name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
PowerSeries.HasSubst.smul_X' | Mathlib.RingTheory.PowerSeries.Substitution | [
"CommRing",
"instHSMul",
"PowerSeries.HasSubst.smul'",
"CommSemiring.toSemiring",
"PowerSeries.HasSubst.X'",
"PowerSeries.HasSubst",
"Algebra",
"Algebra.toSMul",
"MvPowerSeries.instAlgebra",
"PowerSeries.X",
"MvPowerSeries.instSemiring",
"Unit",
"CommRing.toCommSemiring",
"HSMul.hSMul",
... | true |
_private.Mathlib.Order.GaloisConnection.Basic.0.GaloisConnection.bddBelow_u_image.match_1_1 | Mathlib.Order.GaloisConnection.Basic | [
"lowerBounds",
"Preorder.toLE",
"Membership.mem",
"Exists.casesOn",
"BddBelow",
"Exists.intro",
"Set.image",
"Set.instMembership",
"Preorder",
"Set"
] | false |
Lean.Meta.instMonadMetaM | Lean.Meta.Basic | [
"Applicative.toSeqLeft",
"Pure.pure",
"Monad.toApplicative",
"Lean.Meta.State",
"ReaderT.instMonad",
"inferInstance",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Pure.mk",
"Applicative.toPure",
"Applicative.mk",
"Lean.Core.CoreM",
"StateRefT'",
"StateRefT'.instMonad",
"Monad.toBind",
"Bind.bin... | true |
Set.injOn_subtype_val | Mathlib.Data.Set.Function | [
"Function.Injective.injOn",
"Subtype",
"Subtype.coe_injective",
"Set.InjOn",
"Subtype.val",
"Set"
] | true |
Std.Iter.atIdxSlow?._proof_8 | Init.Data.Iterators.Consumers.Access | [
"PSigma.snd",
"InvImage",
"WellFoundedRelation.rel",
"Std.IterStep.skip",
"id",
"Prod.Lex",
"Prod.mk",
"sizeOfWFRel",
"Id",
"Std.Iterator",
"Prod.Lex.right",
"Std.Iter",
"Std.IterM.TerminationMeasures.Productive",
"Nat",
"LT.lt",
"PSigma.mk",
"Std.Iter.IsPlausibleStep",
"Std.IterM.... | false |
Array.getElem_set_self | Init.Data.Array.Lemmas | [
"congrArg",
"List.getElem_toArray._proof_1",
"Array.set",
"Array.casesOn",
"id",
"List.set",
"List.toArray",
"List.getElem_set_self",
"Array",
"GetElem.getElem",
"Array.getElem_set_self._proof_1",
"List",
"Array.instGetElemNatLtSize",
"Nat",
"LT.lt",
"True",
"eq_self",
"of_eq_true"... | true |
Batteries.Tactic.Alias.AliasInfo.forward.elim | Batteries.Tactic.Alias | [
"PULift.up",
"Batteries.Tactic.Alias.AliasInfo.forward",
"Batteries.Tactic.Alias.AliasInfo.ctorElim",
"Batteries.Tactic.Alias.AliasInfo",
"Nat",
"Lean.Name",
"Eq.symm",
"Eq",
"Batteries.Tactic.Alias.AliasInfo.ctorIdx"
] | false |
UniformSpace.noConfusion | Mathlib.Topology.UniformSpace.Defs | [
"UniformSpace",
"HEq.refl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"nhds",
"Prod.mk",
"LE.le",
"SetRel.comp",
"TopologicalSpace",
"Filter.lift'",
"Filter.Tendsto",
"UniformSpace.casesOn",
"UniformSpace.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Prod.swap",
"Prod",
"E... | false |
CategoryTheory.ModObj.assoc_flip | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionS... | true |
Filter.Tendsto.isCompact_insert_range | Mathlib.Topology.Compactness.Compact | [
"Filter.Tendsto.isCompact_insert_range_of_cofinite",
"nhds",
"Eq.rec",
"Insert.insert",
"Filter.atTop",
"TopologicalSpace",
"Set.instInsert",
"Filter.Tendsto",
"Nat.instPreorder",
"Nat",
"Filter.cofinite",
"Set.range",
"Nat.cofinite_eq_atTop",
"Eq.symm",
"Eq",
"Filter",
"IsCompact",
... | true |
Mathlib.Tactic.BicategoryLike.StructuralAtom.rec | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.StructuralAtom.coherenceHom",
"Mathlib.Tactic.BicategoryLike.CoherenceHom",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.StructuralAtom.rightUnitor",
"Mathlib.Tactic.BicategoryLike.StructuralAtom",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"Mathlib.Tactic.BicategoryLike.Structu... | false |
CochainComplex.ConnectData.X | Mathlib.Algebra.Homology.Embedding.Connect | [
"CategoryTheory.Limits.HasZeroMorphisms",
"ChainComplex",
"Nat.instOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"CochainComplex.ConnectData.X._proof_1",
"Nat.instAddCancelCommMonoid",
"Int",
"AddSemigroup.toAdd",
"CochainComplex",
"Nat",
"CochainCom... | true |
