name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ContinuousOn.div₀ | Mathlib.Topology.Algebra.GroupWithZero | [
"GroupWithZero.toMonoidWithZero",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"GroupWithZero.toDivInvMonoid",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"GroupWithZero",
"ContinuousInv₀",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"HDiv.hDiv",
"Ne",
"ContinuousOn.div... | true |
CategoryTheory.Presieve.bind | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"Exists",
"And",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | true |
HasSum.tsum_fiberwise | Mathlib.Topology.Algebra.InfiniteSum.Constructions | [
"Iff.mpr",
"UniformSpace",
"CompleteSpace",
"Equiv.instEquivLike",
"AddCommGroup.toAddCommMonoid",
"Equiv.sigmaFiberEquiv",
"Summable.subtype",
"Equiv.hasSum_iff",
"IsTopologicalAddGroup.regularSpace",
"AddCommGroup.toAddGroup",
"Function.comp",
"Membership.mem",
"AddCommGroup",
"Set.Elem"... | true |
_private.Mathlib.Algebra.Star.LinearMap.0.LinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star._simp_1_3 | Mathlib.Algebra.Star.LinearMap | [
"InvolutiveStar",
"star_eq_iff_star_eq",
"propext",
"InvolutiveStar.toStar",
"Eq",
"Star.star"
] | false |
FourierInvModule.toFourierTransformInv | Mathlib.Analysis.Fourier.Notation | [
"outParam",
"SMul",
"FourierInvModule",
"FourierTransformInv",
"Add"
] | true |
_private.Lean.Compiler.ExternAttr.0.Lean.parseOptNum._sunfold | Lean.Compiler.ExternAttr | [
"String.Pos.next",
"HMul.hMul",
"String",
"HSub.hSub",
"Char.toNat",
"_private.Lean.Compiler.ExternAttr.0.Lean.parseOptNum.match_1",
"Bool.and",
"instDecidableEqBool",
"Prod.mk",
"instSubNat",
"instMulNat",
"instOfNatNat",
"LE.le",
"dite",
"Bool.true",
"instHAdd",
"instHSub",
"HAdd... | false |
StandardSubspace.mulI._proof_1 | Mathlib.Analysis.InnerProductSpace.StandardSubspace | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"ClosedSubmodule.mulI",
"congrArg",
"NormedAddCommGroup.toMetricSpace",
"AddCommGroup.toAddCommMonoid",
"OrderBot.toBot",
"NormedSpace.toModule",
"EMetricSpace.metrizableSpace",
"ClosedSubmodule.instPartialOrder",
"PartialOrder.toPreorder",
... | false |
differentiableAt_comp_const_sub | Mathlib.Analysis.Calculus.Deriv.Add | [
"Differentiable.const_sub",
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace",
"Differentiable.differentiableAt",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"Diffe... | true |
MeasureTheory.Measure.IsNegInvariant.recOn | Mathlib.MeasureTheory.Group.Measure | [
"MeasureTheory.Measure.neg",
"MeasureTheory.Measure",
"MeasureTheory.Measure.IsNegInvariant.rec",
"MeasureTheory.Measure.IsNegInvariant.mk",
"MeasureTheory.Measure.IsNegInvariant",
"MeasurableSpace",
"Neg",
"Eq"
] | false |
ContinuousMap.Homotopy.comp._proof_2 | Mathlib.Topology.Homotopy.Basic | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"congrArg",
"ContinuousMap",
"ContinuousMap.comp",
"Real.semiring",
"Set.Elem",
"Prod.mk",
"Prod.fst",
"TopologicalSpace",
"True",
"ContinuousMap.Homotopy.apply_zero",
"eq_self",
"ContinuousMap.Homotopy.instFunL... | false |
_private.Mathlib.Tactic.ITauto.0.Mathlib.Tactic.ITauto.search._sparseCasesOn_16 | Mathlib.Tactic.ITauto | [
"Mathlib.Tactic.ITauto.AndKind",
"Mathlib.Tactic.ITauto.IProp",
"Mathlib.Tactic.ITauto.IProp.and'",
"Mathlib.Tactic.ITauto.IProp.var",
"Nat.ne_of_beq_eq_false",
"Mathlib.Tactic.ITauto.IProp.false",
"Mathlib.Tactic.ITauto.IProp.imp",
"Mathlib.Tactic.ITauto.IProp.true",
"Nat.shiftRight",
"Nat.hasNot... | false |
Hyperreal.isSt_refl_real | Mathlib.Analysis.Real.Hyperreal | [
"Iff.mpr",
"Real",
"tendsto_const_nhds",
"PseudoMetricSpace.toUniformSpace",
"nhds",
"Filter.hyperfilter",
"Hyperreal.ofReal",
"Filter.Tendsto",
"Nat",
"Real.pseudoMetricSpace",
"Hyperreal.IsSt",
"UniformSpace.toTopologicalSpace",
"Hyperreal.ofSeq",
"Ultrafilter.toFilter",
