name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
Polynomial.card_roots_le_map | Mathlib.Algebra.Polynomial.Roots | [
"Eq.mpr",
"IsDomain",
"CommRing",
"Polynomial.roots",
"Multiset.map",
"congrArg",
"CommSemiring.toSemiring",
"Multiset.card_le_card",
"RingHom",
"id",
"Ne",
"Polynomial.map_roots_le",
"LE.le",
"instLENat",
"Polynomial",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"Nat",
"Ze... | true |
Lean.Compiler.LCNF.CacheAuxDeclResult.ctorElim | Lean.Compiler.LCNF.AuxDeclCache | [
"Lean.Compiler.LCNF.CacheAuxDeclResult.new",
"Lean.Compiler.LCNF.CacheAuxDeclResult.ctorIdx",
"Lean.Compiler.LCNF.CacheAuxDeclResult.ctorElimType",
"Lean.Compiler.LCNF.CacheAuxDeclResult.alreadyCached",
"Lean.Compiler.LCNF.CacheAuxDeclResult",
"Nat",
"Eq.ndrec",
"Lean.Name",
"PULift.down",
"Eq",
... | false |
mul_invOf_cancel_right | Mathlib.Algebra.Group.Invertible.Defs | [
"Monoid",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"Invertible.invOf",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Invertible",
"Eq",
"mul_invOf_cancel_right'",
"instHMul"
] | true |
CategoryTheory.Limits.pullbackPullbackRightIsPullback._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.pullbackPullbackRightIsPullback._proof_3",
"CategoryTheory.Limits.pullback.lift",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.PullbackCone.pasteVert._proof_1",
"Ca... | false |
MonoidHom.coe_mrangeRestrict | Mathlib.Algebra.Group.Submonoid.Operations | [
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"MonoidHom",
"Membership.mem",
"Subtype",
"Submonoid.toMulOneClass",
"MulOneClass.toMulOne",
"MonoidHom.mrange",
"MonoidHom.mrangeRestrict",
"Submonoid.instSetLike",
"MulOneClass",
"Subtype.val",
"Eq",
"DFunLike.coe",
"SetLike.inst... | true |
Std.DTreeMap.Internal.Impl.ExplorationStep.casesOn | Std.Data.DTreeMap.Internal.Model | [
"Ordering.gt",
"Ord",
"Std.DTreeMap.Internal.Impl.ExplorationStep.gt",
"Std.DTreeMap.Internal.Impl.ExplorationStep.lt",
"Ordering",
"Std.DTreeMap.Internal.Impl.ExplorationStep.eq",
"Std.DTreeMap.Internal.Impl.ExplorationStep",
"Std.DTreeMap.Internal.Cell",
"List",
"Ordering.lt",
"Std.DTreeMap.In... | false |
FreeAlgebra.instNoZeroDivisors | Mathlib.Algebra.FreeAlgebra | [
"MonoidAlgebra.semiring",
"CancelMonoid.toRightCancelMonoid",
"FreeMonoid",
"FreeAlgebra.instSemiring",
"FreeAlgebra.instAlgebra",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"FreeMonoid.instCancelMonoid",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"FreeAlgebra.instMul",
"Algebra.id",
... | true |
CategoryTheory.Comma.mapLeftId | Mathlib.CategoryTheory.Comma.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Comma.mapLeftId._proof_2",
"CategoryTheory.Comma.isoMk",
"CategoryTheory.Iso.refl",
"CategoryTheo... | true |
Batteries.RBNode.balLeft.match_4.congr_eq_1 | Batteries.Data.RBMap.WF | [
"Batteries.RBNode",
"Batteries.RBNode.balLeft.match_4",
"id",
"Nat.hasNotBit",
"Batteries.RBNode.ctorIdx",
"Batteries.RBColor.ctorIdx",
"heq_of_eq",
"Batteries.RBColor.red",
"Batteries.RBNode.balance1._sparseCasesOn_2",
"Batteries.RBColor",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Batteries.RBNode.b... | true |
_private.Mathlib.Combinatorics.Enumerative.Catalan.0.gosperCatalan | Mathlib.Combinatorics.Enumerative.Catalan | [
"Rat.instOfNat",
"Rat.instSub",
"Rat.instMul",
"instHDiv",
"HMul.hMul",
"Rat",
"HSub.hSub",
"HDiv.hDiv",
"instSubNat",
"Nat.centralBinom",
"Nat.cast",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"Rat.instAdd",
"OfNat.ofNat",
"Rat.instDiv",
"Rat.instNatCast",
"instHMul"
] | true |
_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.applyReplacementFun.visitLambda | Mathlib.Tactic.Translate.Core | [
"Lean.instBEqFVarId",
"Inhabited.default",
"Array.mkEmpty",
"Lean.LocalContext.mk",
"Lean.PersistentArrayNode.node",
"Lean.Core.instMonadLiftIOCoreM",
"instInhabitedOfMonad",
