name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.MorphismProperty.commShift_Q' | Mathlib.CategoryTheory.Shift.Localization | [
"CategoryTheory.MorphismProperty.IsCompatibleWithShift",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.instCategoryLocalization'",
"CategoryTheory.MorphismProperty.HasLocalization",
"CategoryTheory.Functor.CommShift.localized",
"CategoryTheory.MorphismProperty.instIsLocalizationLocal... | true |
AddEquiv.neg_apply | Mathlib.Algebra.Group.Units.Equiv | [
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddEquiv.neg",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"AddEquiv",
"AddZero.toAdd",
"Eq.refl",
"SubNe... | true |
csSup_inter_le | Mathlib.Order.ConditionallyCompleteLattice.Basic | [
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toMin",
"LE.le",
"Set.instInter",
"le_inf",
"BddAbove",
"Inter.inter",
"Set.Nonempty",
"And.right",
"And.left",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"Conditiona... | true |
Lean.getStructureParentInfo | Lean.Structure | [
"Lean.StructureInfo.parentInfo",
"Array",
"Lean.StructureParentInfo",
"Lean.Name",
"Lean.getStructureInfo",
"Lean.Environment"
] | true |
List.map_length_splitWrtComposition | Mathlib.Combinatorics.Enumerative.Composition | [
"Nat.instMulZeroClass",
"List.map",
"Composition.blocks",
"List.sum",
"Composition",
"Composition.blocks_sum",
"List",
"List.splitWrtComposition",
"Nat.instPreorder",
"Nat",
"instAddNat",
"le_of_eq",
"Eq",
"List.length",
"List.map_length_splitWrtCompositionAux",
"MulZeroClass.toZero"
] | true |
Filter.hyperfilter.congr_simp | Mathlib.Analysis.Real.Hyperreal | [
"Filter.hyperfilter",
"Eq.refl",
"Infinite",
"Ultrafilter",
"Eq"
] | true |
right_le_lineMap_iff_le | Mathlib.LinearAlgebra.AffineSpace.Ordered | [
"Preorder.toLT",
"Semiring.toModule",
"AffineMap.instFunLike",
"OrderDual.instIsStrictOrderedModule",
"AddGroupWithOne.toAddGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"OrderDual.instPosSMulReflectLE",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreor... | true |
QuaternionAlgebra.imJₗ._proof_2 | Mathlib.Algebra.Quaternion | [
"QuaternionAlgebra.instModule",
"CommRing",
"instHSMul",
"Semiring.toModule",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"QuaternionAlgebra",
"AddZeroClass.toAddZero",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Dis... | false |
CategoryTheory.Abelian.SpectralObject.isoMapFourδ₄Toδ₃' | Mathlib.Algebra.Homology.SpectralObject.EpiMono | [
"CategoryTheory.Abelian.SpectralObject.E",
"CategoryTheory.Abelian.SpectralObject.isoMapFourδ₄Toδ₃'._auto_1",
"CategoryTheory.IsIso",
"CategoryTheory.Abelian.SpectralObject.mapFourδ₄Toδ₃'",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Preord... | true |
_private.Mathlib.Order.KrullDimension.0.Order.coheight_of_noMaxOrder.match_1_1 | Mathlib.Order.KrullDimension | [
"Fin.casesOn",
"Fin.mk",
"Nat",
"LT.lt",
"instLTNat",
"Fin"
] | false |
Std.DTreeMap.forM_eq_forM | Std.Data.DTreeMap.Lemmas | [
"ForM.forM",
"Std.DTreeMap",
"Ordering",
"LawfulMonad",
"Std.DTreeMap.instForMSigmaOfMonad",
"Sigma.fst",
"PUnit",
"Std.DTreeMap.forM",
"Monad",
"Sigma.snd",
"Eq",
"Sigma",
"rfl"
] | true |
Lattice.toLinearOrder | Mathlib.Order.Lattice | [
"Lattice",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ord.mk",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"Lattice.toLinearOrder._proof_2",
"Lattice.toLinearOrder._proof_4",
"Lattice.toLinearOrder._proof_3",
"compare... | true |
