name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Limits.isLimitEquivIsColimitOp | Mathlib.CategoryTheory.Limits.HasLimits | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.IsLimit.op",
"Opposite",
"CategoryTheory.Limits.IsLimit.subsingleton",
"CategoryTheory.Limits.isLimitOfOp",
"CategoryTheory.Limits.IsColimit",
"Equiv",
"CategoryTheory.Limits.IsLimit",
"Ca... | true |
_private.Mathlib.MeasureTheory.VectorMeasure.BoundedVariation.0.BoundedVariationOn.vectorMeasure_Iic._proof_1_2 | Mathlib.MeasureTheory.VectorMeasure.BoundedVariation | [
"AddCommGroup.toAddGroup",
"AddTorsor.nonempty",
"addGroupIsAddTorsor",
"Nonempty",
"NormedAddCommGroup.toAddCommGroup",
"NormedAddCommGroup"
] | false |
AddSemigroupIdeal.FG | Mathlib.Algebra.Group.Ideal | [
"AddSemigroupIdeal.closure",
"Set.Finite",
"Exists",
"And",
"AddSemigroupIdeal",
"Eq",
"Add",
"Set"
] | true |
Algebra.map_intTraceAux | Mathlib.RingTheory.IntegralClosure.IntegralRestrict | [
"Subalgebra.instSetLike",
"AlgHom.toLinearMap",
"Submodule",
"IsIntegralClosure",
"CommRing",
"LinearMap.restrictScalars",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsIntegralClosure.of_isIntegrallyClosed",
"IsPurelyInseparable.isIntegral",
"Semiring.toModule",
"IsScalarTower.right",
"... | true |
AugmentedSimplexCategory.inl' | Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Monoidal | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithInitial.of",
"AugmentedSimplexCategory.tensorObjOf",
"CategoryTheory.WithInitial.down",
"SimplexCategory",
"CategoryTheory.Category.toCategoryStruct",
"SimplexCategory.smallCategory",
"AugmentedSimplexCategory.inl"
] | true |
CategoryTheory.FreeBicategory.mk_left_unitor_hom | Mathlib.CategoryTheory.Bicategory.Free | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.FreeBicategory.categoryStruct",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.FreeBicategory.bicategory",
"CategoryTheory.Bicategory.leftUnitor",
"CategoryTheory.FreeBicategory.q... | true |
Finset.union_assoc | Mathlib.Data.Finset.Lattice.Basic | [
"Lattice.toSemilatticeSup",
"Finset.instUnion",
"Finset",
"sup_assoc",
"Finset.instLattice",
"Union.union",
"Eq",
"DecidableEq"
] | true |
Finset.set_biUnion_option_toFinset | Mathlib.Order.CompleteLattice.Finset | [
"Option.instMembership",
"Finset",
"Membership.mem",
"Option.toFinset",
"Finset.instSetLike",
"CompleteBooleanAlgebra.toCompleteLattice",
"Finset.iSup_option_toFinset",
"Eq",
"Set.iUnion",
"SetLike.instMembership",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"Set.instCompleteAtomi... | true |
Representation.character.eq_1 | Mathlib.RepresentationTheory.Character | [
"LinearMap.trace",
"Monoid",
"Representation",
"MonoidHom.instFunLike",
"Semiring.toModule",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Representation.character",
"Module.End.instSemiring",
"LinearMap.instFunLike",
"AddCommGroup",
"LinearMap.module",
... | true |
MeasureTheory.StronglyAdapted.isStoppingTime_crossing | Mathlib.Probability.Martingale.Upcrossing | [
"Eq.mpr",
"MeasureTheory.upperCrossingTime_succ_eq",
"MeasureTheory.IsStoppingTime",
"WithTop.charZero",
"WithTop.instPartialOrder",
"instClosedIicTopology",
"Real",
"DiscreteTopology.toAlexandrovDiscrete",
"Nat.recAux",
"Nat.instIsOrderedAddMonoid",
"Set.Ici",
"Real.lattice",
"_private.Math... | true |
ContinuousMap.instAddCommSemigroupOfContinuousAdd | Mathlib.Topology.ContinuousMap.Algebra | [
"ContinuousMap",
"ContinuousMap.instAddSemigroupOfContinuousAdd",
"AddCommSemigroup.mk",
"AddCommSemigroup.toAddSemigroup",
"TopologicalSpace",
"AddCommSemigroup.toAddCommMagma",
"AddCommSemigroup",
"ContinuousMap.instAddCommSemigroupOfContinuousAdd._proof_1",
"ContinuousAdd",
"AddCommMagma.toAdd"... | true |
PFunctor.MIntl.noConfusion | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"HEq.refl",
"PFunctor.MIntl.casesOn",
"PFunctor.Approx.AllAgree",
"PFunctor.Approx.CofixA",
"Nat",