"instInfiniteN... | true |
Nat.bodd_one | Mathlib.Data.Nat.Bits | [
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Nat.bodd",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
Subgroup.inclusion_inj | Mathlib.Algebra.Group.Subgroup.Defs | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"Function.Injective.eq_iff",
"Group",
"Preorder.toLE",
"Membership.mem",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"LE.le",
"Group.toDivInvMonoid",
"Subgroup.inclusion",
"MulOneClass.toMulOne",... | true |
_private.Mathlib.AlgebraicGeometry.Morphisms.Affine.0.AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpen._simp_1_2 | Mathlib.AlgebraicGeometry.Morphisms.Affine | [
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"Lattice.toSemilatticeSup",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"PrimeSpectrum.basicOpen",
"CompleteLattice.toLattice",
"TopologicalSpace.Opens.instCompleteLatti... | false |
Lean.Meta.CaseArraySizesSubgoal | Lean.Meta.Match.CaseArraySizes | [
"Lean.Meta.CaseArraySizesSubgoal.mk"
] | true |
_private.Lean.PrettyPrinter.Delaborator.Builtins.0.Lean.PrettyPrinter.Delaborator.needsExplicit._sparseCasesOn_4 | Lean.PrettyPrinter.Delaborator.Builtins | [
"Nat.ne_of_beq_eq_false",
"Lean.BinderInfo.rec",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Lean.BinderInfo.ctorIdx",
"Nat",
"Bool",
"Lean.BinderInfo.instImplicit",
"Eq.refl",
"Lean.BinderInfo.default",
"Lean.BinderInfo",
"OfNat.ofNat",
"Bool.false",
"Lean.BinderIn... | false |
RootPairing.restrictScalars'._proof_5 | Mathlib.LinearAlgebra.RootSystem.BaseChange | [
"SMulMemClass.smul_mem",
"Set.mem_range_self",
"RootPairing.restrictScalars'._proof_3",
"LinearMap.restrictScalarsRange₂",
"Eq.mpr",
"Submodule",
"IsScalarTower.to_smulCommClass'",
"Subtype.mk.congr_simp",
"RootPairing.pairing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNon... | false |
Batteries.BinomialHeap.Imp.HeapNode.rankTR.go | Batteries.Data.BinomialHeap.Basic | [
"Batteries.BinomialHeap.Imp.HeapNode",
"Batteries.BinomialHeap.Imp.HeapNode.brecOn",
"Batteries.BinomialHeap.Imp.HeapNode.rankTR.go._f",
"Nat"
] | true |
QuotientAddGroup.lift.eq_1 | Mathlib.GroupTheory.QuotientGroup.Defs | [
"AddCon.lift",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"QuotientAddGroup.Quotient.addGroup",
"AddZeroClass.toAddZero",
"LE.le",
"AddSubgroup",
"AddSubgroup.Normal",
"HasQuotient.Quotient",
"AddGroup",
"QuotientAddGroup.con",
"... | true |
AlgebraicGeometry.Scheme.Modules.fromTildeΓ._proof_2 | Mathlib.AlgebraicGeometry.Modules.Tilde | [
"AlgebraicGeometry.Spec",
"CategoryTheory.Functor",
"Opposite",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"PrimeSpectrum.basicOpen",
"AlgebraicGeometry.tilde",
"AlgebraicGeometry.tilde.toOpen",
"ModuleCat",
"TopologicalSp... | false |
Std.Http.Chunk.instDecidableEqExtensionValue | Std.Internal.Http.Data.Chunk | [
"Std.Http.Chunk.instDecidableEqExtensionValue.decEq",
"Std.Http.Chunk.ExtensionValue",
"DecidableEq"
] | true |
AddSubmonoid.subPairs.eq_1 | Mathlib.GroupTheory.MonoidLocalization.DivPairs | [
"AddSubmonoid.instTop",
"AddMonoidHomClass.toAddMonoidHom",
"AddCommGroup.toAddCommMonoid",
"Prod.instAddZeroClass",
"AddMonoid.toAddZeroClass",
"subAddMonoidHom",
"AddSubmonoid.subPairs._proof_2",
"AddCommGroup.toAddGroup",
"AddSubmonoid.LocalizationMap",
"AddZeroClass.toAddZero",
"AddCommGroup... | true |
Lean.Server.CodeActionResolveData.noConfusion | Lean.Server.CodeActions.Basic | [
"Lean.Server.CodeActionResolveData.casesOn",
"Lean.Lsp.CodeActionParams",
"Nat",
"Lean.Server.CodeActionResolveData.noConfusionType",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq",
"Lean.Server.CodeActionResolveData"
] | false |
_private.Lean.Elab.Structure.0.Lean.Elab.Command.Structure.State.mk | Lean.Elab.Structure | [
"Lean.NameMap",
"_private.Lean.Elab.Structure.0.Lean.Elab.Command.Structure.State.mk",