CategoryTheory.Localization.Monoidal.leftUnitor | Mathlib.CategoryTheory.Localization.Monoidal.Basic | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Localization.liftNatIso",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory.leftUnitorNatIso",
"CategoryTheory.MorphismProperty.IsMonoidal",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
... | true |
BoxIntegral.HasIntegral.tendsto | Mathlib.Analysis.BoxIntegral.Basic | [
"BoxIntegral.IntegrationParams.toFilteriUnion",
"Real",
"NormedSpace",
"BoxIntegral.Prepartition",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousLinearMap.addCommMonoid",
"AddCommGroup.toAddGroup",
"BoxIntegral.integralSum",
"nhds",
"Rea... | true |
Finsupp.tail._proof_1 | Mathlib.Data.Finsupp.Fin | [
"Finite",
"Finite.of_fintype",
"Fin.fintype",
"Nat",
"Fin"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.size_filterMap_le_size._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
Subgroup.inf_subgroupOf_left | Mathlib.Algebra.Group.Subgroup.Map | [
"Eq.mpr",
"Subgroup.subgroupOf",
"CompleteLattice.toLattice",
"congrArg",
"Group",
"Membership.mem",
"id",
"Subtype",
"Subgroup",
"SemilatticeInf.toMin",
"Subgroup.inf_subgroupOf_right",
"inf_comm",
"Subgroup.instMin",
"Subgroup.instCompleteLattice",
"Eq.refl",
"Subgroup.toGroup",
"E... | true |
Lean.Lsp.DocumentHighlightParams.mk.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.DocumentHighlightParams._sizeOf_inst",
"instOfNatNat",
"Lean.Lsp.DocumentHighlightParams",
"Lean.Lsp.DocumentHighlightParams.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.Lsp.TextDocumentPositionParams",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Lsp.TextDo... | true |
ZeroAtInftyContinuousMap.copy | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"ContinuousMap.mk",
"ZeroAtInftyContinuousMap.instFunLike",
"TopologicalSpace",
"ZeroAtInftyContinuousMap.mk",
"ZeroAtInftyContinuousMap",
"Eq",
"DFunLike.coe",
"ZeroAtInftyContinuousMap.copy._proof_1",
"Zero",
"ZeroAtInftyContinuousMap.copy._proof_2"
] | true |
CategoryTheory.Functor.colimitIsoColimitGrothendieck._proof_2 | Mathlib.CategoryTheory.Functor.KanExtension.Adjunction | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Functor.leftKanExtension",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.HasColimit",
"CategoryTheory.Functor.HasPointwiseLeftKanExtension",
"CategoryTheory.Functor.instHasLeftKanExtens... | false |
_private.Mathlib.Data.List.Sublists.0.List.nodup_sublistsLen._simp_1_1 | Mathlib.Data.List.Sublists | [
"eq_comm",
"propext",
"Eq"
] | false |
map_eq_zero_iff | Mathlib.Algebra.Group.Hom.Defs | [
"ZeroHomClass",
"map_zero",
"Function.Injective.eq_iff'",
"Iff",
"Zero.toOfNat0",
"Function.Injective",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"FunLike",
"Zero"
] | true |
_private.Init.Data.Ord.Array.0.Array.compareLex.match_1.eq_1 | Init.Data.Ord.Array | [
"Ordering.gt",
"Unit.unit",
"Ordering",
"Ordering.eq",
"Unit",
"Ordering.lt",
"Eq.refl",
"_private.Init.Data.Ord.Array.0.Array.compareLex.match_1",
"Eq"
] | true |
TensorAlgebra.ι_eq_zero_iff | Mathlib.LinearAlgebra.TensorAlgebra.Basic | [
"Eq.mpr",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"CommSemiring.toSemiring",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"AddZeroClass.toAddZero",
"map_zero",
"Algebra.toModule",
"Algebra.id",
"id",
"LinearMap.semilinearMapClass",
"Te... | true |
Std.Iterators.Types.ListIterator.mk | Init.Data.Iterators.Producers.Monadic.List | [
"Std.Iterators.Types.ListIterator",