"PFunctor.MIntl.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"PFunctor.MIntl",
"HEq",
"Eq"
] | false |
Submodule.reflection_apply | Mathlib.Analysis.InnerProductSpace.Projection.Reflection | [
"LinearIsometryEquiv.instEquivLike",
"InnerProductSpace.toNormedSpace",
"Submodule",
"instHSMul",
"Submodule.starProjection",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"HSub.hSub",
"AddMonoid.toNSMul",
"PseudoMetricSpace.toUniformSpace",
"AddCommGro... | true |
_private.Mathlib.LinearAlgebra.AffineSpace.Ceva.0.Affine.Triangle.prod_eq_prod_one_sub_of_mem_line_point_lineMap._proof_1_6 | Mathlib.LinearAlgebra.AffineSpace.Ceva | [
"instNeZeroNatHAdd_1",
"Lean.RArray.leaf",
"False",
"CommRing",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"Nat.le_refl",
"Lean.Grind.CommRing.Poly.add",
"Ring.toNonAssocRing",
"Lean.Grind.CommRing.Expr.var",
"CommSemiring.toSemiring",
"AddMonoid.... | false |
Std.HashMap.find?_toArray_eq_none_iff_contains_eq_false | Std.Data.HashMap.Lemmas | [
"Std.HashMap.contains",
"Std.HashMap",
"LawfulHashable",
"Prod.fst",
"Option.none",
"BEq.beq",
"Iff",
"EquivBEq",
"Bool",
"Std.DHashMap.Const.find?_toArray_eq_none_iff_contains_eq_false",
"Hashable",
"Std.HashMap.toArray",
"Prod",
"Std.HashMap.inner",
"Bool.false",
"BEq",
"Eq",
"Op... | true |
isDomain_iff_noZeroDivisors_and_nontrivial | Mathlib.Algebra.Ring.Basic | [
"Nontrivial",
"Eq.mpr",
"IsDomain",
"isDomain_iff_cancelMulZero_and_nontrivial",
"Ring.toNonAssocRing",
"congrArg",
"Iff.rfl",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"IsCancelMulZero",
"NonAssocRing.toNonUnitalNonAssocRing",
"in... | true |
EStateM.Backtrackable.noConfusionType | Init.Prelude | [
"EStateM.Backtrackable.casesOn",
"HEq",
"EStateM.Backtrackable"
] | false |
ProbabilityTheory.cdf_le_one | Mathlib.Probability.CDF | [
"Unit.unit",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"PseudoMetricSpace.toUniformSpace",
"StieltjesFunction.toFun",
"LE.le",
"MeasureTheory.Measure.dirac",
"Real.instOne",
"Unit",
"Real.measurableSpace",
"MeasureTheory.Measure.prod",
"ProbabilityTheory.condCDF_le_one",
"PUnit.instM... | true |
CategoryTheory.AddGrpObj.neg_comp_assoc | Mathlib.CategoryTheory.Monoidal.Cartesian.Grp | [
"AddGroup.toSubtractionMonoid",
"CategoryTheory.Category.assoc",
"NegZeroClass.toNeg",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.IsAddMonHom",
"Eq.mp",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.... | true |
ProofWidgets.Util.joinArrays | ProofWidgets.Util | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Monad.toApplicative",
"Lean.SourceInfo",
"Array.mkArray0",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.TSyntax.raw",
"instOfNatNat",
"Lean.Syntax.Term",
"Applicative.toPure",
"Lean.MonadQu... | true |
Finsupp.comapDistribMulAction._proof_2 | Mathlib.Data.Finsupp.SMul | [
"Finsupp.instFunLike",
"Monoid",
"instHSMul",
"Finsupp.ext",
"AddMonoid.toAddSemigroup",
"congrArg",
"Finsupp.mapDomain",
"AddMonoid.toAddZeroClass",
"Finsupp.instAddMonoid",
"AddZeroClass.toAddZero",
"id",
"AddCommMonoid",
"Finsupp.comapMulAction",
"AddZero.toZero",
"instHAdd",
"Finsu... | false |
Set.Icc.instMonoidWithZero._proof_2 | Mathlib.Algebra.Order.Interval.Set.Instances | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semigroup.toMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"IsOrderedRing",
"PartialOrder.toPreorder",
"Semigroup.mk",
"MulOneClass.one_mul",
"Membership.mem",
"PartialOrder",
"Set.Icc.coe_mul",
"Set.Elem",
"Subtype",
"AddCommMonoidWithOne.toAddMonoi... | false |
Function.Injective.divInvMonoid._proof_8 | Mathlib.Algebra.Group.InjSurj | [
"DivInvMonoid.toInv",
"Inv",
"Pow",
"Function.Injective.divInvMonoid._proof_4",
"DivInvMonoid.toZPow",
"Int",
"Nat.cast",
"DivInvMonoid",
"Inv.inv",
"HPow.hPow",
"Nat",
"instNatCastInt",
"instHPow",
"Function.Injective",
"Int.negSucc",
"Nat.succ",
"Eq"
] | false |
_private.Lean.Compiler.LCNF.Specialize.0.Lean.Compiler.LCNF.Specialize.visitFunDecl | Lean.Compiler.LCNF.Specialize | [