"IO.instMonadLiftSTRealWorldBaseIO",
"Lean.FVarIdMap",
"Lean.Meta.State",
"Std.HashSet",
"IO",
"Lean.instEmptyCollect... | true |
Lean.Lsp.TextDocumentClientCapabilities.completion? | Lean.Data.Lsp.Capabilities | [
"Lean.Lsp.CompletionClientCapabilities",
"Lean.Lsp.TextDocumentClientCapabilities",
"Option"
] | true |
List.replaceIf | Mathlib.Data.List.Defs | [
"List.brecOn",
"instDecidableEqBool",
"List.cons",
"Bool.true",
"List",
"Bool",
"List.below",
"List.replaceIf.match_1",
"Eq",
"List.nil",
"ite"
] | true |
MonCat.FilteredColimits.colimitCocone._proof_2 | Mathlib.Algebra.Category.MonCat.FilteredColimits | [
"CategoryTheory.Functor",
"MonCat.FilteredColimits.colimit",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"MonCat.FilteredColimits.coconeMorphism",
"MonCat",
"CategoryTheory.SmallCategory",
"CategoryTheory.Category.comp_id",
"MonCat.instC... | false |
LieEquiv.left_inv | Mathlib.Algebra.Lie.Basic | [
"LieAlgebra.toModule",
"Function.LeftInverse",
"CommRing",
"LieRing.toAddCommGroup",
"LieEquiv.toLieHom",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieEquiv",
"LinearMap.toAddHom",
"LieRing",
"CommRing.toCommSemiring",
"LieAlgebra",
"AddCommSemigroup.toAddCommMagma",
"Lie... | true |
Lean.Elab.Tactic.Do.SpecAttr.SpecProof.recOn | Lean.Elab.Tactic.Do.Attr | [
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof.rec",
"Lean.Syntax",
"Lean.Expr",
"Lean.FVarId",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof.global",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof.local",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof.stx",
"Lean.Name",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof"
] | false |
CategoryTheory.SingleFunctors.postcompIsoOfIso_hom_hom_app | Mathlib.CategoryTheory.Shift.SingleFunctors | [
"CategoryTheory.Functor",
"CategoryTheory.SingleFunctors.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.SingleFunctors.postcompIsoOfIso",
"CategoryTheory.Iso",
"CategoryTheory.SingleFunctors.functor",
"CategoryTheory.SingleFu... | true |
_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_22 | Mathlib.Data.List.Triplewise | [
"_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_6",
"instOfNatNat",
"LE.le",
"instLENat",
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"List.length"
] | false |
IsometryEquiv.subRight_apply | Mathlib.Topology.MetricSpace.IsometricSMul | [
"IsIsometricVAdd",
"AddMonoid.toAddSemigroup",
"IsometryEquiv.instEquivLike",
"HSub.hSub",
"AddOpposite",
"PseudoEMetricSpace",
"SubNegMonoid.toSub",
"AddAction.toAddSemigroupAction",
"AddGroup",
"instHSub",
"AddSemigroupAction.toVAdd",
"IsometryEquiv.subRight",
"AddGroup.toSubNegMonoid",
... | true |
PresheafOfModules.Derivation.d_one | Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"instHSMul",
"PresheafOfModules.Derivation.d",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Opposite",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"CommRingCat.carrier",
"CommRing.toNonUnitalCommRing",
"CategoryTheory.Categ... | true |
MonoidHom.submonoidComap_surjective_of_surjective | Mathlib.Algebra.Group.Submonoid.Operations | [
"Iff.mpr",
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"MonoidHom",
"congrArg",
"Subtype.val_injective",
"Submonoid.mem_comap",
"Membership.mem",
"Exists",
"Eq.rec",
"Subtype",
"Submonoid.toMulOneClass",
"Subtype.mk",
"MulOneClass.toMulOne",
"Exists.casesOn",
"Submonoid.co... | true |
AddSubmonoidClass.subtype | Mathlib.Algebra.Group.Submonoid.Defs | [
"SetLike",
"AddSubmonoidClass.toAddZeroClass",
"AddSubmonoidClass.subtype._proof_2",
"Membership.mem",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"Subtype",
"ZeroHom.mk",
"AddZero.toZero",
"AddZeroClass",
"AddSubmonoidClass.subtype._proof_1",
"AddMonoidHom",
"Subtype... | true |
UInt8.add_right_neg | Init.Data.UInt.Lemmas | [
"BitVec.add_right_neg",
"UInt8.instOfNat",
"BitVec",
"instOfNatNat",