"Std.Iterators.Types.ListIterator.mk",
"List"
] | true |
Lean.Parser.Term.hole | Lean.Parser.Term.Basic | [
"Lean.Parser.Parser",
"Lean.Parser.leadingNode",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.withAntiquot",
"Bool.true",
"Nat",
"Lean.Parser.withCache",
"OfNat.ofNat",
"Lean.Parser.mkAntiquot",
"Bool.false",
"Lean.Name.mkStr4"
] | true |
Lean.Meta.Grind.EMatchTheoremConstraint.check.injEq | Lean.Meta.Tactic.Grind.Extension | [
"Lean.Meta.Grind.EMatchTheoremConstraint",
"Eq.propIntro",
"Lean.Expr",
"Lean.Meta.Grind.EMatchTheoremConstraint.check",
"Eq.ndrec",
"Eq.refl",
"Lean.Meta.Grind.EMatchTheoremConstraint.check.inj",
"Eq"
] | true |
NonUnitalStarAlgHom.restrictScalars_apply | Mathlib.Algebra.Star.StarAlgHom | [
"Monoid",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"NonUnitalStarAlgHom.restrictScalars",
"DistribSMul.toSMulZeroClass",
"NonUnitalStarAlgHom.instFunLike",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"Star",
"Mu... | true |
CategoryTheory.ObjectProperty.ContainsZero.mk | Mathlib.CategoryTheory.ObjectProperty.ContainsZero | [
"CategoryTheory.ObjectProperty.ContainsZero.mk",
"Exists",
"And",
"CategoryTheory.Limits.IsZero",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty.ContainsZero",
"CategoryTheory.ObjectProperty",
"CategoryTheory.Category"
] | true |
_private.Lean.Meta.Tactic.Grind.Injective.0.Lean.Meta.Grind.getSymbols | Lean.Meta.Tactic.Grind.Injective | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Std.TreeSet.toList",
"Lean.Expr.isAppOfArity",
"Lean.Meta.forallTelescope",
"Lean.NameSet",
"instMonadControlTOfPure",
"String",
"List.map",
"Std.TreeSet.isEmpty",
"Lean.Meta.State",
"Lean.instA... | true |
AddGrpCat.limitAddGroup._proof_16 | Mathlib.Algebra.Category.Grp.Limits | [
"CategoryTheory.Functor",
"AddGrpCat.limitAddGroup._proof_7",
"Equiv.instEquivLike",
"CategoryTheory.Limits.Types.Small.limitCone",
"AddMonoid.toAddSemigroup",
"Equiv.addGroup._proof_2",
"AddGrpCat.limitAddGroup._proof_10",
"AddGrpCat.instCategory",
"Add.mk",
"AddMonoid.toAddZeroClass",
"Neg.mk"... | false |
Quaternion.algebra._proof_3 | Mathlib.Algebra.Quaternion | [
"NegZeroClass.toNeg",
"CommRing",
"QuaternionAlgebra.instAlgebra._proof_5",
"HMul.hMul",
"CommSemiring.toSemiring",
"Quaternion.algebra._aux_1",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra",
"RingHom",
"QuaternionAlgebra",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroC... | false |
TopCat.Presheaf.stalkPushforward._proof_3 | Mathlib.Topology.Sheaves.Stalks | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"Opposite",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategoryPresheaf",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"TopologicalSpace.Opens",
"TopCat.Presh... | false |
CategoryTheory.ShortComplex.RightHomologyMapData.neg | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"NegZeroClass.toNeg",
"CategoryTheory.ShortComplex.RightHomologyMapData.φH",
"CategoryTheory.ShortComplex.instNegHom",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ShortComplex.RightHomologyMapData.neg._proof_4",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomologyData",
"CategoryTheo... | true |
Monoid.Coprod.range_inl_sup_range_inr | Mathlib.GroupTheory.Coprod.Basic | [
"Subgroup.closure_eq",
"Eq.mpr",
"MonoidHom.range",
"Lattice.toSemilatticeSup",
"MonoidHom.instFunLike",
"Subgroup.closure",
"MonoidHom",
"CompleteLattice.toLattice",
"Monoid.toMulOneClass",
"congrArg",