Monotone.ae_differentiableAt | Mathlib.Analysis.Calculus.Monotone | [
"MeasureTheory.ae",
"IsModuleTopology.toContinuousSMul",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"ConditionallyCompleteLinearOrder.toCompactIccSpace",
"Real",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.... | true |
AList.lookup.eq_1 | Mathlib.Data.List.AList | [
"AList.lookup",
"AList",
"Eq.refl",
"Eq",
"List.dlookup",
"Option",
"DecidableEq",
"AList.entries"
] | true |
_private.Mathlib.Analysis.Calculus.DSlope.0.differentiableAt_dslope_of_ne._simp_1_1 | Mathlib.Analysis.Calculus.DSlope | [
"AddCommGroup.toAddCommMonoid",
"DifferentiableAt",
"Set.univ",
"NormedField.toField",
"AddCommGroup",
"Field.toSemifield",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"propext",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"DifferentiableWithinAt",
"NontriviallyNormedFi... | false |
Lean.Lsp.DidSaveTextDocumentParams | Lean.Data.Lsp.TextSync | [
"Lean.Lsp.DidSaveTextDocumentParams.mk"
] | true |
Complex.sin_sub_nat_mul_two_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Real.pi",
"HMul.hMul",
"Complex.commRing",
"Complex.sin",
"Nat.instAtLeastTwoHAddOfNat",
"HSub.hSub",
"Complex.instMul",
"instOfNatNat",
"Complex.instNatCast",
"CommRing.toNonAssocCommRing",
"Complex.ofReal",
"Nat.cast",
"Complex.sin_periodic",
"instHSub",
"Nat.instNeZeroSucc",
"Nat",... | true |
BitVec.DivModState.recOn | Init.Data.BitVec.Bitblast | [
"BitVec.DivModState.mk",
"BitVec",
"BitVec.DivModState.rec",
"Nat",
"BitVec.DivModState"
] | false |
_private.Mathlib.Combinatorics.Quiver.SingleObj.0.Quiver.SingleObj.toPrefunctor_symm_comp._simp_1_1 | Mathlib.Combinatorics.Quiver.SingleObj | [
"Equiv.instEquivLike",
"Equiv.symm_apply_eq",
"Equiv",
"propext",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryTheory.coherentTopology.preimage | Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit | [
"CategoryTheory.Functor",
"CategoryTheory.Preregular",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom.op",
"CategoryTheory.FinitaryExtensive",
"CategoryTheory.Functor.category",
"TypeCat.instFunLikeFun",
"_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryThe... | true |
Nat.ofDigits_lt_base_pow_length' | Mathlib.Data.Nat.Digits.Defs | [
"Int.instAddCommGroup",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Nat.zero_le",
"MulOne.toOne",
"Int.ofNat_lt._simp_2",
"le_refl",... | true |
String.Pos.next.eq_1 | Init.Data.String.Basic | [
"String.toSlice",
"String.Pos.next",
"String.Pos.next._proof_2",
"String",
"String.Pos.toSlice",
"String.Slice.Pos.next",
"Ne",
"String.Pos.ofToSlice",
"String.endPos",
"String.Pos",
"Eq.refl",
"Eq"
] | true |
Std.Internal.List.getValueCast!_filter | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"congrArg",
"Std.Internal.List.getValueCast?",
"LawfulBEq",
"Option.get!",
"Sigma.fst",
"List",
"Option.filter",
"Std.Internal.List.getValueCast!",
"Std.Internal.List.getValueCast!_eq_getValueCast?",
"List.filter",
"True",
"eq_self",
"Std.Internal.List.get... | true |
_private.Mathlib.Topology.Homeomorph.Defs.0.Homeomorph.isInducing._simp_1_1 | Mathlib.Topology.Homeomorph.Defs | [
"Topology.IsInducing.id",
"id",
"Topology.IsInducing",
"TopologicalSpace",
"True",
"eq_true",
"Eq"
] | false |
Lean.Server.RequestHandlerCompleteness.rec | Lean.Server.Requests | [
"Lean.Server.RequestHandlerCompleteness",
"String",
"Nat",
"Lean.Server.RequestHandlerCompleteness.complete",
"Lean.Server.RequestHandlerCompleteness.partial"
] | false |
CategoryTheory.PreGaloisCategory.IsFundamentalGroup.rec | Mathlib.CategoryTheory.Galois.IsFundamentalgroup | [
"CategoryTheory.Functor",
"instHSMul",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"ContinuousSMul",
"Finite",
"FintypeCat",
"Group",
"MulAction.IsPretransitive",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"DivInvMonoid.toMonoid",
"CategoryTheory.ObjectProperty.F... | false |