"UInt8.toBitVec",
"instAddUInt8",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instNegUInt8",
"Iff.mp",
"UInt8.toBitVec_inj",
"OfNat.ofNat",
"UInt8",
"Eq",
"Neg.neg"
] | true |
Lean.Meta.getIntrosSize._unsafe_rec | Lean.Meta.Tactic.Intro | [
"_private.Lean.Meta.Tactic.Intro.0.Lean.Meta.getIntrosSize.match_1",
"Lean.Meta.getIntrosSize._unsafe_rec",
"Lean.Expr",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Lean.MData",
"Nat",
"Bool",
"instAddNat",
"Lean.Name",
"Lean.BinderInfo",
"OfNat.ofNat"
] | false |
CategoryTheory.Functor.instMonoidalMonMapAddMon | Mathlib.CategoryTheory.Monoidal.Mon_ | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.instMonoidalMonMapAddMon._proof_9",
"CategoryTheory.AddMon.instCategory",
"CategoryTheory.AddMon.monMonoidal",
"CategoryTheory.Functor.instMonoidalMonMapAddMon._proof_2",
"CategoryTheory.Functor.instMonoidalMonMapAddMon... | true |
InnerProductSpace.laplacianWithin.congr_simp | Mathlib.Analysis.InnerProductSpace.Laplacian | [
"InnerProductSpace.toNormedSpace",
"Real",
"NormedSpace",
"Real.instRCLike",
"NormedSpace.toModule",
"Eq.rec",
"FiniteDimensional",
"Real.instDivisionRing",
"NormedAddCommGroup.toAddCommGroup",
"Eq.refl",
"InnerProductSpace.laplacianWithin",
"Real.normedField",
"NormedAddCommGroup.toSeminorm... | true |
Finsupp.lsingle_apply | Mathlib.LinearAlgebra.Finsupp.Defs | [
"Finsupp.module",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"LinearMap",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"AddZero.toZero",
"Semiring",
"AddCommMonoid.toAddMonoid",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.co... | true |
Function.Injective.cancelMonoid.eq_1 | Mathlib.Algebra.Group.InjSurj | [
"MulOne.toOne",
"CancelMonoid.toRightCancelMonoid",
"One",
"HMul.hMul",
"Monoid.toMulOneClass",
"Pow",
"CancelMonoid.toLeftCancelMonoid",
"Mul",
"MulOne.toMul",
"RightCancelMonoid.toIsRightCancelMul",
"Monoid.toPow",
"Function.Injective.rightCancelMonoid",
"MulOneClass.toMulOne",
"HPow.hPo... | true |
Homeomorph.piSplitAt | Mathlib.Topology.Homeomorph.Lemmas | [
"Homeomorph.mk",
"Pi.topologicalSpace",
"Homeomorph.piSplitAt._proof_3",
"instTopologicalSpaceProd",
"Equiv",
"Subtype",
"Ne",
"Equiv.piSplitAt",
"Homeomorph.piSplitAt._proof_2",
"TopologicalSpace",
"Homeomorph",
"Prod",
"Subtype.val",
"DecidableEq"
] | true |
QuotientAddGroup.preimage_mk_zero | Mathlib.GroupTheory.Coset.Defs | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Set.image_singleton",
"congrArg",
"Set.image_id'",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"QuotientAddGroup.mk",
"Set.instSingletonSet",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"QuotientAddGroup.preimage_image_... | true |
_private.Lean.Meta.GeneralizeVars.0.Lean.Meta.getFVarSetToGeneralize.match_1 | Lean.Meta.GeneralizeVars | [
"MProd.casesOn",
"MProd.mk",
"MProd",
"Lean.FVarIdSet"
] | false |
DihedralGroup.Product | Mathlib.GroupTheory.CommutingProbability | [
"Fin.val",
"DihedralGroup.Product._proof_2",
"GetElem.getElem",
"List",
"Fin.instGetElemFinVal",
"Nat",
"DihedralGroup",
"LT.lt",
"instLTNat",
"List.instGetElemNatLtLength",
"Fin",
"List.length"
] | true |
_private.Mathlib.Analysis.InnerProductSpace.LinearPMap.0.LinearPMap.graph_adjoint_toLinearPMap_eq_adjoint._simp_1_2 | Mathlib.Analysis.InnerProductSpace.LinearPMap | [
"Exists",
"Subtype.exists",
"Subtype",
"Subtype.mk",
"propext",
"Eq"
] | false |
Lean.MetavarContext.UnivMVarParamResult.recOn | Lean.MetavarContext | [
"Lean.MetavarContext",
"Lean.Expr",
"Lean.MetavarContext.UnivMVarParamResult.mk",
"Array",
"Lean.MetavarContext.UnivMVarParamResult.rec",
"Nat",
"Lean.Name",
"Lean.MetavarContext.UnivMVarParamResult"
] | false |
Std.TreeMap.recOn | Std.Data.TreeMap.Basic | [
"Std.DTreeMap",
"Std.TreeMap.mk",
"Ordering",
"Std.TreeMap.rec",
"Std.TreeMap"
] | false |
Array.append_ne_empty_of_left_ne_empty | Init.Data.Array.Lemmas | [