"Inhabited.default",
"instInhabitedOfMonad",
"_private.Lean.Compiler.LCNF.Specialize.0.Lean.Compiler.LCNF.Specialize.SpecializeM",
"_private.Lean.Compiler.LCNF.Specialize.0.Lean.Compiler.LCNF.Specialize.State",
"IO.RealWorld",
"Lean.Compiler.LCNF.FunDecl",
"Lean.Compiler.LCNF.Purity.pure",
"StateRefT'... | true |
Sigma.fst_injective | Mathlib.Data.Sigma.Basic | [
"Sigma.fst",
"congr_arg",
"Eq.ndrec",
"Subsingleton",
"Sigma.mk",
"Function.Injective",
"Sigma.casesOn",
"Subsingleton.elim",
"Eq",
"Sigma"
] | true |
cfcₙ_zero | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Nontrivial",
"cfcₙ",
"Eq.mpr",
"MonoidHom.instFunLike",
"NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass",
"Semiring.toModule",
"instSMulOfMul",
"Continuous.continuousOn",
"outParam",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toD... | true |
_private.Lean.Compiler.LCNF.Specialize.0.Lean.Compiler.LCNF.Specialize.getRemainingArgs.match_1 | Lean.Compiler.LCNF.Specialize | [
"Unit.unit",
"Lean.Compiler.LCNF.SpecParamInfo.other",
"Lean.Compiler.LCNF.SpecParamInfo",
"Nat.hasNotBit",
"Unit",
"Lean.Compiler.LCNF.SpecParamInfo.ctorIdx",
"_private.Lean.Compiler.LCNF.Specialize.0.Lean.Compiler.LCNF.Specialize.getRemainingArgs._sparseCasesOn_1"
] | false |
Lean.Grind.GrobnerConfig.noConfusion | Init.Grind.Config | [
"Lean.Grind.GrobnerConfig.casesOn",
"Lean.Grind.NoopConfig",
"Eq.ndrec",
"Lean.Grind.GrobnerConfig",
"Eq.refl",
"Lean.Grind.GrobnerConfig.noConfusionType",
"Eq"
] | false |
CategoryTheory.Bimon.mk'X_X | Mathlib.CategoryTheory.Monoidal.Bimon_ | [
"CategoryTheory.MonoidalCategory",
"CategoryTheory.BimonObj",
"CategoryTheory.Bimon.mk'X",
"CategoryTheory.BraidedCategory",
"CategoryTheory.Mon.X",
"Eq.refl",
"Eq",
"CategoryTheory.Category"
] | true |
Lean.Meta.Grind.NormalizePattern.State.bvarsFound | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"Std.HashSet",
"instHashableNat",
"instBEqOfDecidableEq",
"Nat",
"instDecidableEqNat",
"Lean.Meta.Grind.NormalizePattern.State"
] | true |
_private.Mathlib.RingTheory.Unramified.LocalRing.0.Localization.exists_awayMap_bijective_of_localRingHom_bijective._simp_1_10 | Mathlib.RingTheory.Unramified.LocalRing | [
"instHSMul",
"HMul.hMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toSMul",
"instDistribOfSemiring",
"CommSemiring",
"RingHom.instFunLike",
"Distrib.toMul",
"Semiring",
"HSMul.hSMul",
"Algebra.smul_def",
"Eq.symm",
"Semiring.toNonAssocSemiring",
... | false |
Plausible.TotalFunction.reprAux | Plausible.Functions | [
"String.join",
"String",
"List.map",
"HSub.hSub",
"instToStringFormat",
"Array.qsort",
"String.decidableLT",
"instSubNat",
"Sigma.fst",
"instOfNatNat",
"ToString.toString",
"Array.toList",
"List.toArray",
"instAppendString",
"instHAppendOfAppend",
"List",
"instHSub",
"String.instLT... | true |
IsPredArchimedean.findAtom_le._simp_1 | Mathlib.Order.SuccPred.Tree | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"PartialOrder",
"LE.le",
"IsPredArchimedean",
"IsPredArchimedean.findAtom",
"True",
"IsPredArchimedean.findAtom_le",
"eq_true",
"PredOrder",
"Eq",
"DecidableEq"
] | false |
IsFreeGroup.definition._proof_1._@.Mathlib.GroupTheory.FreeGroup.IsFreeGroup.3798820966._hygCtx._hyg.2 | Mathlib.GroupTheory.FreeGroup.IsFreeGroup | [
"Exists.choose_spec",
"Group",
"IsFreeGroup.nonempty_basis",
"FreeGroupBasis",
"Nonempty",
"Exists.choose",
"IsFreeGroup"
] | false |
CategoryTheory.OrthogonalReflection.isLocal_reflectionObj | Mathlib.CategoryTheory.Presentable.OrthogonalReflection | [
"le_max_right",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.OrthogonalReflection.D₁",
"CategoryTheory.OrthogonalReflection.reflection",
"CategoryTheory.Functor",
"CategoryTheory.OrthogonalReflection.D₁.obj₂",
"Lattice.toSemilatticeSup",
"CategoryTh... | true |
Lean.Internal.isStage0 | Init.Meta.Defs | [
"Inhabited.default",
"instInhabitedBool",
"Unit",
"Bool"