Lean.LBool.false.elim | Lean.Data.LBool | [
"PULift.up",
"Lean.LBool.false",
"Lean.LBool.ctorIdx",
"Nat",
"Eq.symm",
"Eq",
"Lean.LBool",
"Lean.LBool.ctorElim"
] | false |
String.Slice.dropPrefix_char_eq_dropPrefix_beq | Init.Data.String.Lemmas.Pattern.Char | [
"String.Slice.dropPrefix",
"String.Slice",
"instBEqOfDecidableEq",
"BEq.beq",
"String.Slice.Pattern.CharPred.instForwardPatternForallCharBool",
"Bool",
"Char",
"String.Slice.Pattern.Char.instForwardPatternChar",
"Eq",
"rfl",
"instDecidableEqChar"
] | true |
TopologicalSpace.Opens.mapId._proof_3 | Mathlib.Topology.Category.TopCat.Opens | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategory",
"CategoryTheory.eqToHom",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"TopologicalSpace.Opens",
"TopologicalSpace.Opens.map_id_obj",... | false |
WeierstrassCurve.Affine.CoordinateRing.quotientXYIdealEquiv._proof_3 | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | [
"Polynomial.C",
"WeierstrassCurve.Affine.CoordinateRing.quotientXYIdealEquiv._proof_2",
"CommRing",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"HSub.hSub",
"RingHom",
"Algebra.id",
"Set.instSingletonSet",
"Ideal.map",
"Insert.insert",
"Ideal.IsTwo... | false |
DeltaGenerated.instLargeCategory._proof_7 | Mathlib.Topology.Category.DeltaGenerated | [
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"DeltaGenerated.instLargeCategory._aux_5",
"TopCat.instCategory",
"DeltaGenerated.instLargeCategory._aux_1",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Category.id_comp._autoParam",
"D... | false |
_private.Init.Data.String.Lemmas.Pattern.Pred.0.String.Slice.Pattern.Model.CharPred.Decidable.instLawfulToForwardSearcherModelForallCharPropDefaultForwardSearcherForallBoolDecide._simp_1 | Init.Data.String.Lemmas.Pattern.Pred | [
"String.Slice.Pattern.Model.IsValidSearchFrom",
"String.Slice.Pattern.Model.CharPred.Decidable.instPatternModelForallCharPropOfDecidablePred",
"String.Slice.Pattern.SearchStep",
"String.Slice",
"List",
"String.Slice.Pattern.Model.CharPred.instPatternModelForallCharBool",
"DecidablePred",
"String.Slice... | false |
midpoint_mem_segment | Mathlib.Analysis.Convex.Segment | [
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"IsStrictOrderedRing",
"midpoint_mem_openSegment",
"AddCommGroup.toAddGroup",
"Membership.mem",
"SemilatticeInf.toPart... | true |
CategoryTheory.Monad.Algebra.Hom.mk.congr_simp | Mathlib.CategoryTheory.Monad.Algebra | [
"CategoryTheory.Monad",
"CategoryTheory.Monad.Algebra.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Monad.Algebra.a",
"Eq.rec",
"CategoryTheory.Monad.Algebra.A",
"CategoryTheory.Functor.map",
"CategoryTheory.Monad.toFunctor",
"CategoryTheory.Monad.Algebra.Hom.mk",
... | true |
_private.Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition.0.Submodule.rank_le_one_iff_isPrincipal._simp_1_1 | Mathlib.LinearAlgebra.Dimension.FreeAndStrongRankCondition | [
"instHSMul",
"Cardinal.instOne",
"Cardinal",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Exists",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"LE.le",
"Cardinal.instLE",
"Module.Free"... | false |
upperBounds_prod | Mathlib.Order.Bounds.Basic | [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"Prod.instLE_mathlib",
"SProd.sprod",
"congrArg",
"and_self",
"Set.mem_prod._simp_1",
"Set.nonempty_coe_sort",
"Prod.forall._simp_1",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Eq.mp",
"Set.Elem",
"id",
"upperBounds",
"Prod.mk",
... | true |
Algebra.Generators.Hom.mk.sizeOf_spec | Mathlib.RingTheory.Extension.Generators | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.Generators.Ring",
"MvPolynomial.aeval",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"Algebra",
"Nat.instAddMonoid",
"RingHom",
"... | true |
Lean.Meta.Grind.Filter.fvar | Lean.Meta.Tactic.Grind.Filter | [
"Lean.Meta.Grind.Filter",
"Lean.FVarId",
"Lean.Meta.Grind.Filter.fvar"
] | true |