"Array.instAppend",
"False",
"eq_false",
"congrArg",
"List.append_eq_nil_iff._simp_1",
"false_and",
"id",
"Ne",
"Array.toList_eq_nil_iff._simp_1",
"Array.toList",
"List.toArray",
"Array",
"instHAppendOfAppend",
"List",
"And",
"congr",
"True",
"Array.append_eq_toArray_iff._simp_1",
... | true |
Set.image2_union_inter_subset_union | Mathlib.Data.Set.NAry | [
"Eq.mpr",
"Set.union_subset_union",
"congrArg",
"Set.instUnion",
"id",
"Set.inter_subset_left",
"HasSubset.Subset",
"Set.image2_subset_left",
"Set.instInter",
"Inter.inter",
"Set.image2",
"Union.union",
"Set.image2_union_left",
"Eq",
"Set.inter_subset_right",
"Set.instHasSubset",
"Se... | true |
CategoryTheory.Abelian.SpectralObject.cyclesIso_inv_cyclesMap | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.SpectralObject.shortComplexMap",
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Abelian.SpectralObject.shortComplexMap._proof_21",
"CategoryTheory.Limits.HasZeroMorphisms",
"instNeZeroNatHAdd_1",
"CategoryTheory.Abelian.Spectr... | true |
Nat.factorial_eq_one._simp_1 | Mathlib.Data.Nat.Factorial.Basic | [
"Nat.factorial_eq_one",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.factorial",
"Nat",
"propext",
"OfNat.ofNat",
"Eq"
] | false |
Lean.Lsp.SymbolKind.key.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolKind._sizeOf_inst",
"instOfNatNat",
"Lean.Lsp.SymbolKind.key",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Lean.Lsp.SymbolKind",
"Eq"
] | true |
CommGrpCat.coyoneda_obj_obj_coe | Mathlib.Algebra.Category.Grp.Yoneda | [
"CategoryTheory.Functor",
"Opposite",
"CommGrpCat.coyoneda",
"MonoidHom",
"Monoid.toMulOneClass",
"CategoryTheory.Functor.category",
"CommGrpCat.instCategory",
"CommGrpCat.str",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"CommGrpCat.carrier",
"CommGrpCat",
"Ca... | true |
CompleteLat.instConcreteCategoryCompleteLatticeHomCarrier._proof_4 | Mathlib.Order.Category.CompleteLat | [
"CompleteLat.instLargeCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteLat.carrier",
"id",
"CompleteLatticeHom.instFunLike",
"CompleteLat",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"CompleteLatticeHom",
"CategoryTheory.Category.toCategoryStruct",
"CompleteLat... | false |
TopologicalSpace.Opens.comap_comp | Mathlib.Topology.Sets.Opens | [
"FrameHom",
"TopologicalSpace.Opens.instCompleteLattice",
"ContinuousMap",
"ContinuousMap.comp",
"TopologicalSpace.Opens",
"FrameHom.comp",
"TopologicalSpace",
"TopologicalSpace.Opens.comap",
"Eq",
"rfl"
] | true |
CategoryTheory.NatTrans.Equifibered.whiskerLeft | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Equifibered | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.whiskerLeft",
"CategoryTheory.Functor.map",
"CategoryTheory.NatTrans.Equifibered",
"CategoryTheory.Category.toCategoryStruct",
... | true |
GeneralizedBooleanAlgebra.toNonUnitalCommRing._proof_7 | Mathlib.Algebra.Ring.BooleanRing | [
"Lattice.toSemilatticeSup",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"bot_symmDiff",
"Preorder.toLE",
"SemilatticeSup.toMax",
"Bot.bot",
"GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra",
"GeneralizedCoheytingAlgebra.toOrderBot",
"GeneralizedBooleanAlgebra",
"GeneralizedCoheytingAlge... | false |
_private.Mathlib.Algebra.Group.WithOne.Defs.0.WithZero.unzero.match_1.splitter | Mathlib.Algebra.Group.WithOne.Defs | [
"WithZero.unzero.match_1",
"Option.some",
"Ne",
"WithZero.instZero",
"WithZero",
"WithZero.coe",
"Zero.toOfNat0",
"OfNat.ofNat"
] | true |
Lean.Compiler.LCNF.Code.inc.injEq | Lean.Compiler.LCNF.Basic | [
"Eq.propIntro",
"Lean.Compiler.LCNF.Code.inc.inj",
"Lean.Compiler.LCNF.Alt._auto_11",
"Lean.injEq_helper",
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"autoParam",
"Lean.Compiler.LCNF.Code",
"And",
"Lean.Compiler.LCNF.Purity.impure",
"Nat",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Lean.Compiler.L... | true |