"Lean.FVarIdMap",
"Lean.Elab.Command.Structure.StructParentInfo",
"Array",
"_private.Lean.Elab.Structure.0.Lean.Elab.Command.Structure.State",
"Nat",
"Lean.Elab.Command.Structure.StructFieldInfo"
] | true |
List.rdrop.eq_1 | Mathlib.Data.List.DropRight | [
"List.rdrop",
"HSub.hSub",
"instSubNat",
"List",
"instHSub",
"Nat",
"Eq.refl",
"Eq",
"List.take",
"List.length"
] | true |
CategoryTheory.Limits.MulticospanIndex.multicospan_map | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingMulticospan.functorExt.match_1",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.MulticospanIndex",
... | true |
_private.Aesop.Forward.State.0.Aesop.VariableMap.modifyM.match_1 | Aesop.Forward.State | [
"Aesop.InstMap",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Lean.Lsp.DocumentSymbolAux.children?._default | Lean.Data.Lsp.LanguageFeatures | [
"id",
"Array",
"Option.none",
"Option"
] | false |
UInt8.ofNat_eq_iff_mod_eq_toNat | Init.Data.UInt.Lemmas | [
"instPowNat",
"congrArg",
"UInt8.toNat_ofNat'",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"iff_self",
"instNatPowNat",
"HMod.hMod",
"Iff",
"HPow.hPow",
"Nat",
"True",
"of_eq_true",
"congrFun'",
"_private.Init.Data.UInt.Lemmas.0.UInt8.ofNat_eq_iff_mod_eq_toNat._simp_1_1",
"instHPow",... | true |
_private.Init.Data.List.Sort.Impl.0.List.mergeSort.match_1.eq_2 | Init.Data.List.Sort.Impl | [
"_private.Init.Data.List.Sort.Basic.0.List.mergeSort.match_1",
"List.cons",
"List",
"Bool",
"Eq.refl",
"Eq",
"List.nil"
] | true |
CategoryTheory.MorphismProperty.map_mem_map | Mathlib.CategoryTheory.MorphismProperty.Basic | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Exists",
"CategoryTheory.Iso.refl",
"CategoryTheory.Iso",
"CategoryTheory.instCategoryArrow",
"Nonempty.intro",
"CategoryTheory.Functor.map",
"CategoryTheory.MorphismProperty.map... | true |
CategoryTheory.PreZeroHypercover.Hom._sizeOf_1 | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PreZeroHypercover.X",
"instOfNatNat",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover.Hom.rec",
"CategoryTheory.PreZeroHypercover",
"Nat",
"CategoryTheory.Category... | false |
_private.Mathlib.Order.Monotone.Basic.0.not_monotone_not_antitone_iff_exists_lt_lt._simp_1_1 | Mathlib.Order.Monotone.Basic | [
"not_monotone_not_antitone_iff_exists_le_le",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"Exists",
"LE.le",
"Antitone",
"And",
"LT.lt",
"propext",
"Or",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
TensorialAt.mkHom._proof_6 | Mathlib.Geometry.Manifold.VectorBundle.Tensoriality | [
"NormedField.toField",
"Field.toSemifield",
"RingHomInvPair",
"Semifield.toDivisionSemiring",
"RingHomInvPair.ids",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
Matroid.eRk_union_closure_right_eq | Mathlib.Combinatorics.Matroid.Rank.ENat | [
"Eq.mpr",
"congrArg",
"Set.instUnion",
"id",
"Matroid.closure_union_closure_right_eq",
"ENat",
"Matroid.eRk",
"Matroid.closure",
"Eq.refl",
"Union.union",
"Eq.symm",
"Eq",
"Matroid",
"Matroid.eRk_closure_eq",
"Set"
] | true |
PolynomialLaw.mk | Mathlib.RingTheory.PolynomialLaw.Basic | [
"PolynomialLaw.isCompat'._autoParam",
"AlgHom.toLinearMap",
"CommSemiring.toSemiring",
"AlgHom",
"TensorProduct.addCommMonoid",
"LinearMap.instFunLike",
"Algebra",
"Function.comp",
"Algebra.toModule",
"PolynomialLaw",
"autoParam",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"NonUnitalN... | true |
AlgebraicGeometry.StructureSheaf.const_algebraMap | Mathlib.AlgebraicGeometry.StructureSheaf | [
"AlgebraicGeometry.StructureSheaf.Localizations",
"Iff.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CategoryTheory.Functor",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Opposite",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"PrimeSpectrum.basicOpen",
"Algeb... | true |
Lean.Elab.Tactic.evalSym | Lean.Elab.Tactic.Grind.Main | [