_private.Lean.Compiler.LCNF.Visibility.0.Lean.Compiler.LCNF.markDeclPublicRec.match_1 | Lean.Compiler.LCNF.Visibility | [
"Option.ctorIdx",
"Option.some",
"Lean.Compiler.LCNF.Decl",
"Nat.hasNotBit",
"_private.Lean.Compiler.LCNF.Visibility.0.Lean.Compiler.LCNF.markDeclPublicRec._sparseCasesOn_1",
"Lean.Compiler.LCNF.Phase",
"Lean.Compiler.LCNF.Phase.toPurity",
"Option"
] | false |
_private.Lean.Meta.Tactic.Subst.0.Lean.Meta.subst.match_3 | Lean.Meta.Tactic.Subst | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Option.none",
"Unit",
"Prod",
"Option"
] | false |
_private.Init.Data.Fin.Lemmas.0.Fin.reverseInduction_castSucc_aux | Init.Data.Fin.Lemmas | [
"dite_cond_eq_true",
"Eq.mpr",
"Nat.recAux",
"Fin.reverseInduction._proof_1",
"Fin.succ",
"congrArg",
"False.elim",
"Classical.byContradiction",
"Fin.reverseInduction._proof_9",
"cast",
"Fin.mk",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.le_of_lt",
"eq_comm",
"Fin.val",
"d... | true |
RootPairing.smul_coroot_eq_of_root_eq_smul | Mathlib.LinearAlgebra.RootSystem.Defs | [
"Set.mem_range_self",
"Eq.mpr",
"Module.eq_of_mapsTo_reflection_of_mem",
"RootPairing.coreflection",
"RootPairing.pairing",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"SemilinearMapClass.toMulActio... | true |
_private.Lean.Meta.Tactic.Grind.Theorems.0.Lean.Meta.Grind.Theorems.insert._sparseCasesOn_7 | Lean.Meta.Tactic.Grind.Theorems | [
"Nat.ne_of_beq_eq_false",
"Lean.HeadIndex.sort",
"Lean.HeadIndex.lam",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.FVarId",
"Nat.hasNotBit",
"Lean.HeadIndex.rec",
"instOfNatNat",
"Lean.Literal",
"Lean.HeadIndex.fvar",
"Nat.land",
"Lean.HeadIndex.mvar",
"Nat",
"Lean.HeadIndex.const",
"Bool",... | false |
Finset.mem_powersetCard._simp_1 | Mathlib.Data.Finset.Powerset | [
"Finset",
"Membership.mem",
"HasSubset.Subset",
"Finset.mem_powersetCard",
"And",
"Finset.instSetLike",
"Finset.powersetCard",
"Nat",
"propext",
"Finset.instHasSubset",
"Finset.card",
"Eq",
"SetLike.instMembership"
] | false |
BoxIntegral.Prepartition.instOrderTop | Mathlib.Analysis.BoxIntegral.Partition.Basic | [
"BoxIntegral.Prepartition.instOrderTop._proof_1",
"BoxIntegral.Prepartition",
"BoxIntegral.Prepartition.single",
"Top.mk",
"OrderTop.mk",
"OrderTop",
"BoxIntegral.Prepartition.instLE",
"BoxIntegral.Box",
"BoxIntegral.Prepartition.instOrderTop._proof_3"
] | true |
CategoryTheory.LocalizerMorphism.arrow | Mathlib.CategoryTheory.Localization.LocalizerMorphism | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.LocalizerMorphism.functor",
"CategoryTheory.instCategoryArrow",
"CategoryTheory.LocalizerMorphism.arrow._proof_1",
"CategoryTheory.LocalizerMorphism.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Arrow",
"CategoryTheory.Functor.mapAr... | true |
Lean.Lsp.instToJsonRange | Lean.Data.Lsp.BasicAux | [
"Lean.ToJson.mk",
"Lean.ToJson",
"Lean.Lsp.Range",
"Lean.Lsp.instToJsonRange.toJson"
] | true |
Units.instMulDistribMulAction._proof_2 | Mathlib.Algebra.GroupWithZero.Action.Units | [
"Monoid",
"Units.val",
"instHSMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"Units",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Monoid.toSemigroup",
"MulDistribMulAction.toMulAction",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"MulDistribMulAction",
"Eq",
"smul_... | false |
Affine.Simplex.faceOpposite | Mathlib.LinearAlgebra.AffineSpace.Simplex.Basic | [
"Nat.instMulZeroClass",
"AddCommGroup.toAddCommMonoid",
"Compl.compl",
"Finset",
"instDecidableEqFin",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"BooleanAlgebra.toCompl",
"AddCommGroup",
"Affine.Simplex",
"instSubNat",
"instOfNatNat",
"Affine.Simplex.faceOpposite._proof_2",
"Fin.fintype",
... | true |
UniformSpace.hausdorff._proof_1 | Mathlib.Topology.UniformSpace.Closeds | [
"Filter.instMembership",
"Iff.mpr",
"Filter.tendsto_lift'",
"UniformSpace",
"SetRel",
"Filter.Eventually",
"SetRel.inv",
"uniformity",