"Monoid.Coprod.closure_range_inl_union_inr",
"Group",
"Set.instUnion",
"SemilatticeSup.... | true |
LieAlgebra.SemiDirectSum.right | Mathlib.Algebra.Lie.SemiDirect | [
"LieHom",
"LieAlgebra.toModule",
"CommRing",
"LieDerivation",
"LieRing.toAddCommGroup",
"lieAlgebraSelfModule",
"LieRing",
"LieAlgebra",
"LieDerivation.instLieRing",
"LieDerivation.instLieAlgebra",
"lieRingSelfModule",
"LieAlgebra.SemiDirectSum"
] | true |
definition._proof_8._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2 | Mathlib.MeasureTheory.Measure.Typeclasses.Finite | [
"Eq.mpr",
"congrArg",
"Set.univ",
"Set.sUnion",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"_private.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.0.definition._simp_6._@.Mathlib.MeasureTheory.Measure.Typeclasses.Finite.588747923._hygCtx._hyg.2",
"funext",
"And",
"_private.Mathlib.MeasureTh... | false |
IsStablyFiniteRing.mk | Mathlib.Data.Matrix.Mul | [
"Matrix.instMulOneOfFintypeOfDecidableEqOfAddCommMonoid",
"IsStablyFiniteRing",
"Matrix",
"instDecidableEqFin",
"AddCommMonoid",
"Fin.fintype",
"IsDedekindFiniteMonoid",
"Nat",
"IsStablyFiniteRing.mk",
"MulOne",
"Fin"
] | true |
DomMulAct.instIsRightCancelMulOfMulOpposite | Mathlib.GroupTheory.GroupAction.DomAct.Basic | [
"DomMulAct",
"MulOpposite",
"Mul",
"DomMulAct.instMulOfMulOpposite",
"IsRightCancelMul"
] | true |
IsAddKleinFour.card_four | Mathlib.GroupTheory.SpecificGroups.KleinFour | [
"Nat.card",
"instOfNatNat",
"IsAddKleinFour",
"AddGroup",
"Nat",
"OfNat.ofNat",
"Eq"
] | true |
Combinatorics.Additive.«termE[_]» | Mathlib.Combinatorics.Additive.Energy | [
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
Nat.ofDigits | Mathlib.Data.Nat.Digits.Defs | [
"List.brecOn",
"List",
"Nat",
"Semiring",
"Nat.ofDigits._f"
] | true |
Nat.SOM.Expr.var | Init.Data.Nat.SOM | [
"Nat.Linear.Var",
"Nat.SOM.Expr",
"Nat.SOM.Expr.var"
] | true |
Preorder.mk._flat_ctor | Mathlib.Order.Defs.PartialOrder | [
"LT.mk",
"Preorder.mk",
"Preorder.lt_iff_le_not_ge._autoParam",
"autoParam",
"And",
"Iff",
"LE.mk",
"Not",
"Preorder"
] | false |
CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryTheory.Functor.FullyFaithful.compUliftYonedaCompWhiskeringLeft._proof_1",
"Cat... | true |
Lean.Syntax.SepArray.recOn | Init.Prelude | [
"Lean.Syntax.SepArray.mk",
"String",
"Lean.Syntax",
"Lean.Syntax.SepArray.rec",
"Array",
"Lean.Syntax.SepArray"
] | false |
Multiset.keys | Mathlib.Data.Finmap | [
"Multiset.map",
"Multiset",
"Sigma.fst",
"Sigma"
] | true |
CategoryTheory.InjectiveResolution.extMk._proof_3 | Mathlib.CategoryTheory.Abelian.Injective.Ext | [
"_private.Mathlib.CategoryTheory.Abelian.Injective.Ext.0.CategoryTheory.InjectiveResolution.extMk._proof_2",
"instOfNatNat",
"Int",
"Nat.cast",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Nat",
"Int.instAdd",
"instAddNat",
"instNatCastInt",
"OfNat.ofNat",
"Eq"
] | false |
Filter.instCompleteLatticeFilter._proof_3 | Mathlib.Order.Filter.Basic | [
"Filter.instMembership",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"And",
"And.intro",
"Filter",
"Filter.instPartialOrder",
"Set"
] | false |
Std.Time.PlainDateTime.ctorIdx | Std.Time.DateTime.PlainDateTime | [
"Nat",
"Std.Time.PlainDateTime"
] | false |
Lean.Elab.Command.Structure.StructFieldViewDefault.autoParam | Lean.Elab.Structure | [
"Lean.Elab.Command.Structure.StructFieldViewDefault",
"Lean.Elab.Command.Structure.StructFieldViewDefault.autoParam",
"Lean.Syntax"
] | true |
Unitary.coe_symm_linearIsometryEquiv_apply | Mathlib.Analysis.InnerProductSpace.Adjoint | [