"Lean.Elab.Tactic.Grind.evalGrindTactic",
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"cond",
"Lean.Syntax.TSepArray.mk",
"Lean.instMonadEnvOfMonadLift",
"Lean.Meta.Grind.Params",
"Lean.TSyntax",
"Lean.Elab.Tactic.instMonadExceptExceptionTacticM",
"Lean.MessageData",
"Lean.MonadError.mk",
"U... | true |
CategoryTheory.enrichedNatTransYonedaTypeIsoYonedaNatTrans | Mathlib.CategoryTheory.Enriched.Basic | [
"CategoryTheory.categoryOfEnrichedCategoryType",
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.enrichedNatTransYonedaTypeIsoYonedaNatTrans._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"CategoryTheor... | true |
_private.Init.Data.Array.Lemmas.0.Array.getElem?_size._simp_1_1 | Init.Data.Array.Lemmas | [
"False",
"eq_false",
"Nat",
"Nat.lt_irrefl",
"LT.lt",
"instLTNat",
"Eq"
] | false |
Convex.lift | Mathlib.Analysis.Convex.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"smul_le_smul_of_nonneg_right",
"smul_assoc",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Module.toMulActionWithZero",
"Preorder.to... | true |
Std.Time.instReprOffsetO.repr | Std.Time.Format.Basic | [
"Std.Format.group",
"GE.ge",
"instOfNatNat",
"Int",
"instLENat",
"Unit",
"instOfNat",
"Nat",
"Std.Format",
"Repr.addAppParen",
"Std.Time.OffsetO",
"OfNat.ofNat",
"Nat.decLe",
"Std.Format.nest",
"Std.Format.text",
"_private.Std.Time.Format.Basic.0.Std.Time.instReprOffsetO.repr.match_1",... | true |
Filter.EventuallyEq.of_eventually_mem_of_forall_separating_preimage | Mathlib.Order.Filter.CountableSeparatingOn | [
"Filter.EventuallyEq.of_eventually_mem_of_forall_separating_mem_iff",
"Filter.Eventually",
"Filter.EventuallyEq.mem_iff",
"Membership.mem",
"Filter.EventuallyEq",
"CountableInterFilter",
"Set.preimage",
"HasCountableSeparatingOn",
"Set.instMembership",
"Filter",
"Set"
] | true |
_private.Lean.Compiler.LCNF.Simp.JpCases.0.Lean.Compiler.LCNF.Simp.simpJpCases?.visitJmp?.match_5 | Lean.Compiler.LCNF.Simp.JpCases | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Compiler.LCNF.Simp.JpCases.0.Lean.Compiler.LCNF.Simp.collectJpCasesInfo.go._sparseCasesOn_1",
"Lean.Compiler.LCNF.Simp.CtorInfo",
"Option"
] | false |
_private.Mathlib.RingTheory.WittVector.FrobeniusFractionField.0.WittVector.frobeniusRotationCoeff.match_1.eq_2 | Mathlib.RingTheory.WittVector.FrobeniusFractionField | [
"WittVector.frobeniusRotationCoeff.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
AmpleSet.vadd_iff | Mathlib.Analysis.Convex.AmpleSet | [
"Real",
"instSeparatelyContinuousAddOfContinuousAdd",
"instVAddOfAdd",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Real.semiring",
"Set.vaddSet",
"addGroupIsAddTorsor",
"Real.instRing",
"HVAdd.hVAdd",
"TopologicalSpace",
"AmpleSet.image_iff",
"Iff",
"Conti... | true |
_private.Mathlib.Topology.MetricSpace.HausdorffDistance.0.IsOpen.exists_iUnion_isClosed._simp_1_4 | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Set.Ioc.coe_sup._simp_1 | Mathlib.Order.LatticeIntervals | [
"Set.Ioc",
"PartialOrder.toPreorder",
"Set.Ioc.semilatticeSup",
"Membership.mem",
"SemilatticeSup.toMax",
"Set.Elem",
"Max.max",
"SemilatticeSup.toPartialOrder",
"Eq.symm",
"Subtype.val",
"Eq",
"SemilatticeSup",
"Set.instMembership",
"Set.Ioc.coe_sup",
"Set"
] | false |
Std.LawfulBCmp.rec | Batteries.Classes.Order | [
"Std.LawfulBCmp",
"Ordering",
"LE.le",
"Std.TransCmp",
"LE",
"Bool.true",
"Iff",
"Ordering.lt",
"Std.LawfulBEqCmp",
"LT.lt",
"Bool",
"Ordering.isLE",
"BEq",
"Eq",
"Std.LawfulBCmp.mk",
"LT"
] | false |
_private.Init.Data.String.PosRaw.0.String.Pos.Raw.offsetBy_unoffsetBy_of_le._simp_1_1 | Init.Data.String.PosRaw | [
"LE.le",
"instLENat",
"String.Pos.Raw",
"Nat",
"String.instLERaw",
"propext",
"String.Pos.Raw.byteIdx",
"String.Pos.Raw.le_iff",
"Eq"
] | false |
Function.instIsStrictWeakOrderOnFun | Mathlib.Logic.Function.Basic | [
"Function.instIsStrictOrderOnFun",
"Function.onFun",