AddMonoidAlgebra.mapDomainAddEquiv._proof_3 | Mathlib.Algebra.MonoidAlgebra.MapDomain | [
"Finsupp.instFunLike",
"Equiv.instEquivLike",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.nonUnitalNonAssocSemiring",
"AddMonoidAlgebra.ext",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddZeroClass.toAddZero",
"Equiv",
"Distrib.toAdd",
"AddMonoidAlgebra.mapDomain",
"NonUnitalNo... | false |
CategoryTheory.MorphismProperty.Over.homMk | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Over",
"CategoryTheory.Comma.right",
"trivial",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.IsMultiplicative.instTop",
"CategoryTheory.Morphis... | true |
CategoryTheory.FreeBicategory.bicategory._proof_7 | Mathlib.CategoryTheory.Bicategory.Free | [
"CategoryTheory.FreeBicategory.Hom₂.vcomp",
"Quot.sound",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.FreeBicategory.Rel.whisker_right",
"CategoryTheory.FreeBicategory.Rel.whisker_left",
"CategoryTheory.FreeBicategory.homCategory",
"Quot.ind",
"CategoryTheory.FreeBicatego... | false |
MeasurableEquiv.IicProdIoc._proof_5 | Mathlib.Probability.Kernel.IonescuTulcea.Maps | [
"not_le",
"Iff.mpr",
"MeasurableEquiv.IicProdIoc._proof_1",
"Preorder.toLT",
"Equiv.instEquivLike",
"measurable_pi_lambda",
"Finset.Ioc_subset_Iic_self",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Measurable",
"Finset.mem_Iic",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf... | false |
Std.Internal.List.getValueCastD_filter_not_contains_of_containsKey_eq_false_left | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"Bool.not",
"Std.Internal.List.getValueCastD_eq_fallback",
"List.contains",
"LawfulBEq",
"Std.Internal.List.getValueCastD",
"Sigma.fst",
"List",
"Std.Internal.List.containsKey",
"List.filter",
"Bool",
"instEquivBEqOfLawfulBEq",
"Std.Internal.List.containsKey... | true |
_private.Init.Data.List.MapIdx.0.List.mapIdx_eq_replicate_iff._simp_1_1 | Init.Data.List.MapIdx | [
"List.replicate",
"Membership.mem",
"List",
"And",
"List.instMembership",
"Nat",
"propext",
"List.eq_replicate_iff",
"Eq",
"List.length"
] | false |
rightAddCoset_mem_rightAddCoset | Mathlib.GroupTheory.Coset.Basic | [
"AddGroup.toSubtractionMonoid",
"Set.ext",
"NegZeroClass.toNeg",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddOpposite",
"Set.vaddSet",
"SubtractionMonoid.toSubNegZeroMonoid",
"mem_rightAddCoset_iff",
"SubNegZeroMonoid.to... | true |
Lean.Order.FlatOrder.rel.refl | Init.Internal.Order.Basic | [
"Lean.Order.FlatOrder.rel.refl",
"Lean.Order.FlatOrder",
"Lean.Order.FlatOrder.rel"
] | true |
HasFDerivAt.const_mul | Mathlib.Analysis.Calculus.FDeriv.Mul | [
"HasFDerivAt",
"NormedCommRing.toSeminormedCommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"IsScalarTower.right",
"NormedSpac... | true |
Lean.Elab.InfoTree.node.noConfusion | Lean.Elab.InfoTree.Types | [
"Lean.Elab.InfoTree",
"id",
"Lean.Elab.InfoTree.noConfusion",
"Lean.PersistentArray",
"Lean.Elab.InfoTree.node",
"Lean.Elab.Info",
"Eq"
] | false |
MvPowerSeries.isWeightedHomogeneous_weightedHomogeneousComponent | Mathlib.RingTheory.MvPowerSeries.Order | [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"Semiring.toModule",
"Finsupp.weight",
"congrArg",
"not_imp_comm",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"MvPowerSeries",
"AddZe... | true |
exists_pos_rat_lt | Mathlib.Algebra.Order.Archimedean.Basic | [
"Rat.instOfNat",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"DivisionRing.toRatCast",
"congrArg",
"LinearOrder",
"Rat",
"PartialOrder.toPreorder",
"_private.Mathlib.Algebra.Order.Archimedean.Basic.0.exists_pos_rat_lt._simp_1_1",
"IsStrictOrd... | true |
NonUnitalStarAlgHomClass.map_cfcₙ._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
AddSubgroup.isComplement'_top_right._simp_1 | Mathlib.GroupTheory.Complement | [
"AddSubgroup.instBot",
"Bot.bot",
"AddSubgroup.isComplement'_top_right",
"AddSubgroup",