] | true |
AdjoinRoot.isAlgebraic_root | Mathlib.RingTheory.AdjoinRoot | [
"CommRing",
"AdjoinRoot",
"IsAlgebraic",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Algebra.id",
"Ne",
"Polynomial",
"And",
"AdjoinRoot.instAlgebra",
"CommRing.toCommSemiring",
"AdjoinRoot.eval₂_root",
"Polynomial.semiring",
"And.intro",
"A... | true |
ProofWidgets.RpcEncodablePacket.mk._flat_ctor._@.ProofWidgets.Component.Basic.2987839534._hygCtx._hyg.1 | ProofWidgets.Component.Basic | [
"ProofWidgets.RpcEncodablePacket._@.ProofWidgets.Component.Basic.2987839534._hygCtx._hyg.1",
"Lean.Json",
"ProofWidgets.RpcEncodablePacket.mk._@.ProofWidgets.Component.Basic.2987839534._hygCtx._hyg.1"
] | false |
CompactlySupportedContinuousMap.pullback_addMonoidHom | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"R1Space",
"CompactlySupportedContinuousMap",
"ContinuousMap.mk",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddZeroClass.toAddZero",
"CompactlySupportedContinuousMap.pullback_addMonoidHom._proof_1",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"... | true |
_private.Std.Data.ExtDHashMap.Lemmas.0.Std.ExtDHashMap.Const.alter_eq_empty_iff_erase_eq_empty._simp_1_2 | Std.Data.ExtDHashMap.Lemmas | [
"Option.isNone",
"Option.isNone_iff_eq_none",
"Bool.true",
"Option.none",
"propext",
"Bool",
"Eq.symm",
"Eq",
"Option"
] | false |
Lean.PrettyPrinter.Unexpander | Init.Prelude | [
"Lean.PrettyPrinter.UnexpandM",
"Lean.Syntax"
] | true |
lt_mul_iff_one_lt_right' | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"mul_lt_mul_iff_left",
"congrArg",
"Iff.rfl",
"id",
"MulOne.toMul",
"MulLeftStrictMono",
"MulOneClass.toMulOne",
"Iff",
"LT.lt",
"Iff.trans",
"One.toOfNat1",
"MulLeftReflectLT",
"mul_one",
"MulOneClass",
"OfNat.ofNat",
"Eq",
"LT",
"instH... | true |
Std.Net.instDecidableEqSocketAddressV6.decEq._proof_4 | Std.Net.Addr | [
"False",
"Std.Net.IPv6Addr",
"Std.Net.SocketAddressV6.mk",
"Std.Net.SocketAddressV6.mk.noConfusion",
"UInt16",
"Std.Net.SocketAddressV6",
"Eq",
"Not"
] | false |
Std.TreeSet.Raw.mk.injEq | Std.Data.TreeSet.Raw.Basic | [
"Std.TreeSet.Raw.mk",
"Eq.propIntro",
"Std.TreeSet.Raw.mk.inj",
"Ordering",
"Std.TreeSet.Raw._auto_1",
"autoParam",
"Std.TreeMap.Raw",
"Std.TreeSet.Raw",
"Unit",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
groupCohomology.cocyclesMap._proof_1 | Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | [
"CommRing",
"Nat.instOne",
"ModuleCat",
"CommSemiring.toSemiring",
"CategoryTheory.ShortComplex.HasHomology",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Group",
"Nat.instAddCancelCommMonoid",
"DivInvMonoid.toMonoid",
"groupCohomology.inhomogeneousCochain... | false |
SimpleGraph.Preconnected | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph",
"SimpleGraph.Reachable"
] | true |
EReal.instPosMulReflectLT | Mathlib.Data.EReal.Inv | [
"EReal.instPosMulMono",
"PartialOrder.toPreorder",
"EReal",
"instZeroEReal",
"instLinearOrderEReal",
"PosMulReflectLT",
"PosMulMono.toPosMulReflectLT",
"instPartialOrderEReal",
"EReal.instMul"
] | true |
_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_count_eq_one._proof_1_6 | Mathlib.Data.List.Nodup | [
"Lean.Grind.eq_false_of_not_eq_true",
"congrArg",
"Eq.mp",
"List.count_eq_length_filter",
"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_count_eq_one._proof_1_5",
"instOfNatNat",
"LE.le",
"instLENat",
"_private.Mathlib.Data.List.Nodup.0.List.nodup_iff_count_eq_one._proof_1_3",
"GetElem.getElem... | false |
RatFunc.mk.congr_simp | Mathlib.FieldTheory.RatFunc.Defs | [
"IsDomain",
"CommRing",
"CommSemiring.toSemiring",
"Eq.rec",
"Polynomial",
"CommRing.toCommSemiring",
"RatFunc",
"RatFunc.mk",
"Eq.refl",
"Eq"
] | true |
DifferentiableOn.fun_sub | Mathlib.Analysis.Calculus.FDeriv.Add | [
"NormedSpace",
"DifferentiableOn.sub",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"id",
"SubNegMonoid.toSub",
"instHSub",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"DifferentiableOn",