"setOf",
"Membership.mem",
"Filter.mem_lift'",
"Set.instReflSubset",
"inv_hausdorffEntourage",
"Eq.subset",
"symm_le_uniformity",
"Filter.lift'",
"Se... | false |
DirectSum.decomposeAlgEquiv_apply | Mathlib.RingTheory.GradedAlgebra.Basic | [
"GradedRing.toGradedMonoid",
"Submodule",
"Submodule.addSubmonoidClass",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"DirectSum.decomposeAlgEquiv",
"Submodule.addCommMonoid",
"Algebra",
"Membership.mem",
"GradedRing.toDecomposition",
"Algebra.toModule",
"Equiv",
"Subtype",
"AddSubmon... | true |
CategoryTheory.δ_naturality_assoc | Mathlib.CategoryTheory.Monoidal.End | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"Eq.mp",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"C... | true |
symmDiff_symmDiff_cancel_left | Mathlib.Order.SymmDiff | [
"Lattice.toSemilatticeSup",
"congrArg",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"bot_symmDiff",
"Preorder.toLE",
"SemilatticeSup.toMax",
"Bot.bot",
"GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra",
"symmDiff_self",
"GeneralizedCoheytingAlgebra.toOrderBot",
"_private.Mathlib.Order... | true |
NumberField.instCommRingAdeleRing._proof_25 | Mathlib.NumberTheory.NumberField.AdeleRing | [
"NumberField.instCommRingAdeleRing._proof_10",
"Prod.instSemiring._proof_7",
"IsDedekindDomain.instCommRingFiniteAdeleRing",
"NumberField.instCommRingAdeleRing._proof_6",
"NumberField.instCommRingAdeleRing._aux_16",
"Mul.mk",
"NumberField.instCommRingAdeleRing._proof_23",
"Semigroup.toMul",
"CommRin... | false |
PMF.binomial_apply_zero | Mathlib.Probability.ProbabilityMassFunction.Binomial | [
"PMF.binomial",
"instNeZeroNatHAdd_1",
"MulOne.toOne",
"Nat.instOrderedSub",
"ENNReal.ofNNReal",
"Nat.choose",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"PMF",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"HSub.hSub",
"PMF.instFunLike",
"Preorder.toLE",
"Fin.instOfNat",... | true |
Ne.dite_ne_right_iff | Mathlib.Logic.Basic | [
"exists_iff_of_forall",
"Decidable",
"dite_ne_right_iff",
"Exists",
"Ne",
"dite",
"Iff",
"Iff.trans",
"Not"
] | true |
Std.HashMap.size_insertIfNew | Std.Data.HashMap.Lemmas | [
"Membership.mem",
"instOfNatNat",
"Std.HashMap",
"LawfulHashable",
"instHAdd",
"EquivBEq",
"HAdd.hAdd",
"Nat",
"Std.HashMap.instDecidableMem",
"Std.HashMap.insertIfNew",
"Std.HashMap.size",
"instAddNat",
"Hashable",
"Std.DHashMap.size_insertIfNew",
"Std.HashMap.inner",
"OfNat.ofNat",
... | true |
CategoryTheory.EnrichedCat.bicategory._proof_14 | Mathlib.CategoryTheory.Enriched.EnrichedCat | [
"CategoryTheory.Category.assoc",
"CategoryTheory.categoryForgetEnrichment",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.EnrichedCat.associator_inv_out_app",
"CategoryTheory.ForgetEnrichment.of",
"CategoryTheory.EnrichedNatTrans.out",
... | false |
_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.go._unary._proof_11 | Init.Data.String.Pattern.String | [
"HSub.hSub",
"String.Slice",
"instSubNat",
"instOfNatNat",
"Array",
"instHSub",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Nat.decLt",
"instLTNat",
"OfNat.ofNat",
"Array.size",
"Not",
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable._pro... | false |
SSet.horn₃₁.desc | Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | [
"SSet.Subcomplex.toSSet",
"CompleteLattice.MulticoequalizerDiagram.multispanIndex",
"Opposite",
"CategoryTheory.Limits.WalkingMultispan",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Compl.compl",
"Finset",
"CategoryTheory.... | true |
BoundedContinuousFunction._aux_Mathlib_Topology_ContinuousMap_Bounded_Basic___unexpand_BoundedContinuousFunction_1 | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
NormedAlgebra.restrictScalars._proof_1 | Mathlib.Analysis.Normed.Module.Basic | [
"NormedCommRing.toSeminormedCommRing",
"HMul.hMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra.commutes'",
"SeminormedRing.toRing",
"RingHom",