"AddGroup",
"propext",
"AddSubgroup.IsComplement'",
"Top.top",
"AddSubgroup.instTop",
"Eq"
] | false |
CategoryTheory.Limits.Cocone.equivStructuredArrow_unitIso | Mathlib.CategoryTheory.Limits.ConeCategory | [
"CategoryTheory.Limits.Cocone.fromStructuredArrow",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Equivalence.unitIso",
"CategoryTheory.Limits.Cocone.eta",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso",... | true |
CategoryTheory.MonoOver.image._proof_5 | Mathlib.CategoryTheory.Subobject.MonoOver | [
"CategoryTheory.Over",
"CategoryTheory.Limits.HasImages.has_image",
"CategoryTheory.Comma.right",
"CategoryTheory.Mono",
"CategoryTheory.Limits.HasImages",
"CategoryTheory.Comma.left",
"CategoryTheory.Limits.image.ι",
"CategoryTheory.Functor.id",
"CategoryTheory.Comma.hom",
"CategoryTheory.Limits.... | false |
Lean.JsonRpc.MessageMetaData.responseError.inj | Lean.Data.JsonRpc | [
"Lean.Json",
"Lean.JsonRpc.ErrorCode",
"String",
"Lean.JsonRpc.MessageMetaData",
"And",
"Lean.JsonRpc.MessageMetaData.responseError.noConfusion",
"And.intro",
"Lean.JsonRpc.MessageMetaData.responseError",
"Lean.JsonRpc.RequestID",
"Eq",
"Option"
] | true |
Int.Linear.eq_def_cert.eq_1 | Init.Data.Int.Linear | [
"Int.Linear.Poly.beq'",
"Int.instNegInt",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.add",
"Int.Linear.eq_def_cert",
"instOfNat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"Int.Linear.Poly"
] | true |
NNRatCast.noConfusionType | Mathlib.Data.Rat.Init | [
"NNRatCast",
"NNRat",
"HEq",
"NNRatCast.casesOn"
] | false |
_private.Mathlib.RingTheory.LaurentSeries.0.LaurentSeries.Cauchy.exists_lb_eventual_support._simp_1_1 | Mathlib.RingTheory.LaurentSeries | [
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Preorder.toLT",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"ValuationClass.toMonoidWithZeroHomClass",
"MonoidWithZeroHomClass.toMonoidWithZeroHom",
... | false |
Aesop.StatsExtensionEntry._sizeOf_inst | Aesop.Stats.Extension | [
"Aesop.StatsExtensionEntry._sizeOf_1",
"SizeOf.mk",
"Aesop.StatsExtensionEntry",
"SizeOf"
] | false |
pi_properSpace | Mathlib.Topology.MetricSpace.ProperSpace | [
"Eq.mpr",
"Real.instLE",
"Real",
"pseudoMetricSpacePi",
"Real.instZero",
"congrArg",
"Set.univ",
"PseudoMetricSpace.toUniformSpace",
"id",
"isCompact_univ_pi",
"LE.le",
"ProperSpace",
"closedBall_pi",
"PseudoMetricSpace",
"Fintype",
"PseudoEMetricSpace.toUniformSpace",
"Zero.toOfNat0... | true |
Order.pred_eq_iff_covBy | Mathlib.Order.SuccPred.Basic | [
"Preorder.toLT",
"CovBy.pred_eq",
"NoMinOrder",
"CovBy",
"PartialOrder.toPreorder",
"PartialOrder",
"Order.pred_covBy",
"Iff",
"Order.pred",
"Iff.intro",
"Eq.ndrec",
"PredOrder",
"Eq"
] | true |
Real.pow_arith_mean_le_arith_mean_pow_of_even | Mathlib.Analysis.MeanInequalitiesPow | [
"NormedCommRing.toSeminormedCommRing",
"Mul.mk",
"Real.partialOrder",
"Real.instLE",
"Real",
"One.mk",
"HMul.hMul",
"Real.instZero",
"Finset",
"Set.univ",
"NormedSpace.toModule",
"Membership.mem",
"IsStrictOrderedRing.toIsStrictOrderedModule",
"Real.semiring",
"ConvexOn.map_sum_le",
"L... | true |
_private.Init.Data.Nat.Lemmas.0.Nat.pow_self_pos._simp_1_1 | Init.Data.Nat.Lemmas | [
"instPowNat",
"Nat.pow_pos_iff",
"instOfNatNat",
"instNatPowNat",
"HPow.hPow",
"Nat",
"LT.lt",
"propext",
"Or",
"instHPow",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | false |
Finset.inf_inv | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Inv",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finset.inf_image",
"SemilatticeInf.toPartialOrder",
"OrderTop",
"SemilatticeInf",
"Inv.inv",
"Finset.inf",
"Eq",
"DecidableEq",
"Finset.inv"
] | true |
Submodule.module'._proof_5 | Mathlib.Algebra.Module.Submodule.Defs | [
"Submodule",
"Semigroup.toMul",
"instHSMul",
"HMul.hMul",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"SMul",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"DistribSMul.toSMulZeroClass",