"NontriviallyNormedF... | true |
_private.Std.Tactic.BVDecide.Normalize.BitVec.0.Std.Tactic.BVDecide.Normalize.BitVec.signExtend_elim._proof_1 | Std.Tactic.BVDecide.Normalize.BitVec | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Om... | false |
AffineEquiv.toAffineMap | Mathlib.LinearAlgebra.AffineSpace.AffineEquiv | [
"AffineEquiv.linear",
"AffineMap.mk",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Equiv.toFun",
"AffineMap",
"LinearEquiv.toLinearMap",
"AddTorsor",
"AffineEquiv.toEquiv",
"AffineEquiv.toAffineMap._proof_1",
"Module",
"AffineEquiv.map_vadd'",
"AffineEquiv",
... | true |
_private.Lean.Meta.Sym.Simp.App.0.Lean.Meta.Sym.Simp.propagateOverApplied.visit._f | Lean.Meta.Sym.Simp.App | [
"Pure.pure",
"ReaderT",
"Lean.Meta.Sym.Simp.MethodsRef",
"_private.Lean.Meta.Sym.Simp.App.0.Lean.Meta.Sym.Simp.mkCongrFun",
"instMonadLiftT",
"HSub.hSub",
"Lean.Meta.Sym.Context",
"panicWithPosWithDecl",
"ReaderT.instMonad",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBoo... | false |
HopfAlgCat.MonoidalCategory.inducingFunctorData._proof_3 | Mathlib.Algebra.Category.HopfAlgCat.Monoidal | [
"BialgCat.Hom.toBialgHom",
"BialgCat.instBialgebra",
"BialgCat.category",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"HopfAlgebraStruct.toBialgebra",
"BialgCat",
"CategoryTheory.CategoryStruct.toQuiver",
"Ring.toNonAssocRing",
"Quiver.Hom",
"Bialgebra.toCoalgebra",
"HopfAlgCat.concreteCategory... | false |
HomologicalComplex.Hom.mk.noConfusion | Mathlib.Algebra.Homology.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.Hom.mk",
"HEq.refl",
"HomologicalComplex",
"id",
"ComplexShape",
"autoParam",
"heq_of_eq",
"HomologicalComplex.Hom",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"HEq",... | false |
Std.ExtDTreeMap.Const.getThenInsertIfNew?_fst | Std.Data.ExtDTreeMap.Lemmas | [
"Std.DTreeMap",
"Ordering",
"Std.TransCmp",
"Prod.fst",
"Std.ExtDTreeMap.Const.get?",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Std.DTreeMap.Const.getThenInsertIfNew?_fst",
"Std.ExtDTreeMap.Const.getThenInsertIfNew?",
"Eq",
"Option"
] | true |
CategoryTheory.CoreSmallCategoryOfSet.functor._proof_1 | Mathlib.CategoryTheory.SmallRepresentatives | [
"Eq.mpr",
"CategoryTheory.SmallCategoryOfSet.id_def",
"CategoryTheory.CoreSmallCategoryOfSet.objEquiv",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.SmallCategoryOfSet.obj",
"CategoryTheory.CategoryStruct.id",
... | false |
_private.Mathlib.AlgebraicTopology.SimplexCategory.Basic.0.SimplexCategory.δ_comp_σ_self._simp_1_1 | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"Fin.val",
"Fin.lt_def",
"Nat",
"LT.lt",
"instLTFin",
"propext",
"instLTNat",
"Fin",
"Eq"
] | false |
_private.Mathlib.Data.WSeq.Basic.0.Stream'.WSeq.destruct.match_1.eq_1 | Mathlib.Data.WSeq.Basic | [
"Unit.unit",
"Stream'.Seq",
"Option.some",
"Prod.mk",
"Option.none",
"Unit",
"Stream'.WSeq.destruct.match_1",
"Stream'.Seq1",
"Eq.refl",
"Eq",
"Option"
] | true |
MulDistribMulAction | Mathlib.Algebra.Group.Action.Defs | [
"Monoid",
"MulDistribMulAction.mk"
] | true |
cfcₙL.congr_simp | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Integral | [
"Nontrivial",
"Semiring.toModule",
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"quasispectrum.instZero",
"IsTopologicalSemiring",
"IsScalarTower",
"ContinuousStar",
"SeparatelyContinuousMul.to_continuousSMul",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing... | true |
_private.Mathlib.Algebra.Lie.Ideal.0.LieHom.isIdealMorphism_iff._simp_1_6 | Mathlib.Algebra.Lie.Ideal | [
"Submodule.exists_lieSubmodule_coe_eq_iff",
"Submodule",
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Bracket.bracket",
"LieSubmodule.toSubmodule",
"LieSubmodule",
"Membership.mem",
"Exists",
"AddCommGroup",
"LieRingModule.toBracket",
"LieRing",
"CommRing.toCommS... | false |
CategoryTheory.InducedWideCategory.Hom._sizeOf_inst | Mathlib.CategoryTheory.Widesubcategory | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.InducedWideCategory.Hom",