"InnerProductSpace.toNormedSpace",
"MulEquiv.instEquivLike",
"LinearIsometryEquiv.instGroup",
"CompleteSpace",
"ContinuousLinearMap.semiring",
"Submonoid.mul",
"Monoid.toMulOneClass",
"AddCommGroup.toAddCommMonoid",
"unitary",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"AddCom... | true |
Quotient.«_aux_Mathlib_Data_Quot___macroRules_Quotient_term⟦_⟧_1» | Mathlib.Data.Quot | [
"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.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",... | false |
VAdd.mk.noConfusion | Mathlib.Algebra.Notation.Defs | [
"VAdd",
"id",
"VAdd.noConfusion",
"VAdd.mk",
"heq_of_eq",
"Eq.refl",
"HEq",
"Eq"
] | false |
RingCat.Colimits.Prequotient.below | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CategoryTheory.SmallCategory",
"RingCat.Colimits.Prequotient",
"RingCat",
"PProd",
"PUnit",
"RingCat.instCategory",
"RingCat.Colimits.Prequotient.rec",
"RingCat.carrier",
"CategoryTheory.Functor.obj"
] | false |
_private.Lean.Compiler.LCNF.ExtractClosed.0.Lean.Compiler.LCNF.ExtractClosed.extractFVar.match_1 | Lean.Compiler.LCNF.ExtractClosed | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.Compiler.LCNF.Purity.pure",
"_private.Lean.Compiler.LCNF.ExtractClosed.0.Lean.Compiler.LCNF.ExtractClosed.extractFVar._sparseCasesOn_1",
"Lean.Compiler.LCNF.LetDecl",
"Option"
] | false |
UniformOnFun.inf_eq | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"cond",
"UniformSpace",
"Eq.mpr",
"iInf",
"inf_eq_iInf",
"CompleteLattice.toLattice",
"congrArg",
"UniformOnFun.uniformSpace",
"iInf_congr",
"id",
"instMinUniformSpace",
"SemilatticeInf.toMin",
"CompleteLattice.toCompleteSemilatticeInf",
"Bool.true",
"Bool.casesOn",
"instCompleteLattic... | true |
FirstOrder.Language.Substructure.mem_carrier | Mathlib.ModelTheory.Substructures | [
"Iff.rfl",
"Membership.mem",
"FirstOrder.Language.Substructure.instSetLike",
"FirstOrder.Language.Substructure",
"FirstOrder.Language.Structure",
"Iff",
"FirstOrder.Language",
"Set.instMembership",
"SetLike.instMembership",
"FirstOrder.Language.Substructure.carrier",
"Set"
] | true |
CategoryTheory.instPreservesFiniteColimitsObjFunctorRightExactFunctor | Mathlib.CategoryTheory.Limits.ExactFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.ObjectProperty.FullSubcategory.property",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.Limits.PreservesFiniteColimits",
"CategoryTheory.RightExactFunctor",
"CategoryTheory.Category",
"CategoryTheory.ri... | true |
isArtinianRing_iff | Mathlib.RingTheory.Artinian.Defs | [
"Semiring.toModule",
"IsArtinianRing",
"Iff.rfl",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Iff",
"IsArtinian",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"Semiring.toNonAssocSemiring"
] | true |
DirectSum.gMulHom._proof_4 | Mathlib.Algebra.DirectSum.Ring | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DirectSum.GNonUnitalNonAssocSemiring.mul_zero",
"GradedMonoid.GMul.mul",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"DirectSum.GNonUnitalNonAssocSemiring",
"HAdd.hAdd",
"AddZero.toAdd",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"... | false |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0.iteratedDerivWithin_tsum_exp_aux_eq._simp_1_5 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | [
"False",
"eq_false",
"OfNat.ofNat_ne_zero",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"CharZero",
"AddZero.toZero",
"Nat",
"Zero.toOfNat0",
"AddMonoidWithOne.toAddMonoid",