"Submodule.toSubMulAction",
"AddCommMonoid",
"AddZero.toZ... | false |
_private.Std.Internal.Async.System.0.Std.Internal.IO.Async.System.Environment.mk.noConfusion | Std.Internal.Async.System | [
"String",
"Std.Internal.IO.Async.System.Environment.noConfusion",
"id",
"Std.HashMap",
"instHashableString",
"instBEqOfDecidableEq",
"instDecidableEqString",
"Std.Internal.IO.Async.System.Environment",
"Eq",
"_private.Std.Internal.Async.System.0.Std.Internal.IO.Async.System.Environment.mk"
] | false |
_private.Mathlib.Tactic.Explode.0.Mathlib.Explode.explodeCore.match_11 | Mathlib.Tactic.Explode | [
"Lean.Expr.letE",
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Expr.lam",
"_private.Mathlib.Tactic.Explode.0.Mathlib.Explode.explodeCore._sparseCasesOn_11",
"Bool",
"Lean.Name",
"Lean.Expr.app",
"Lean.BinderInfo",
"Lean.Expr.ctorIdx"
] | false |
_private.Lean.Meta.Sym.Simp.DiscrTree.0.Lean.Meta.Sym.mkPathAux.match_1 | Lean.Meta.Sym.Simp.DiscrTree | [
"Lean.Expr",
"Prod.mk",
"Lean.Meta.DiscrTree.Key",
"Array",
"Prod",
"Prod.casesOn"
] | false |
MonoidHom.map_pow | Mathlib.Algebra.Group.Hom.Defs | [
"Monoid",
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"map_pow",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"instHPow",
"Eq",
"DFunLike.coe"
] | true |
_private.Mathlib.GroupTheory.Perm.Centralizer.0.Equiv.Perm.Basis.toCentralizer_equivariant._simp_1_1 | Mathlib.GroupTheory.Perm.Centralizer | [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"propext",
"InvOneClass.toInv",
"Eq",
"mul_inv_... | false |
Nat.ne_zero_iff_zero_lt | Init.Data.Nat.Basic | [
"Nat.pos_iff_ne_zero",
"Ne",
"instOfNatNat",
"Iff",
"Nat",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"Iff.symm"
] | true |
CategoryTheory.Limits.preservesColimits_unop | Mathlib.CategoryTheory.Limits.Preserves.Opposites | [
"CategoryTheory.Limits.PreservesColimits",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.unop",
"CategoryTheory.Limits.PreservesColimitsOfSize.mk",
"CategoryTheory.Limits.PreservesLimitsOfSize.preservesLimitsOfShape",
"CategoryTheory.Category.opposite",
"CategoryTheory.Limits.Preserves... | true |
Set.image_neg_uIcc | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"Set.image_neg_eq_neg",
"Set.neg_uIcc",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"SubtractionMonoid.toSubNegZeroM... | true |
CategoryTheory.Limits.coconeOfConeUnop_ι | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"Opposite",
"CategoryTheory.Limits.coconeOfConeUnop",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.unop",
"CategoryTheory.Limits.Cone.pt",
... | true |
System.Platform.numBits_pos._simp_1 | Init.System.Platform | [
"instOfNatNat",
"System.Platform.numBits",
"Nat",
"LT.lt",
"True",
"System.Platform.numBits_pos",
"eq_true",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | false |
CategoryTheory.Functor.mapDifferentialObject._proof_3 | Mathlib.CategoryTheory.DifferentialObject | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.DifferentialObject.Hom.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Diffe... | false |
CategoryTheory.Limits.Cocone.fromStructuredArrow_map_hom | Mathlib.CategoryTheory.Limits.ConeCategory | [
"CategoryTheory.Limits.Cocone.fromStructuredArrow",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.CoconeMorphism.hom",
"CategoryTheory.Comma.hom... | true |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.saveState | Lean.Elab.StructInst | [
"Pure.pure",
"Lean.Core.instMonadLiftIOCoreM",
"Lean.Elab.Term.instMonadTermElabM",
"IO.instMonadLiftSTRealWorldBaseIO",
"ReaderT",
"Lean.Meta.State",
"instMonadLiftT",
"MonadState.get",
"IO",
"StateRefT'.instMonadStateOfOfMonadLiftTST",
"ReaderT.instMonad",
"_private.Lean.Elab.StructInst.0.Le... | true |
_aux_Mathlib_Algebra_Group_Equiv_Defs___unexpand_AddEquiv_1 | Mathlib.Algebra.Group.Equiv.Defs | [