"CategoryTheory.InducedWideCategory.Hom._sizeOf_1",
"CategoryTheory.InducedWideCategory",
"SizeOf.mk",
"CategoryTheory.Category.toCategoryStruct",
"SizeOf",
"Categor... | false |
Lean.Compiler.LCNF.Simp.CtorInfo | Lean.Compiler.LCNF.Simp.DiscrM | [
"Lean.Compiler.LCNF.Simp.CtorInfo.natVal",
"Lean.Compiler.LCNF.Simp.CtorInfo.ctor"
] | true |
Lean.Elab.Term.exceptionToSorry | Lean.Elab.Term.TermElabM | [
"Lean.Core.instMonadLiftIOCoreM",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Meta.State",
"instMonadLiftT",
"IO",
"Lean.Core.instMonadOptionsCoreM",
"Lean.instMonadOptionsOfMonadLift",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"ReaderT.instMonadLift",
"_private.Lean.Elab.Term.TermElabM.0... | true |
FirstOrder.Language.Term.func | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.Term",
"FirstOrder.Language.Term.func",
"Nat",
"FirstOrder.Language.Functions",
"FirstOrder.Language",
"Fin"
] | true |
Std.DHashMap.Internal.Raw₀.get_insertMany_list_of_contains_eq_false | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Std.Internal.List.containsKey_of_perm",
"Std.DHashMap.Internal.Raw₀.get_eq_getValueCast",
"Std.Internal.List.insertList",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw.WF.out",
"instLawfulHashableOfLawfulBEq",
... | true |
LinearMap.iterateMapComap_le_succ | Mathlib.Algebra.Module.Submodule.IterateMapComap | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"le_refl",
"Nat.recAux",
"Trans.trans",
"Submodule.comap_mono",
"congrArg",
"Function.iterate_succ'",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.comp",
"id",
"Submodule.instPartialOrder",
"instOfNatNat",
"LE.le",
"Submodule.l... | true |
MonoidAlgebra.unique | Mathlib.Algebra.MonoidAlgebra.Defs | [
"Unique.mk",
"MonoidAlgebra.unique._proof_1",
"Unique",
"MonoidAlgebra.inhabited",
"MonoidAlgebra",
"Semiring",
"Subsingleton"
] | true |
_private.Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs.0.ComputeAsymptotics.MultiseriesExpansion.Multiseries.Sorted.cons._proof_1_1 | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | [
"Lean.Grind.eq_false_of_not_eq_true",
"ComputeAsymptotics.MultiseriesExpansion.Multiseries.instMembershipProdReal",
"ComputeAsymptotics.Basis",
"False",
"Real",
"Lean.Grind.not_and",
"Classical.byContradiction",
"Membership.mem",
"Eq.mp",
"id",
"Lean.Grind.or_eq_of_eq_false_right",
"Prod.mk",
... | false |
Lean.Lsp.instToJsonLeanModule | Lean.Data.Lsp.Extra | [
"Lean.Lsp.instToJsonLeanModule.toJson",
"Lean.ToJson.mk",
"Lean.ToJson",
"Lean.Lsp.LeanModule"
] | true |
HomologicalComplex.Acyclic | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.ExactAt",
"HomologicalComplex",
"ComplexShape",
"CategoryTheory.Category"
] | true |
Int.Linear.instBEqExpr.beq._f | Init.Data.Int.Linear | [
"Int.Linear.Expr.mulR",
"Int.instDecidableEq",
"Int.Linear.Expr.add",
"Bool.and",
"Int",
"Int.Linear.Var",
"instBEqOfDecidableEq",
"BEq.beq",
"Int.Linear.Expr",
"Int.Linear.Expr.below",
"Int.Linear.Expr.mulL",
"Bool",
"Int.Linear.Expr.var",
"instDecidableEqNat",
"Int.Linear.Expr.neg",
... | false |
iInf₂_eq_top | Mathlib.Order.CompleteLattice.Basic | [
"iInf",
"iInf_eq_top",
"CompleteLattice.toLattice",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toBoundedOrder",
"iff_self",
"CompleteLattice.toCompleteSemilatticeInf",
"Iff",
"OrderTop.toTop",
"BoundedOrder.toOrderTop",
"True",... | true |
HasFPowerSeriesAt.tendsto_partialSum_prod_of_comp | Mathlib.Analysis.Analytic.Inverse | [
"NNReal.instTopologicalSpace",
"Filter.instMembership",
"NNReal.summable_coe",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"FormalMultilinearSeries.comp_partialSum",
"Real.instIsOrderedRing",
"Norm.norm",
"eq_sub_iff_add_eq'",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedC... | true |
_private.Mathlib.Analysis.Calculus.IteratedDeriv.Defs.0.contDiff_nat_succ_iff_contDiff_one_iteratedDeriv._simp_1_2 | Mathlib.Analysis.Calculus.IteratedDeriv.Defs | [