"IsStrictWeakOrder.mk",
"IsStrictWeakOrder.incomp_trans",
"IsStrictWeakOrder.toIsStrictOrder",
"IsStrictWeakOrder"
] | true |
CategoryTheory.Functor.mapConePostcomposeEquivalenceFunctor._proof_2 | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso.refl",
"CategoryTheory.Iso",
"CategoryTheory.Equivalen... | false |
_private.Mathlib.Analysis.Complex.CanonicalDecomposition.0.Complex.meromorphicOrderAt_canonicalFactor._proof_1_1 | Mathlib.Analysis.Complex.CanonicalDecomposition | [
"instLawfulOrderLT_mathlib",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"NormedCommRing.toSeminormedCommRing",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.Order.lt_unsat_k",
"Real.partialOrder",
"Real.instLE",
"Real",
"Lean.Grind.not_not",
"Lean.Grind.Order.le_lt_trans_k",
"Classical.... | false |
Filter.EventuallyEq.trans_le | Mathlib.Order.Filter.Basic | [
"Preorder.toLE",
"Filter.EventuallyEq",
"Filter.EventuallyEq.le",
"Filter.EventuallyLE",
"Filter.EventuallyLE.trans",
"Filter",
"Preorder"
] | true |
GromovHausdorff.premetricOptimalGHDist._proof_1 | Mathlib.Topology.MetricSpace.GromovHausdorffRealized | [
"Real",
"ENNReal.ofNNReal",
"_private.Mathlib.Topology.MetricSpace.GromovHausdorffRealized.0.GromovHausdorff.optimalGHDist_mem_candidatesB",
"ENNReal.ofReal",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"Sum",
"BoundedContinuousFunction.instFunLike",
"NNReal.mk",
"Prod.mk",
"... | false |
CategoryTheory.MorphismProperty.LeftFraction.Localization.instIsIsoQinv | Mathlib.CategoryTheory.Localization.CalculusOfFractions | [
"CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions",
"CategoryTheory.MorphismProperty",
"CategoryTheory.IsIso",
"_private.Mathlib.CategoryTheory.Localization.CalculusOfFractions.0.CategoryTheory.MorphismProperty.LeftFraction.Localization.instIsIsoQinv._proof_1",
"CategoryTheory.CategoryStruct.toQui... | true |
_private.Mathlib.Algebra.Ring.Subsemiring.Basic.0.RingHom.rangeSRestrict_surjective.match_1_3 | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"Subsemiring.instSetLike",
"Subtype.casesOn",
"RingHom",
"Membership.mem",
"Subtype",
"Subsemiring",
"Subtype.mk",
"NonAssocSemiring",
"SetLike.instMembership",
"RingHom.rangeS"
] | false |
RingHom.inverse._proof_6 | Mathlib.Algebra.Ring.Equiv | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Function.LeftInverse",
"RingHom.inverse._proof_3",
"AddMonoidHomClass.toAddMonoidHom",
"ZeroHom.toFun",
"AddMonoid.toAddZeroClass",
"ZeroHom.map_zero'",
"RingHom",
"AddMonoidHom.toZeroHom",
"AddZeroClass.toAddZero",
"AddCommMonoidWithOne.toAddMonoidWit... | false |
IO.FS.Mode.append | Init.System.IO | [
"IO.FS.Mode",
"IO.FS.Mode.append"
] | true |
Int.sub_one_lt_of_le | Init.Data.Int.Order | [
"HSub.hSub",
"Int",
"LE.le",
"Int.instLTInt",
"instHSub",
"instOfNat",
"LT.lt",
"Int.instSub",
"OfNat.ofNat",
"Int.sub_right_lt_of_lt_add",
"Int.instLEInt",
"Int.lt_add_one_of_le"
] | true |
CategoryTheory.categoryOfElements._proof_8 | Mathlib.CategoryTheory.Elements | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"Subtype.mk.congr_simp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"Subtype",
"Sigma.fst",
"CategoryTheory.Fu... | false |
Lean.LibrarySuggestions.localSymbolFrequency | Lean.LibrarySuggestions.SymbolFrequency | [
"Pure.pure",
"_private.Lean.LibrarySuggestions.SymbolFrequency.0.Lean.LibrarySuggestions.cachedLocalSymbolFrequencyMap",
"Lean.NameMap",
"Lean.Meta.State",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instOfNatNat",
"Applicative.toPure",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"Sta... | true |
Lean.Elab.DefView._sizeOf_inst | Lean.Elab.DefView | [
"Lean.Elab.DefView._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Elab.DefView"
] | false |
Lean.Syntax.node2 | Init.Prelude | [
"Lean.Syntax.node",
"Lean.SourceInfo",
"Array.mkArray2",
"Lean.Syntax",
"Lean.SyntaxNodeKind"