"NormedField.toField",
"Field.toSemifield",
"NormedField",
"instDistribOfSemiring",
"RingHom.instFunLike",
"Distrib.toMul",
"Algebra... | false |
IsHomeomorph.surjective | Mathlib.Topology.Homeomorph.Defs | [
"TopologicalSpace",
"Function.Bijective.surjective",
"IsHomeomorph.bijective",
"Function.Surjective",
"IsHomeomorph"
] | true |
_private.Batteries.Data.List.Basic.0.List.dropSlice_zero₂.match_1_1 | Batteries.Data.List.Basic | [
"Unit.unit",
"instOfNatNat",
"List.cons",
"List",
"Unit",
"Nat",
"List.casesOn",
"Nat.zero",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn",
"List.nil"
] | false |
CategoryTheory.Iso.inv_ext' | Mathlib.CategoryTheory.Iso | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.CategoryStruct.comp",
"Iff.mp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"CategoryTheory.Iso.hom_comp_eq_id",
"Eq",
"CategoryTheory.Iso.i... | true |
List.Vector.«_aux_Mathlib_Data_Vector_Basic___macroRules_List_Vector_term_::ᵥ__1» | Mathlib.Data.Vector.Basic | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",... | false |
ContinuousOn.image_Icc_of_antitoneOn | Mathlib.Topology.Order.Compact | [
"OrderDual.toDual",
"Eq.mpr",
"OrderTopology",
"Preorder.toLT",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"id",
"Equiv",
"AntitoneOn.dual_right",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditi... | true |
LieAlgebra.IsExtension.casesOn | Mathlib.Algebra.Lie.Extension | [
"LieHom",
"LieAlgebra.toModule",
"CommRing",
"LieAlgebra.IsExtension.rec",
"LieSubmodule.instBot",
"LieRing.toAddCommGroup",
"LieHom.range",
"Bot.bot",
"LieSubalgebra.instTop",
"LieRing",
"LieHom.ker",
"LieIdeal.toLieSubalgebra",
"LieAlgebra.IsExtension",
"LieIdeal",
"LieSubalgebra",
"... | false |
_private.Mathlib.RingTheory.MvPowerSeries.Rename.0.MvPowerSeries.renameFunAuxImage.match_1 | Mathlib.RingTheory.MvPowerSeries.Rename | [
"Nat.instMulZeroClass",
"Prod.mk",
"Nat",
"Prod",
"Prod.casesOn",
"Finsupp",
"MulZeroClass.toZero"
] | false |
Polynomial.reflect.match_1 | Mathlib.Algebra.Polynomial.Reverse | [
"Polynomial.casesOn",
"Polynomial",
"Nat",
"Semiring",
"AddMonoidAlgebra",
"Polynomial.ofFinsupp"
] | false |
cfcHom_predicate | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Exists.choose_spec",
"Continuous",
"spectrum",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"IsTopologicalSemiring",
"ContinuousStar",
"ContinuousMap",
"cfcHom",
"PseudoMetricSpace.toUniformSpace",
"Algebra",
"Membership.mem",
"StarAlgHom.instFunLike",
"Set.Elem",
"Algebra.id",
"... | true |
_private.Init.Data.List.ToArray.0.List.findSomeRevM?_find_toArray | Init.Data.List.ToArray | [
"Pure.pure",
"Eq.mpr",
"Array.forIn'.loop._proof_1",
"GetElem",
"Nat.recAux",
"List.findSomeM?",
"congrArg",
"Option.toList",
"Monad.toApplicative",
"Option.casesOn",
"List.instGetElem?NatLtLength",
"Option.some",
"Eq.rec",
"Eq.mp",
"List.findSomeM?_nil",
"id",
"LawfulMonad",
"inst... | true |
_private.Mathlib.Geometry.Euclidean.Angle.Oriented.Basic.0.Orientation.inner_eq_norm_mul_norm_mul_cos_oangle._simp_1_7 | Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | [
"False",
"eq_false",
"pow_ne_zero",
"Ne",
"Monoid.toPow",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Nat",
"Zero.toOfNat0",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZero",
"IsReduced"
] | false |
ContinuousLinearEquiv.submoduleMap._proof_2 | Mathlib.Topology.Algebra.Module.Equiv | [
"ContinuousLinearMap.comp",
"Submodule.subtypeL",
"Submodule",
"Continuous",
"ContinuousLinearEquiv.toLinearEquiv",
"ContinuousLinearMap.funLike",
"Submodule.addCommMonoid",
"RingHom",
"RingHomSurjective.invPair",
"Membership.mem",
"Subtype",
"ContinuousLinearMap.codRestrict",
"Submodule.mod... | false |
apply_dite | Init.ByCases | [
"dite_cond_eq_true",
"of_eq_false",
"eq_false",
"congrArg",
"Decidable",
"dite",
"congr",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"dite_cond_eq_false",
"Eq",