"Differentiable",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Continuous",
"Semiring.toModule",
"NormedRing.toRing",
"instAddMonoidWithOneENat",
"NormedSpace",
"deriv",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"ContDiff",
... | false |
CategoryTheory.MonoidalCategory.MonoidalRightAction.id_actionHomLeft_assoc | Mathlib.CategoryTheory.Monoidal.Action.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionObj",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"id",
"CategoryTheory.MonoidalCategory.MonoidalRightAction.toMonoidalRightActionS... | true |
Lean.Parser.termParser.parenthesizer | Lean.Parser.Extra | [
"Lean.PrettyPrinter.Parenthesizer.categoryParser.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Nat",
"optParam",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
_private.Mathlib.Analysis.Analytic.Order.0.AnalyticOnNhd.isClopen_setOf_analyticOrderAt_eq_top._proof_1_2 | Mathlib.Analysis.Analytic.Order | [
"NormedCommRing.toSeminormedCommRing",
"of_eq_false",
"False",
"forall_not_of_not_exists",
"Lean.Grind.nestedProof",
"Lean.Grind.not_and",
"eq_false",
"Lean.Grind.iff_eq",
"Set.subset_def",
"congrArg",
"Classical.byContradiction",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Subtype.cases... | false |
IsCompact.cofinite_inf_le_codiscreteWithin | Mathlib.Topology.DiscreteSubset | [
"Filter.instMembership",
"Eq.mpr",
"congrArg",
"Compl.compl",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Set.Finite",
"Membership.mem",
"id",
"LE.le",
"Filter.instInf",
"Set.instCompl",
"TopologicalSpace",
"funext",
"And",
"Filter.codiscreteWithin",
"Filter.principal",
... | true |
_private.Mathlib.Data.Finset.Union.0.Finset.coe_disjiUnion._simp_1_1 | Mathlib.Data.Finset.Union | [
"Membership.mem",
"Iff",
"propext",
"Set.ext_iff",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Batteries.Tactic.SqueezeScope.0.Batteries.Tactic._aux_Batteries_Tactic_SqueezeScope___elabRules__private_Batteries_Tactic_SqueezeScope_0_Batteries_Tactic_squeezeScopeIn_1._sparseCasesOn_5 | Batteries.Tactic.SqueezeScope | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Lean.Meta.trySubstVar | Lean.Meta.Tactic.Subst | [
"Pure.pure",
"Lean.Meta.State",
"Option.getD",
"Lean.MVarId",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.FVarId",
"Applicative.toPure",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"Monad.toBind",
"Bind.bind",
"Lean.Core.instMonadCoreM",
"ReaderT.i... | true |
hasFDerivAt_ringInverse | Mathlib.Analysis.Calculus.FDeriv.Mul | [
"HasFDerivAt",
"NormedCommRing.toNormedRing",
"Norm.norm",
"Units.val",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"Real",
"Algebra.to_smulCommClass",
"Nat.instIsOrderedAddMonoid",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
... | true |
instT1SpaceCofiniteTopology | Mathlib.Topology.Separation.Basic | [
"Iff.mpr",
"TopologicalSpace.cofinite",
"congrArg",
"Set.univ",
"Set.Finite",
"Set.instSingletonSet",
"Set.finite_singleton._simp_1",
"T1Space.mk",
"IsClosed",
"CofiniteTopology.isClosed_iff",
"True",
"of_eq_true",
"Or",
"WithTopology.instTopologicalSpace",
"T1Space",
"Singleton.single... | true |
Lean.Server.RpcProcedure.noConfusionType | Lean.Server.Rpc.RequestHandling | [
"Lean.Json",
"Lean.Server.RpcProcedure",
"UInt64",
"Lean.Server.RequestM",
"Lean.Server.RpcProcedure.casesOn",
"Lean.Server.RequestTask",
"Eq"
] | false |
PiTensorProduct.toDualContinuousMultilinearMap._proof_6 | Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm | [
"SeminormedAddCommGroup",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"Field.toSemifield",
"Field.toCommRing",
"smulCommClass_self",
"Semifield.toDivisionSemiring",
"CommMonoid.toMonoid",
"SeminormedAddCommGroup.toAddCommGroup",
"Monoid.toSemig... | false |
CategoryTheory.Functor.LaxMonoidal.mk.congr_simp | Mathlib.CategoryTheory.Monoidal.Braided.Transport | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"Eq.rec",