"OfNat.ofNat",
"Eq",
"instOfNatAtLeastTwo",
"AddMonoidWithOne",
"Nat.AtL... | false |
AlgebraicGeometry.GeometricallyReduced.eq_geometrically | Mathlib.AlgebraicGeometry.Geometrically.Reduced | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.geometricallyReduced_iff",
"AlgebraicGeometry.geometrically",
"funext",
"AlgebraicGeometry.IsReduced",
"AlgebraicGeometry.GeometricallyReduced",
"propext",
"CategoryTheory.Category.toCategoryStru... | true |
Int.instCommRing._proof_4 | Mathlib.Algebra.Ring.Int.Defs | [
"instOfNatNat",
"Int",
"Nat.cast",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"instNatCastInt",
"OfNat.ofNat",
"Eq",
"rfl"
] | false |
Std.TreeMap.minEntry! | Std.Data.TreeMap.Basic | [
"Std.TreeMap.inner",
"Ordering",
"Inhabited",
"Std.DTreeMap.Const.minEntry!",
"Prod",
"Std.TreeMap"
] | true |
_private.Mathlib.Data.Set.Lattice.0.Set.nonempty_sUnion._simp_1_1 | Mathlib.Data.Set.Lattice | [
"Ne",
"Set.Nonempty",
"propext",
"Set.instEmptyCollection",
"Set.nonempty_iff_ne_empty",
"EmptyCollection.emptyCollection",
"Eq",
"Set"
] | false |
CategoryTheory.Limits.Cocone.isColimitOfIsIsoColimMapι | Mathlib.CategoryTheory.Limits.Connected | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.IsIso",
"CategoryTheory.Limits.Cocone.ext",
"CategoryTheory.Limits.Cocone.isColimitOfIsIsoColimMapι._proof_2",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.colimit.isColimit",
"CategoryTheory.Limits.IsColimit.ofIsoC... | true |
IteratedWreathProduct_zero | Mathlib.GroupTheory.RegularWreathProduct | [
"instOfNatNat",
"PUnit",
"Nat",
"OfNat.ofNat",
"Eq",
"rfl",
"IteratedWreathProduct"
] | true |
EReal.neTopBotEquivReal._proof_3 | Mathlib.Data.EReal.Basic | [
"False",
"Real",
"congrArg",
"Compl.compl",
"EReal.coe_ne_top._simp_1",
"EReal",
"Membership.mem",
"Set.instSingletonSet",
"instTopEReal",
"Insert.insert",
"Bot.bot",
"Set.instCompl",
"EReal.coe_ne_bot._simp_1",
"Set.mem_compl_iff._simp_1",
"Set.instInsert",
"Set.mem_insert_iff._simp_1... | false |
TrivSqZeroExt | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"Prod"
] | true |
CategoryTheory.Functor.PullbackObjObj.mk.noConfusion | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.PullbackObjObj.mk",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"HEq.refl",
"CategoryTheory.IsPullback",
"CategoryTheory.Functor.PullbackObjObj.noConfusion",
"CategoryTheory.Functor.PullbackObjObj",
"Categ... | false |
LocalizedModule.lift | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"Module.End.instMonoid",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"Algebra.algebraMap",
"LocalizedModule",
"CommSemiring.toSemiring",
"Module.End.instSemiring",
"LocalizedModule.lift._proof_1",
"LocalizedModule.algebra'._proof_4",
"IsUnit",
"RingHom",
"Membership.mem",
... | true |
TypeName.recOn | Init.Dynamic | [
"TypeName",
"_private.Init.Dynamic.0.TypeName.mk'",
"TypeNameData",
"NonemptyType.type",
"TypeName.rec"
] | false |
SimplicialObject.opFunctorCompOpFunctorIso | Mathlib.AlgebraicTopology.SimplicialObject.Op | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.whiskeringLeftObjIdIso",
"CategoryTheory.Iso.op",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Functor.opHom",
"SimplexCategory.revCompRevIso... | true |
Int.not_le_of_gt | Init.Data.Int.Order | [
"Int",
"LE.le",
"Int.instLTInt",
"And",
"And.right",
"LT.lt",
"Iff.mp",
"Int.lt_iff_le_and_not_ge",
"Not",
"Int.instLEInt"
] | true |
compl_eq_iff_isCompl | Mathlib.Order.BooleanAlgebra.Basic | [
