
SignType.castHom._proof_3 | Mathlib.Data.Sign.Basic | [
"SignType.cast",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"MulOne.toOne",
"SignType.instCommGroupWithZero",
"MulZeroClass.toMul",
"MulZeroOneClass",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",
"MonoidWithZero.toMulZeroOneClass",
"MulZeroClass.negZeroClass",
"HasDist... | false |
HomotopyCategory.instIsCompatibleWithShiftHomologicalComplexIntUpHomotopic | Mathlib.Algebra.Homology.HomotopyCategory.Shift | [
"Int.instAddCommGroup",
"HomologicalComplex.instCategory",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomRel.IsCompatibleWithShift.mk",
"HomRel.IsCompatibleWithShift",
"Int.instLinearOrder",
"PartialOrder.toPreorder",
"instIsRightCancelAddO... | true |
CoheytingAlgebra.noConfusionType | Mathlib.Order.Heyting.Basic | [
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"GeneralizedCoheytingAlgebra",
"Preorder.toLE",
"CoheytingAlgebra.casesOn",
"CoheytingAlgebra",
"HNot.hnot",
"OrderTop",
"SDiff.sdiff",
"OrderTop.toTop",
"HNot",
"HEq",
"GeneralizedCoheytingAlgebra.toLattice",
"SemilatticeSup.toPartial... | false |
_private.Lean.Meta.Tactic.Grind.0.Lean.initFn._@.Lean.Meta.Tactic.Grind.2205948307._hygCtx._hyg.2 | Lean.Meta.Tactic.Grind | [
"Lean.Name.mkNum",
"IO",
"Lean.Name.mkStr3",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.registerTraceClass",
"Lean.Name.anonymous",
"Unit",
"Nat",
"OfNat.ofNat",
"Bool.false"
] | false |
Equiv.subtypePiEquivPi._proof_2 | Mathlib.Logic.Equiv.Basic | [
"Subtype",
"Subtype.mk",
"funext",
"Function.RightInverse",
"Subtype.val",
"rfl",
"Subtype.property",
"Subtype.ext"
] | false |
_private.Lean.Meta.Sym.AlphaShareCommon.0.Lean.Meta.Sym.alphaEq._sparseCasesOn_4 | Lean.Meta.Sym.AlphaShareCommon | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
_private.Lean.Linter.Util.0.Lean.Linter.collectMacroExpansions?.go.match_4 | Lean.Linter.Util | [
"_private.Lean.Linter.Util.0.Lean.Linter.collectMacroExpansions?.go._sparseCasesOn_4",
"Lean.Elab.MacroExpansionInfo",
"Nat.hasNotBit",
"List.cons",
"List",
"List.ctorIdx"
] | false |
AddSubsemigroup.equivOp_apply_coe | Mathlib.Algebra.Group.Subsemigroup.MulOpposite | [
"AddSubsemigroup.equivOp",
"Equiv.instEquivLike",
"AddSubsemigroup.instSetLike",
"Membership.mem",
"AddOpposite",
"AddOpposite.instAdd",
"AddSubsemigroup.op",
"Equiv",
"Subtype",
"AddSubsemigroup",
"Eq.refl",
"Subtype.val",
"Eq",
"DFunLike.coe",
"SetLike.instMembership",
"AddOpposite.o... | true |
MeasureTheory.Measure.measure_univ_pos._simp_1 | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"MeasureTheory.Measure",
"Preorder.toLT",
"MeasureTheory.Measure.measure_univ_pos",
"Set.univ",
"PartialOrder.toPreorder",
"Ne",
"MeasureTheory.Measure.instZero",
"MeasurableSpace",
"LT.lt",
"ENNReal",
"propext",
"ENNReal.instPartialOrder",
"Zero.toOfNat0",
"ENNReal.instZero",
"OfNat.ofN... | false |
AddCircle.measurableEquivIoc.congr_simp | Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic | [
"Set.Ioc",
"Real",
"Real.instZero",
"Real.instLT",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Fact",
"Set.Elem",
"AddCircle",
"Real.instAddCommGroup",
"Real.instAdd",
"QuotientAddGroup.measurableSpace",
"instHAdd",
"Real.measurableSpace",
"HAdd.hAdd",
"AddSubgroup.zmultiples",
"LT... | true |
MonotoneOn.map_sSup_of_continuousWithinAt | Mathlib.Topology.Order.Monotone | [
"OrderTopology",
"Lattice.toSemilatticeSup",
"ContinuousWithinAt",
"sSup_empty",
"CompleteLattice.toLattice",
"congrArg",
"CompletelyDistribLattice.toCompleteLattice",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderTop.bddAbove",
"CoheytingAlgebra.toOrderTop",
"CompleteL... | true |
_private.LeanSearchClient.LoogleSyntax.0.LeanSearchClient.getLoogleQueryJson.match_4 | LeanSearchClient.LoogleSyntax | [
"Lean.Json",
"Except.ok",
"String",
"Except.error",
"Array",
"Except.casesOn",
"Except"
] | false |
CoalgHomClass | Mathlib.RingTheory.Coalgebra.Hom | [
"CoalgebraStruct",
"outParam",
"CommSemiring.toSemiring",
"CoalgHomClass.mk",
"AddCommMonoid",
"CommSemiring",
"Module",
"FunLike"
] | true |
_private.Lean.Environment.0.Lean.Environment.asyncConstsMap._default | Lean.Environment | [
"Inhabited.default",
"_private.Lean.Environment.0.Lean.instInhabitedAsyncConsts",
"_private.Lean.Environment.0.Lean.VisibilityMap",
"id",
"_private.Lean.Environment.0.Lean.instInhabitedVisibilityMap",