] | true |
LowerSet.instOne | Mathlib.Algebra.Order.UpperLower | [
"One",
"InvOneClass.toOne",
"One.mk",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Preorder.toLE",
"DivisionMonoid.toDivInvOneMonoid",
"CommGroup",
"CommGroup.toDivisionCommMonoid",
"One.toOfNat1",
"OfNat.ofNat",
"LowerSet",
"Preorder",
"LowerSet.Iic"
] | true |
Std.DHashMap.Raw.Const.find?_toList_eq_none_iff_not_mem._simp_1 | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.Const.toList",
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Std.DHashMap.Raw",
"List.find?",
"Membership.mem",
"LawfulHashable",
"Prod.fst",
"Std.DHashMap.Raw.Const.find?_toList_eq_none_iff_not_mem",
"Option.none",
"BEq.beq",
"EquivBEq",
"propex... | false |
CategoryTheory.Adjunction.IsTriangulated.mk'' | Mathlib.CategoryTheory.Triangulated.Adjunction | [
"CategoryTheory.Functor.IsTriangulated",
"CategoryTheory.Functor",
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"inferInstance",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Adjunction.IsTriangulated.mk",
"CategoryTheory.Adjunction.IsTriangulated",
"CategoryTheory.Preadditive",... | true |
ZMod.prodEquivPi | Mathlib.Data.ZMod.QuotientRing | [
"Ideal.quotEquivOfEq",
"Nat.Coprime",
"iInf",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Finset.univ",
"ZMod.commRing",
"Function.onFun",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"RingEquiv.piCongrRight",
"Id... | true |
Complex.cos | Mathlib.Analysis.Complex.Trigonometric | [
"instHDiv",
"HMul.hMul",
"Complex.instDivInvMonoid",
"Complex.instMul",
"Complex.sin._proof_1",
"HDiv.hDiv",
"Complex.instNatCast",
"instHAdd",
"HAdd.hAdd",
"DivInvMonoid.toDiv",
"Complex.exp",
"Complex.instAdd",
"Complex",
"OfNat.ofNat",
"instOfNatAtLeastTwo",
"Complex.instNeg",
"Ne... | true |
_private.Mathlib.LinearAlgebra.AffineSpace.Combination.0.Finset.sum_affineCombinationLineMapWeights._simp_1_4 | Mathlib.LinearAlgebra.AffineSpace.Combination | [
"Finset.mul_sum",
"HMul.hMul",
"Finset",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"NonUnitalNonAssocSemiring",
"Eq.symm",
"Eq",
"Finset.sum",
"instHMul"
] | false |
Filter.bliminf_not_inf | Mathlib.Order.LiminfLimsup | [
"Filter.liminf",
"Order.Coframe.toCompleteLattice",
"CompleteDistribLattice",
"CompleteLattice.toConditionallyCompleteLattice",
"Filter.bliminf",
"SemilatticeInf.toMin",
"CompleteDistribLattice.toCoframe",
"OrderDual.instCompleteDistribLattice",
"ConditionallyCompleteLattice.toLattice",
"Filter.bl... | true |
Std.DHashMap.Raw.get!_diff | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.get!.congr_simp",
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Eq.mpr",
"Inhabited.default",
"Std.DHashMap.Internal.Raw₀.contains",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Std.DHashMap.Raw",
"LawfulBEq",
"Membership.mem",
"Std.DHashMap.Raw.c... | true |
CliffordAlgebra.foldr'._proof_1 | Mathlib.LinearAlgebra.CliffordAlgebra.Fold | [
"CommRing",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"QuadraticForm",
"AddCommGroup",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocRing.toNonUnitalNonAssocRing",
"smul... | false |
Finsupp.embDomain.addMonoidHom._proof_1 | Mathlib.Algebra.Group.Finsupp | [
"Finsupp.instAddZeroClass",
"AddZeroClass.toAddZero",
"Function.Embedding",
"AddZero.toZero",
"AddZeroClass",
"eq_self",
"of_eq_true",
"Finsupp.embDomain",
"Zero.toOfNat0",
"Finsupp.instZero",
"OfNat.ofNat",
"Eq",
"Finsupp"
] | false |
RingQuot.ringQuot_ext' | Mathlib.Algebra.RingQuot | [
"RingQuot.mkAlgHom_surjective",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"Exists",
"RingQuot.instSemiring",
"RingQuot",
"AlgHom.ext",
"RingQuot.mkAlgHom",
"CommSemiring",
"RingQuot.instAlgebra",
"Exists.casesOn",
"AlgHom.congr_fun",
"Eq.ndrec",
"Semiring",
"AlgHom.comp",
"Eq",
"DFunL... | true |