"Eq.mpr",
"BooleanAlgebra",
"congrArg",
"Compl.compl",
"BooleanAlgebra.toCompl",
"SemilatticeInf.toPartialOrder",
"BooleanAlgebra.toBoundedOrder",
"id",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"IsCompl.compl_eq",
"BooleanAlgebra.toBiheytingAlgebra",
"Iff",... | true |
SimpleGraph.preconnected_top._simp_1 | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph.preconnected_top",
"SimpleGraph.Preconnected",
"SimpleGraph",
"BooleanAlgebra.toTop",
"True",
"eq_true",
"SimpleGraph.completeAtomicBooleanAlgebra",
"Top.top",
"CompleteBooleanAlgebra.toBooleanAlgebra",
"Eq",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra"
] | false |
Lean.Meta.Grind.SavedState.casesOn | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.SavedState.rec",
"Lean.Meta.SavedState",
"Lean.Meta.Grind.State",
"Lean.Meta.Grind.SavedState.mk",
"Lean.Meta.Grind.SavedState"
] | false |
WithBot.unbot_le_iff._simp_2 | Mathlib.Order.WithBot | [
"WithBot.some",
"WithBot",
"Ne",
"Bot.bot",
"LE.le",
"LE",
"WithBot.unbot",
"WithBot.unbot_le_iff",
"propext",
"Eq",
"WithBot.instLE",
"WithBot.bot"
] | false |
_private.Mathlib.Data.List.Triplewise.0.List.triplewise_triple._simp_1_1 | Mathlib.Data.List.Triplewise | [
"List.triplewise_cons",
"List.Pairwise",
"List.cons",
"List",
"And",
"propext",
"List.Triplewise",
"Eq"
] | false |
Lean.Elab.Tactic.evalFocus | Lean.Elab.Tactic.BuiltinTactic | [
"Pure.pure",
"Unit.unit",
"Lean.Core.instMonadLiftIOCoreM",
"instMonadReaderOfReaderTOfMonad",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Elab.withInfoContext",
"Lean.Elab.Tactic.focus",
"Lean.Meta.State",
"instMonadLiftT",
"IO",
"Lean.Elab.Tactic.Context",
"Lean.Core.instMonadOptionsCoreM",
... | true |
CochainComplex.HomComplex.instAddCommGroupCohomologyClass._aux_17 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | [
"CochainComplex.HomComplex.coboundaries",
"QuotientAddGroup.Quotient.addGroup._aux_9",
"AddGroupWithOne.toAddMonoidWithOne",
"CochainComplex.HomComplex.instAddCommGroupCocycle",
"AddCancelMonoid.toAddRightCancelMonoid",
"QuotientAddGroup.Quotient.addCommGroup._proof_1",
"AddCommGroup.toAddGroup",
"Int... | false |
_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.getConvTactic.match_1 | Lean.Elab.DocString.Builtin | [
"Prod.mk",
"Unit",
"Lean.SyntaxNodeKind",
"Prod",
"Prod.casesOn"
] | false |
_private.Mathlib.Analysis.Calculus.LHopital.0.HasDerivAt.lhopital_zero_nhdsLT._proof_1_2 | Mathlib.Analysis.Calculus.LHopital | [
"NormedCommRing.toSeminormedCommRing",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"eq_false",
"Lean.Grind.iff_eq",
"Set.subset_def",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.denselyNormedField",
"IsTopo... | false |
Lean.Meta.Grind.Order.Struct | Lean.Meta.Tactic.Grind.Order.Types | [
"Lean.Meta.Grind.Order.Struct.mk"
] | true |
Subtype.forall' | Mathlib.Data.Subtype | [
"Subtype.forall",
"Subtype",
"Subtype.mk",
"Iff",
"Subtype.val",
"Iff.symm",
"Subtype.property"
] | true |
Lean.Parser.Command.openRenamingItem.parenthesizer | Lean.Parser.Command | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.checkColGt.parenthesizer",
"Lean.Parser.ident.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyP... | true |
CategoryTheory.ShortComplex.isoCyclesOfIsLimit_hom_iCycles | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso_hom_comp",
"CategoryTheory.Limits.KernelFork",
"CategoryTheory.Sh... | true |
Multiset.cons_inj_right._simp_1 | Mathlib.Data.Multiset.ZeroCons | [
"Multiset",