"Not",
"Eq.trans"
] | true |
Matrix.normedAddCommGroup._proof_6 | Mathlib.Analysis.Matrix.Normed | [
"Filter.coprodᵢ",
"NNDist.nndist",
"Real.instLE",
"Real",
"pseudoMetricSpacePi._proof_2",
"PseudoMetricSpace.toBornology",
"Finset.univ",
"PseudoMetricSpace.cobounded_sets._autoParam",
"Dist.mk",
"PseudoEMetricSpace.toPseudoMetricSpaceOfDist",
"Matrix",
"Compl.compl",
"Pi.instBornology",
"... | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_105 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Matrix.mul_one | Mathlib.Data.Matrix.Mul | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"HMul.hMul",
"congrArg",
"Matrix",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"id",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoidWithO... | true |
Std.IterM.TerminationMeasures.Productive.casesOn | Init.Data.Iterators.Basic | [
"Std.Iterator",
"Std.IterM.TerminationMeasures.Productive",
"Std.IterM.TerminationMeasures.Productive.rec",
"Std.IterM.TerminationMeasures.Productive.mk",
"Std.IterM"
] | false |
Monoid.End.ext | Mathlib.Algebra.Group.Hom.Defs | [
"Monoid.End.instFunLike",
"DFunLike.ext",
"MulOne",
"Eq",
"DFunLike.coe",
"Monoid.End"
] | true |
ContDiffMapSupportedIn.zero_on_compl | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | [
"Real",
"NormedSpace",
"Compl.compl",
"PseudoMetricSpace.toUniformSpace",
"Pi.instZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"Set.EqOn",
"SubNegZeroMonoid.toNegZeroClass",
"ContDiffMapSupportedIn.toContDiffMapSupportedInClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Set.instCompl",
... | true |
Set.image2_inter_union_subset | Mathlib.Data.Set.NAry | [
"Eq.mpr",
"congrArg",
"Set.image2_inter_union_subset_union",
"Set.instUnion",
"HasSubset.Subset.trans",
"id",
"Set.instIsTransSubset",
"Set.instReflSubset",
"HasSubset.Subset",
"Set.instInter",
"Inter.inter",
"Set.union_subset",
"Eq.subset",
"Set.inter_comm",
"Set.Subset.rfl",
"Set.ima... | true |
Set.Icc_add_Ico_subset | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"add_lt_add_of_le_of_lt",
"Preorder.toLT",
"add_le_add",
"PartialOrder.toPreorder",
"AddRightStrictMono",
"AddLeftMono",
"Preorder.toLE",
"Membership.mem",
"Exists",
"AddRightMono",
"PartialOrder",
"addLeftMono_of_addLeftStrictMono",
"HasSubset.Subset",
"LE.le",
"Set.Ico",
"And.casesOn... | true |
Lean.Grind.Linarith.instBEqPoly.beq._sunfold | Init.Grind.Ordered.Linarith | [
"Lean.Grind.Linarith.instBEqPoly.beq.match_1",
"Int.instDecidableEq",
"Bool.and",
"Int",
"Lean.Grind.Linarith.Var",
"instBEqOfDecidableEq",
"Bool.true",
"BEq.beq",
"Unit",
"Bool",
"instDecidableEqNat",
"Bool.false",
"Lean.Grind.Linarith.instBEqPoly.beq",
"Lean.Grind.Linarith.Poly"
] | false |
WithAbs.instRing._proof_3 | Mathlib.Analysis.Normed.Ring.WithAbs | [
"AddGroup.toSubtractionMonoid",
"Equiv.ring._proof_6",
"Equiv.ring._proof_3",
"NegZeroClass.toNeg",
"RingEquiv.toEquiv",
"instHSMul",
"Function.Injective.addGroupWithOne",
"Equiv.instEquivLike",
"WithAbs",
"AddMonoid.toAddSemigroup",
"Equiv.addGroupWithOne",
"Equiv.ring._proof_10",
"AddGroup... | false |
Con.monoid._proof_4 | Mathlib.GroupTheory.Congruence.Defs | [
"Monoid",
"Semigroup.toMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"Con.instPowQuotientNat",
"Quotient.mk''",
"Monoid.npow_succ._autoParam",
"MulOne.toMul",
"instOfNatNat",
"Con.Quotient",
"autoParam",
"Con.pow",
"Function.Surjective.monoid._proof_4",
"Monoid.toPow",
"Quotient.mk''_surjec... | false |
TopologicalSpace.le_generateFrom_iff_subset_isOpen | Mathlib.Topology.Order | [
"PartialOrder.toPreorder",
"TopologicalSpace.GenerateOpen.basic",
"setOf",
"Preorder.toLE",
"Membership.mem",
"TopologicalSpace.GenerateOpen.recOn",
"HasSubset.Subset",
"LE.le",
"TopologicalSpace.generateFrom",
"isOpen_univ",
"TopologicalSpace",
"Iff",
"TopologicalSpace.GenerateOpen",
"IsO... | true |
DomMulAct.instDistribMulActionSubtypeAEEqFunMemAddSubgroupLp | Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic | [
"Monoid",
"DomMulAct",
"MeasureTheory.Measure",
"DomMulAct.instDistribMulActionSubtypeAEEqFunMemAddSubgroupLp._proof_1",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"DomMulAct.instSMulSubtypeAEEqFunMemAddSubgroupLp._proof_1",
"AddCommGroup.toAddGroup",
"AddSubgroup.toAddGroup",
... | true |
Fin.castSucc_pos | Init.Data.Fin.Lemmas | [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Zero.ofOfNat0",
"Eq.mp",
"id",
"Fin.instOfNat",
"instOfNatNat",
"Fin.val",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"LT.lt",
"instLTFin",
"instAddNat",
"_private.Init.Data.Fin.Lemmas.0.Fin.castSucc_pos._simp_1_1",
"instLTNat",
"Fin.cas... | true |
Std.PRange.UpwardEnumerable.least | Init.Data.Range.Polymorphic.UpwardEnumerable | [
"Std.PRange.UpwardEnumerable.isSome_least?",
"Std.PRange.UpwardEnumerable",
"Std.PRange.LawfulUpwardEnumerableLeast?",
"Option.get",
"Nonempty",
"Std.PRange.Least?",
"Std.PRange.Least?.least?"
] | true |
CategoryTheory.Limits.IsLimit.assoc._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Limits.BinaryFan.assocInv",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.BinaryFan.fst",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.Bin... | false |
Sym.map_mk._proof_1 | Mathlib.Data.Sym.Basic | [
"Multiset.map",
"congrArg",
"Multiset",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Multiset.card",
"congrFun'",
"Eq",
"Eq.trans",
"Multiset.card_map"
] | false |
Function.HasTemperateGrowth.toTemperedDistribution._proof_6 | Mathlib.Analysis.Distribution.TemperedDistribution | [
"Complex.instNormedField",
"NormedField.toField",
"RingHomCompTriple",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Complex",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
Mathlib.Tactic.Linarith.applyContrLemma | Mathlib.Tactic.Linarith.Frontend | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"instMonadExceptOfMonadExceptOf",
"Lean.MonadError.toMonadExceptOf",
"Lean.MVarId.getType'",
"instMonadControlTOfPure",
"Mathlib.Tactic.Linarith.getContrLemma",
"Lean.Meta.State",
"Lean.instAddErrorMes... | true |
Pi.spectrum_eq | Mathlib.Algebra.Algebra.Spectrum.Pi | [
"Eq.mpr",
"compl_compl",
"Algebra.algebraMap",
"spectrum",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"Set.iInter",
"Compl.compl",
"setOf",
"HSub.hSub",
"IsUnit",
"Algebra",
"AddCommGroup.toAddGroup",
"RingHom",
"BooleanAlgebra.toCompl",
"id",
"compl_injec... | true |
Path.Homotopic.Quotient.symm | Mathlib.Topology.Homotopy.Path | [
"Path.symm",
"Path.Homotopic.symm₂",
"Quotient.map",
"Path.Homotopic.Quotient",
"Path.Homotopic.setoid",
"TopologicalSpace",
"HasEquiv.Equiv",
"Path",
"instHasEquivOfSetoid"
] | true |
CategoryTheory.Limits.FormalCoproduct.powerMap_id | Mathlib.CategoryTheory.Limits.FormalCoproducts.Cech | [
"Eq.mpr",
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.Limits.FormalCoproduct.powerMap._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Limits.FormalCoproduct.hom_ext",
"Function.comp",
"CategoryTheory.CategoryStru... | true |
Lean.«binderPred⊃_» | Init.BinderPredicates | [
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
_private.Lean.Parser.Term.Doc.0.Lean.Parser.Term.Doc.getRecommendedSpellingsForName.match_4 | Lean.Parser.Term.Doc | [
"Option.ctorIdx",
"Lean.Parser.Term.Doc.RecommendedSpelling",
"Option.some",
"Nat.hasNotBit",
"Array",
"_private.Lean.Parser.Term.Doc.0.Lean.Parser.Term.Doc.getRecommendedSpellingsForName._sparseCasesOn_1",
"Option"
] | false |
CategoryTheory.InjectiveResolution.isoRightDerivedObj_hom_naturality_assoc | Mathlib.CategoryTheory.Abelian.RightDerived | [
"HomologicalComplex.homologyFunctor",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.assoc",
"CategoryTheory.InjectiveResolution.isoRightDerivedObj",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStru... | true |
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