"CategoryTheory... | true |
CategoryTheory.ProjectiveResolution.extMk._proof_1 | Mathlib.CategoryTheory.Abelian.Projective.Ext | [
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Int.instNegInt",
"Int",
"Nat.cast",
"AddZero.toZero",
"instHAdd",
"AddGroup.toSubNegMonoid",
"neg_add_cancel",
"instOfNat",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Int.instAdd",
"Int.instAddGroup",
"... | false |
AlgebraicGeometry.Scheme.IsLocallyDirected.ι_eq_ι_iff | Mathlib.AlgebraicGeometry.Gluing | [
"AlgebraicGeometry.Scheme.GlueData.ι",
"CategoryTheory.GlueData.t",
"AlgebraicGeometry.PresheafedSpace.Hom",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Equiv.instEquivLike",
... | true |
AddHomClass.map_add | Mathlib.Algebra.Group.Hom.Defs | [
"outParam",
"instHAdd",
"HAdd.hAdd",
"AddHomClass",
"Eq",
"DFunLike.coe",
"Add",
"FunLike"
] | true |
_private.Mathlib.Tactic.Widget.Conv.0.Mathlib.Tactic.Conv.Path.ofSubExprPosArray.appT._sparseCasesOn_1 | Mathlib.Tactic.Widget.Conv | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
CategoryTheory.Pseudofunctor.Grothendieck.recOn | Mathlib.CategoryTheory.Bicategory.Grothendieck | [
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Pseudofunctor.Grothendieck",
"CategoryTheory.Pseudofunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Pseudofunc... | false |
LinearMap.sq_singularValues_fin | Mathlib.Analysis.InnerProductSpace.SingularValues | [
"Finsupp.instFunLike",
"InnerProductSpace.toNormedSpace",
"LinearMap.isPositive_adjoint_comp_self",
"Real",
"LinearMap.IsPositive.nonneg_eigenvalues",
"Real.instZero",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedDivisionRing.toDivisionRing",
"NormedField.toField",
... | true |
SimpleGraph.egirth_eq_top._simp_1 | Mathlib.Combinatorics.SimpleGraph.Girth | [
"instTopENat",
"SimpleGraph.IsAcyclic",
"SimpleGraph.egirth_eq_top",
"SimpleGraph",
"ENat",
"propext",
"SimpleGraph.egirth",
"Top.top",
"Eq"
] | false |
CategoryTheory.MorphismProperty.FunctorialFactorizationData.functorCategory._proof_3 | Mathlib.CategoryTheory.MorphismProperty.Factorization | [
"CategoryTheory.MorphismProperty.FunctorialFactorizationData",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.MorphismProperty.FunctorialFactorizationData.Z",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"CategoryTheory.instC... | false |
Int.toNat_add_nat | Init.Data.Int.Order | [
"Exists",
"Int",
"LE.le",
"Nat.cast",
"Int.eq_ofNat_of_zero_le",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Nat",
"_private.Init.Data.Int.Order.0.Int.toNat_add_nat.match_1_1",
"Int.instAdd",
"instAddNat",
"Int.toNat",
"instNatCastInt",
"OfNat.ofNat",
"Eq",
"rfl",
"Int.instLEInt"
] | true |
BoundedContinuousFunction.mkOfCompact._proof_1 | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"ContinuousMap.continuous",
"Real.instLE",
"Real",
"PseudoMetricSpace.toBornology",
"IsCompact.isBounded",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"Exists",
"Bornology.IsBounded",
"LE.le",
"CompactSpace",
"isCompact_range",
"TopologicalSpace",
"PseudoMetricSpace",
"Iff.mp",
... | false |
ClosedSubgroup.ext_iff | Mathlib.Topology.Algebra.Group.ClosedSubgroup | [
"ClosedSubgroup.ext",
"ClosedSubgroup.toSubgroup",
"Monoid.toMulOneClass",
"HEq.refl",
"Submonoid.toSubsemigroup",
"Group",
"Eq.casesOn",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"TopologicalSpace",
"MulOneClass.toMulOne",
"Iff",
"Iff.intro",
"Subsemigroup.carrier... | true |
Complex.addGroupWithOne._proof_7 | Mathlib.Data.Complex.Basic | [
"SubNegMonoid.zsmul_succ'",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddGroup",
"Int",
"Nat.cast",
"Complex.addCommGroup",
"SubNegMonoid.zsmul",
"instHAdd",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"Nat",
"instNatCastInt",
"SubNegMonoid.toAddMonoid",
"Complex",
... | false |
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