"Multiset.cons",
"propext",
"Multiset.cons_inj_right",
"Eq"
] | false |
_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum.isIrreducible_zeroLocus_iff_of_radical._simp_1_1 | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"IsPreirreducible",
"isPreirreducible_iff_isClosed_union_isClosed",
"Set.instUnion",
"HasSubset.Subset",
"IsClosed",
"TopologicalSpace",
"propext",
"Or",
"Union.union",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
Std.DHashMap.Raw.Const.getD_diff_of_not_mem_right | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.contains",
"congrArg",
"Std.DHashMap.Raw.contains_eq_false_iff_not_mem",
"Std.DHashMap.Raw",
"Membership.mem",
"Std.DHashMap.Raw.contains",
"Eq.mp",
"id",
"Std.DHashMap.Internal.Raw₀.... | true |
_private.Mathlib.Tactic.Translate.GuessName.0.Mathlib.Tactic.GuessName.fixAbbreviationAux.match_3.eq_2 | Mathlib.Tactic.Translate.GuessName | [
"String",
"List.cons",
"List",
"Unit",
"_private.Mathlib.Tactic.Translate.GuessName.0.Mathlib.Tactic.GuessName.fixAbbreviationAux.match_3",
"Eq.refl",
"Eq",
"List.nil"
] | true |
_private.Batteries.Tactic.Trans.0.Batteries.Tactic._aux_Batteries_Tactic_Trans___elabRules_Batteries_Tactic_tacticTrans____1.match_3 | Batteries.Tactic.Trans | [
"DoResultPR",
"Unit",
"DoResultPR.return",
"PUnit",
"DoResultPR.casesOn",
"DoResultPR.pure"
] | false |
ProperCone.innerDual_empty | Mathlib.Analysis.Convex.Cone.InnerDual | [
"ProperCone.mem_innerDual._simp_1",
"Real.instIsOrderedRing",
"InnerProductSpace.toNormedSpace",
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"ProperCone._proof_1",
"CompleteSpace",
"IsOrderedRing.toPosMulMono",
"IsOrderedRing.toZeroLEOneClass",
"Inner.inner",
"Set.mem_empty_iff_fals... | true |
WeierstrassCurve.b₂._proof_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
_private.Mathlib.Computability.Ackermann.0.ack.match_1.eq_2 | Mathlib.Computability.Ackermann | [
"instOfNatNat",
"ack.match_1",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
Submodule.rTensorOne' | Mathlib.LinearAlgebra.TensorProduct.Submodule | [
"Subalgebra.instSetLike",
"Submodule.mulMap",
"Submodule",
"Lattice.toSemilatticeSup",
"Submodule.mulMap'._proof_3",
"Submodule.rTensorOne'._proof_1",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"Submodule.addCommMonoid",
"TensorProduct.addCommMonoid",
"OrderBot.toBot",
"PartialOrd... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coloringTwoOfVert._proof_2 | Mathlib.Combinatorics.SimpleGraph.Acyclic | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"Int.instDiv",
"False",
"instHDiv",
"Lean.Grind.not_not",
"SimpleGraph.dist",
"HMul.hMul",
"Lean.Grind.nestedProof",
"_private.Mathlib.Combinatorics.SimpleGraph.Acyclic.0.SimpleGraph.IsTree.coloringTwoOfVert._proof_1",
"SimpleGraph.Adj",
"Int.Linear... | false |
Std.DHashMap.Internal.Raw₀.getD_insert | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"dite_congr",
"Std.DHashMap.Raw.WF.insert₀",
"Std.Internal.List.getValueCastD_insertEntry",
"Std.DHashMap.Internal.Raw.WF.out",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Std.DHashMap.Raw",
"cast",
"LawfulBEq",
"Std.DHashM... | true |
_private.Mathlib.Tactic.Positivity.Finset.0.Mathlib.Meta.Positivity.evalFinsetDens._proof_2 | Mathlib.Tactic.Positivity.Finset | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Level.instOfNat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Qq.QuotedDefEq.unsafeIntro",
"List.nil"
] | false |
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