_private.Mathlib.Lean.MessageData.ForExprs.0.Lean.MessageData.firstExpr?.match_3 | Mathlib.Lean.MessageData.ForExprs | [
"Lean.Expr",
"Prod.mk",
"Lean.PPContext",
"Prod",
"Prod.casesOn"
] | false |
Mathlib.Meta.FunProp.instBEqTheoremForm | Mathlib.Tactic.FunProp.Theorems | [
"Mathlib.Meta.FunProp.instBEqTheoremForm.beq",
"BEq.mk",
"Mathlib.Meta.FunProp.TheoremForm",
"BEq"
] | true |
String.empty_ne_singleton | Init.Data.String.Lemmas.Basic | [
"False",
"congrArg",
"String",
"String.singleton_ne_empty._simp_1",
"Ne",
"String.empty_eq_iff._simp_1",
"True",
"of_eq_true",
"Char",
"not_false_eq_true",
"String.singleton",
"Eq",
"Not",
"Eq.trans"
] | true |
Ideal.absNorm_dvd_absNorm_of_le | Mathlib.RingTheory.Ideal.Norm.AbsNorm | [
"Nontrivial",
"Iff.mpr",
"Ideal.dvd_iff_le",
"Nat.instMulZeroOneClass",
"CommRing",
"Dvd.dvd",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"Ideal.absNorm",
"CommSemiring.toSemiring",
"Submodule.instNonUnitalSemi... | true |
MeasureTheory.measure_symmDiff_eq_zero_iff._simp_1 | Mathlib.MeasureTheory.OuterMeasure.AE | [
"MeasureTheory.ae",
"Lattice.toSemilatticeSup",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"Filter.EventuallyEq",
"ENNReal",
"propext",
"CompleteBooleanAlgebra.toCompleteLattice",
"Zero.toOfNat0",
"ENNReal.instZero",
"ConditionallyCompleteLattice.toLattice",
"Mea... | false |
Mathlib.Meta.FunProp.instInhabitedConfig.default | Mathlib.Tactic.FunProp.Types | [
"Inhabited.default",
"Mathlib.Meta.FunProp.Config.mk",
"instInhabitedNat",
"Nat",
"Mathlib.Meta.FunProp.Config"
] | true |
AlgHom.IsArithFrobAt.isArithFrobAt_localize | Mathlib.RingTheory.Frobenius | [
"Iff.mpr",
"Eq.mpr",
"RingHom.instRingHomClass",
"Submodule.Quotient.instZeroQuotient",
"IsLocalization.AtPrime.mk'_mem_maximal_iff",
"CommRing",
"RingHomClass.toAddMonoidHomClass",
"Semiring.toModule",
"Submonoid.mul",
"HMul.hMul",
"AlgHom.IsArithFrobAt.mk_apply",
"Localization.localRingHom_m... | true |
Lean.Linter.isDeprecated | Lean.Linter.Deprecated | [
"Lean.Linter.instInhabitedDeprecationEntry",
"Lean.Linter.deprecatedAttr",
"Lean.ParametricAttribute.getParam?",
"Bool",
"Lean.Name",
"Option.isSome",
"Lean.Linter.DeprecationEntry",
"Lean.Environment"
] | true |
IsLocalization.orderIsoOfPrime | Mathlib.RingTheory.Localization.Ideal | [
"Semiring.toModule",
"ChainCompletePartialOrder.instOfCompleteLattice",
"IsLocalization",
"Algebra.algebraMap",
"RelIso.mk",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"RingHom",
"Disjoint",
"Equiv.mk",... | true |
Subrepresentation.instLattice._proof_2 | Mathlib.RepresentationTheory.Subrepresentation | [
"Monoid",
"Submodule",
"Representation",
"Preorder.toLT",
"Submodule.completeLattice",
"Iff.rfl",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toConditionallyCompleteLattice",
"Subrepresentation.toSubmodule",
"Subrepresentation",
"AddCommMonoid",
"Iff",
"LT.... | false |
Aesop.Frontend.BuilderOption.pattern.noConfusion | Aesop.Frontend.RuleExpr | [
"Aesop.Frontend.BuilderOption.noConfusion",
"id",
"Lean.Syntax.Term",
"Aesop.Frontend.BuilderOption.pattern",
"Eq",
"Aesop.Frontend.BuilderOption"
] | false |
Ordinal.opow_lt_opow_left_of_succ | Mathlib.SetTheory.Ordinal.Exponential | [
"zero_le",
"mul_lt_mul_of_le_of_lt_of_nonneg_of_pos",
"Eq.mpr",
"Ordinal.mulRightMono",
"Preorder.toLT",
"HMul.hMul",
"Order.succ",
"Ordinal.partialOrder",
"MulZeroClass.toMul",
"congrArg",
"instIsBotZeroClass",
"Ordinal.instOrderBot",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",... | true |
NumberField.instCommRingInfiniteAdeleRing._proof_11 | Mathlib.NumberTheory.NumberField.InfiniteAdeleRing | [
"NumberField.instCommRingInfiniteAdeleRing._proof_3",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real",
"WithAbs",
"WithAbs.instCommRing",
"Add.mk",
"NumberField.InfiniteAdeleRing",
"Complex.instNormedField",
"IsTopologicalDivisionRing.toIsTopologicalRing",
"PseudoMetricSpace.t... | false |