"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 |
WithLp.prod_nndist_eq_of_L1 | Mathlib.Analysis.Normed.Lp.ProdLp | [
"WithLp",
"NNDist.nndist",
"Real",
"SeminormedAddCommGroup",
"WithLp.instProdPseudoMetricSpace",
"PseudoMetricSpace.toNNDist",
"instAddCommMonoidWithOneENNReal",
"id",
"Distrib.toAdd",
"NNReal.eq",
"NNReal",
"WithLp.snd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",... | true |
CategoryTheory.Equivalence.powNat.match_1 | Mathlib.CategoryTheory.Equivalence | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
_private.Lean.Elab.Tactic.Monotonicity.0.Lean.Meta.Monotonicity.initFn.match_1._@.Lean.Elab.Tactic.Monotonicity.1250514167._hygCtx._hyg.2 | Lean.Elab.Tactic.Monotonicity | [
"Lean.Expr",
"Prod.mk",
"Array",
"Prod",
"Lean.BinderInfo",
"Prod.casesOn"
] | false |
Subsemigroup.unop_sInf | Mathlib.Algebra.Group.Subsemigroup.MulOpposite | [
"OrderIso.map_sInf_eq_sInf_symm_preimage",
"MulOpposite",
"PartialOrder.toPreorder",
"Subsemigroup.instPartialOrder",
"Preorder.toLE",
"Mul",
"Subsemigroup.opEquiv",
"Subsemigroup.instCompleteLattice",
"OrderIso.symm",
"Subsemigroup.op",
"Set.preimage",
"Subsemigroup.unop",
"Subsemigroup",
... | true |
AlgebraicGeometry.AffineSpace.isOpenMap_over | Mathlib.AlgebraicGeometry.AffineSpace | [
"AlgebraicGeometry.AffineSpace.SpecIso",
"Iff.mpr",
"Eq.mpr",
"CategoryTheory.Limits.pullback",
"MvPolynomial.isOpenMap_comap_C",
"AlgebraicGeometry.Spec",
"Nat.instMulZeroClass",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme.Cover.pullbackHom",
"Al... | true |
_private.Mathlib.Combinatorics.Additive.PluenneckeRuzsa.0.Finset.mul_aux | Mathlib.Combinatorics.Additive.PluenneckeRuzsa | [
"Nat.cast_mul._simp_1",
"Iff.mpr",
"Finset.empty_mul",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"Preorder.toLT",
"instHDiv",
"Nat.cast_pos",
"HMul.hMul",
"GroupWithZe... | true |
CategoryTheory.Preadditive.instSemiringEnd._proof_9 | Mathlib.CategoryTheory.Preadditive.Basic | [
"Monoid.npow",
"Semigroup.toMul",
"HMul.hMul",
"instOfNatNat",
"CategoryTheory.End.monoid",
"CategoryTheory.End",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Monoid.npow_succ",
"Monoid.toSemigroup",
"instAddNat",
"CategoryTheory.Category.toCategoryStruct",
"OfNat.ofNat",
"Eq",
"CategoryTheory.Cat... | false |
Bundle.Trivialization.linearMapAt_symmₗ | Mathlib.Topology.VectorBundle.Basic | [
"LinearMap.instFunLike",
"Bundle.Trivialization.linearMapAt",
"Bundle.Pretrivialization.linearMapAt_symmₗ",
"Membership.mem",
"Bundle.Trivialization.toPretrivialization.isLinear",
"LinearMap",
"AddCommMonoid",
"TopologicalSpace",
"Bundle.TotalSpace.proj",
"Bundle.TotalSpace",
"Bundle.Trivializat... | true |
LieModuleHom.restrictLie._proof_1 | Mathlib.Algebra.Lie.Subalgebra | [
"CommRing",
"LieModuleHom",
"LieSubalgebra.instSetLike",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Bracket.bracket",
"Membership.mem",
"AddCommGroup",
"Subtype",
"LieRingModule.toBracket",
"LieRing",
"CommRing.toCommSemiring",
"LieRingModule",
"LieSubalgebra",
"LieAlgeb... | false |
CategoryTheory.linearYoneda._proof_2 | Mathlib.CategoryTheory.Linear.Yoneda | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"LinearMap.ext",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Linear",
"LinearMap.instFunLike",
"Quiver.Hom.unop",
"CategoryTheory.CategoryStruct.id",
"id",
"LinearMap",
"CategoryTheory.Preaddit... | false |
Finset.strongInduction_eq | Mathlib.Data.Finset.Card | [
"Eq.mpr",
"congrArg",
"Finset",
"HasSSubset.SSubset",
"id",
"Finset.card_lt_card",
"Nat",
"LT.lt",
"Finset.card",
"Eq.refl",
"Finset.instHasSSubset",
"Finset.strongInduction.eq_1",
"instLTNat",
"Eq",
"Finset.strongInduction"
] | true |
Std.Internal.IO.Async.Signal.sigtstp | Std.Internal.Async.Signal | [
"Std.Internal.IO.Async.Signal",
"Std.Internal.IO.Async.Signal.sigtstp"
] | true |
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