"_private.Lean.Environment.0.Lean.AsyncConsts"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0.SimpleGraph.completeEquipartiteGraph_succ_isContained_iff._simp_1_15 | Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | [
"imp_self",
"True",
"propext",
"Eq"
] | false |
Polynomial.IsMonicOfDegree.of_mul_left | Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree | [
"Nontrivial",
"_private.Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree.0.Polynomial.IsMonicOfDegree.of_mul_left._simp_1_1",
"Eq.mpr",
"Polynomial.IsMonicOfDegree.natDegree_eq",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"NeZero.one",
"HMul.hMul",
"congrArg",
"Polynomial.Monic.of... | true |
NonUnitalSubalgebra.toNonUnitalSemiring | Mathlib.Algebra.Algebra.NonUnitalSubalgebra | [
"NonUnitalSubalgebra",
"CommSemiring.toSemiring",
"Membership.mem",
"NonUnitalSubalgebra.toNonUnitalSemiring._proof_1",
"inferInstance",
"Subtype",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonUnitalSemiring",
"NonUnitalSubalge... | true |
OrderHom.uliftLeftMap | Mathlib.Order.Hom.Basic | [
"ULift",
"OrderHom.instFunLike",
"OrderHom.mk",
"OrderHom.uliftMap._proof_1",
"ULift.instPreorder",
"DFunLike.coe",
"ULift.down",
"OrderHom",
"Preorder"
] | true |
Std.not_lt_of_ge | Init.Data.Order.Lemmas | [
"LE.le",
"Std.LawfulOrderLT",
"LE",
"imp_not_comm",
"LT.lt",
"Iff.mp",
"Std.not_le_of_gt",
"Not",
"LT"
] | true |
CategoryTheory.MonoidalCategory.associator_naturality_assoc | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.MonoidalCategory.associator_naturality",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
... | true |
ContinuousLinearMap.uniformContinuous | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"UniformContinuous",
"UniformSpace",
"SemilinearMapClass.distribMulActionSemiHomClass",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"AddCommGroup.toAddGroup",
"RingHom",
"AddCommGroup",
"IsUniformAddGroup",
"ContinuousLinearMap",
"ContinuousLinearMap.continuous",
"RingHom.in... | true |
_private.Init.Data.Array.Lemmas.0.Array.append_eq_singleton_iff._simp_1_1 | Init.Data.Array.Lemmas | [
"List.cons",
"List.append_eq_singleton_iff",
"instHAppendOfAppend",
"List",
"And",
"propext",
"Or",
"List.instAppend",
"Eq",
"HAppend.hAppend",
"List.nil"
] | false |
CategoryTheory.Limits.LimitBicone.mk.inj | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.LimitBicone.mk.noConfusion",
"CategoryTheory.Limits.Bicone.IsBilimit",
"CategoryTheory.Limits.LimitBicone",
"And",
"And.intro",
"eq_of_heq",
"CategoryTheory.Limits.LimitBicone.mk",
"HEq",
"CategoryTheory.Limits.Bicone",
"Eq",
"Ca... | true |
DFinsupp.small | Mathlib.Data.DFinsupp.Small | [
"DFinsupp.ext",
"small_of_injective",
"DFinsupp.instDFunLike",
"small_Pi",
"DFinsupp",
"congr_fun",
"Eq",
"DFunLike.coe",
"Small",
"Zero"
] | true |
SSet.N.cast | Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices | [
"SSet.S",
"SSet.N.cast._proof_1",
"SSet",
"SSet.N.mk'",
"SSet.N.toS",
"Nat",
"SSet.S.dim",
"SSet.S.cast",
"SSet.N",
"Eq"
] | true |
Prod.instSemiring._proof_11 | Mathlib.Algebra.Ring.Prod | [
"AddMonoid.toAddSemigroup",
"inferInstance",
"NonAssocSemiring.toOne",
"instOfNatNat",
"NatCast.natCast",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"NonAssocSemiring",
"HAdd.hAdd",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"Prod.instNonAssocS... | false |
Std.Internal.List.isEmpty_filter_containsKey_left | Std.Data.Internal.List.Associative | [
"congrArg",
"Eq.mp",
"Sigma.fst",
"Bool.true",
"List",
"Std.Internal.List.containsKey",
"EquivBEq",
"List.isEmpty",
"List.filter",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"BEq",
"Eq",
"Sigma",
"List.isEmpty_iff._simp_1",
"Eq.trans",
"List.nil"
] | true |
CategoryTheory.PreZeroHypercover.sectionsSaturateEquiv_apply_coe | Mathlib.CategoryTheory.Sites.Hypercover.Saturate | [
"CategoryTheory.Functor",
"CategoryTheory.PreZeroHypercover.f",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.Limits.MulticospanIndex.sections.val",
"Equiv",
"Subtype",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.I₀",
"... | true |
NonUnitalNonAssocCommRing.mul_comm | Mathlib.Algebra.Ring.Defs | [
"HMul.hMul",
"NonUnitalNonAssocRing.toMul",
"NonUnitalNonAssocCommRing",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing",
"Eq",
"instHMul"
] | true |
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