ContinuousAffineMap.ext_iff | Mathlib.Topology.Algebra.ContinuousAffineMap | [
"ContinuousAffineMap.ext",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Eq.casesOn",
"ContinuousAffineMap",
"TopologicalSpace",
"Iff",
"Iff.intro",
"AddTorsor",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Module",
"Eq.symm",
"ContinuousAffineMap.instFunL... | true |
Aesop.RulePatternIndex.getCore | Aesop.Index.RulePattern | [
"Pure.pure",
"Aesop.BaseM",
"Lean.instantiateMVars",
"Aesop.RuleName",
"Lean.instMonadMCtxOfMonadLift",
"StateRefT'.instAlternativeOfMonad",
"Lean.Core.instMonadLiftIOCoreM",
"Aesop.RulePatternIndex",
"IO.instMonadLiftSTRealWorldBaseIO",
"Aesop.RulePatternIndex.isEmpty",
"Lean.Expr.instBEq",
"... | true |
Std.DTreeMap.Internal.Impl.find?_toArray_eq_some_iff_get?_eq_some | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"instDecidableEqOrdering",
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.get?",
"Std.TransOrd",
"Iff.rfl",
"Std.DTreeMap.Internal.Impl.toList",
"List.find?",
"Option.some",
"Ordering",
"Ordering.eq",
"id",
"Sigma.fst",
"Std.DTreeMap.Internal.Impl.WF",
"instBEqOfDecidableEq",... | true |
Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaries.noConfusion | Mathlib.Tactic.Translate.UnfoldBoundary | [
"Lean.NameMap",
"Lean.NameSet",
"Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaries.casesOn",
"Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaries",
"Lean.Meta.SimpTheorem",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaries.noConfusionType",
"Prod",
"Eq"
] | false |
_private.Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs.0.ComputeAsymptotics.MultiseriesExpansion.Approximates.coind._proof_1_4 | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | [
"Lean.Grind.eq_false_of_not_eq_true",
"ComputeAsymptotics.Basis",
"Real.instPow",
"False",
"Real",
"Lean.Grind.not_false",
"HMul.hMul",
"Lean.Grind.not_and",
"Real.instZero",
"congrArg",
"Lean.Grind.not_or",
"Real.instSub",
"False.elim",
"Classical.byContradiction",
"ComputeAsymptotics.M... | false |
Turing.TM1to0.tr.eq_2 | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Option.some",
"Prod.mk",
"Turing.TM1to0.Λ'",
"Turing.TM1to0.tr",
"Turing.TM1to0.trAux",
"Inhabited",
"Eq.refl",
"Prod",
"Eq",
"Turing.TM0.Stmt",
"Turing.TM1.Stmt",
"Option"
] | true |
CategoryTheory.Functor.CoconeTypes.precompose_ι | Mathlib.CategoryTheory.Limits.Types.ColimitType | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"Function.comp",
"CategoryTheory.Functor.CoconeTypes.ι",
"CategoryTheory.Functor.CoconeTypes.precompose",
"CategoryTheory.Functor.CoconeTypes.pt",
"Cat... | true |
MagmaCat.of.eq_1 | Mathlib.Algebra.Category.Semigrp.Basic | [
"MagmaCat.mk",
"Mul",
"MagmaCat.of",
"Eq.refl",
"Eq",
"MagmaCat"
] | true |
LipschitzWith.mul_edist_le | Mathlib.Topology.EMetricSpace.Lipschitz | [
"Eq.mpr",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"ENNReal.ofNNReal",
"DivInvMonoid.toInv",
"LipschitzWith",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.div_le_of_le_mul'",
"id",
"MulOne.toM... | true |
Path.Homotopic.hpath_hext | Mathlib.Topology.Homotopy.Path | [
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"congrArg",
"HEq.refl",
"heq_iff_eq",
"Path.ext",
"Eq.rec",
"Real.semiring",
"Set.Elem",
"Eq.casesOn",
"id",
"Setoid",
"Path.Homotopic.Quotient",
"Quotient.mk",
"Path.Homotopic.setoid",
"Topologi... | true |
String.Slice.Pattern.Model.CharPred.Decidable.isRevMatch_iff_isRevMatch_decide | Init.Data.String.Lemmas.Pattern.Pred | [
"String.Slice.Pattern.Model.IsRevMatch",
"String.Slice.Pattern.Model.CharPred.Decidable.instPatternModelForallCharPropOfDecidablePred",
"String.Slice.Pattern.Model.PatternModel.Matches",
"String.Slice.sliceFrom",
"String.Slice",
"String.Slice.copy",
"Iff",
"String.Slice.Pattern.Model.CharPred.instPatt... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.