name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.GrothendieckTopology.over_forget_coverPreserving | Mathlib.CategoryTheory.Sites.Over | [
"CategoryTheory.Over",
"CategoryTheory.CoverPreserving",
"Membership.mem",
"CategoryTheory.Over.forget",
"CategoryTheory.CoverPreserving.mk",
"CategoryTheory.Sieve",
"CategoryTheory.instCategoryOver",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.GrothendieckTopology.over",
"Set.instMembe... | true |
StarAlgHom.noConfusionType | Mathlib.Algebra.Star.StarAlgHom | [
"MulOne.toOne",
"AlgHom",
"Algebra",
"NonAssocSemiring.toMulZeroOneClass",
"StarAlgHom",
"MulZeroOneClass.toMulOneClass",
"CommSemiring",
"MulOneClass.toMulOne",
"OneHom.toFun",
"AlgHom.toRingHom",
"Star",
"StarAlgHom.casesOn",
"MonoidHom.toOneHom",
"Semiring",
"HEq",
"RingHom.toMonoid... | false |
CategoryTheory.evaluationAdjunctionRight._proof_6 | Mathlib.CategoryTheory.Adjunction.Evaluation | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.NatTrans.mk.congr_simp",
"CategoryTheory.evaluationAdjunctionRight._proof_4",
"CategoryT... | false |
CliffordAlgebra.equivOfIsometry_symm | Mathlib.LinearAlgebra.CliffordAlgebra.Basic | [
"CommRing",
"Semiring.toModule",
"QuadraticMap.IsometryEquiv.symm",
"AlgEquiv.symm",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"QuadraticMap.IsometryEquiv",
"QuadraticForm",
"AddCommGroup",
"NonUnitalNonAssocSemiring.toAddCommMo... | true |
CategoryTheory.Cat.typeToCatObjectsAdj | Mathlib.CategoryTheory.Category.Cat.Adjunction | [
"CategoryTheory.Cat.category",
"CategoryTheory.Adjunction.CoreHomEquivUnitCounit.mk",
"CategoryTheory.Adjunction.mk'",
"_private.Mathlib.CategoryTheory.Category.Cat.Adjunction.0.CategoryTheory.Cat.typeToCatObjectsAdjHomEquiv",
"CategoryTheory.Functor.toCatHom",
"CategoryTheory.Functor.comp",
"CategoryTh... | true |
Subfield.relrank_comap_comap_eq_relrank_of_surjective | Mathlib.FieldTheory.Relrank | [
"Subfield.relrank",
"Subfield.lift_relrank_comap_comap_eq_lift_relrank_of_surjective",
"Cardinal",
"congrArg",
"Cardinal.lift",
"RingHom",
"Field.toDivisionRing",
"Eq.mp",
"Field.toSemifield",
"Subfield.comap",
"RingHom.instFunLike",
"Semifield.toDivisionSemiring",
"congr",
"DivisionSemiri... | true |
Asymptotics.isBigOWith_top._simp_1 | Mathlib.Analysis.Asymptotics.Lemmas | [
"Norm.norm",
"Real.instLE",
"Real",
"HMul.hMul",
"Asymptotics.IsBigOWith",
"Norm",
"LE.le",
"Asymptotics.isBigOWith_top",
"Real.instMul",
"propext",
"Filter.instTop",
"Top.top",
"Eq",
"Filter",
"instHMul"
] | false |
FreeLieAlgebra.Rel.subLeft | Mathlib.Algebra.Lie.Free | [
"Eq.mpr",
"NegZeroClass.toNeg",
"CommRing",
"FreeNonUnitalNonAssocAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"FreeLieAlgebra.Rel.addLeft",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNeg... | true |
DFinsupp.lapply._proof_2 | Mathlib.LinearAlgebra.DFinsupp | [
"instHSMul",
"DFinsupp.smul_apply",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"DFinsupp.instSMulZeroClass",
"AddZeroClass.toAddZero",
"DFinsupp.instDFunLike",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"AddZero.toZero",
"DFinsupp.instZero",
"Semiring.toMonoid",
"Semi... | false |
_private.Mathlib.Order.ConditionallyCompleteLattice.Finset.0.Set.Finite.lt_ciInf_iff._simp_1_3 | Mathlib.Order.ConditionallyCompleteLattice.Finset | [
"Set.mem_image",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
AlgebraicGeometry.ProjectiveSpectrum.Proj.specStalkEquiv._proof_1 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme | [
"SetLike",
"CommRing",
"AddGroupWithOne.toAddGroup",
"ProjectiveSpectrum.zariskiTopology",
"CommSemiring.toSemiring",
"ProjectiveSpectrum.basicOpen",
"TopologicalSpace.Opens",
"Nat.instAddMonoid",
"Membership.mem",
"Subtype",
"AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.carrier._proof_1",
... | false |
SimpleGraph.UnitDistEmbedding.copy._proof_1 | Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic | [
"Real",
"SimpleGraph.Adj",
"SimpleGraph.Hom.map_adj",
"SimpleGraph.Copy",
"SimpleGraph.UnitDistEmbedding.unit_dist",
"Function.Embedding",
"SimpleGraph.Copy.toEmbedding",
"SimpleGraph",
"SimpleGraph.UnitDistEmbedding",
"Real.instOne",
"MetricSpace",
"SimpleGraph.UnitDistEmbedding.p",
"Simple... | false |
Mathlib.Tactic.Ring.Common.ExProd.rec | Mathlib.Tactic.Ring.Common | [
"Lean.Expr.const",
"Mathlib.Tactic.Ring.Common.ExSum",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Mathlib.Tactic.Ring.Common.ExBase",
"Mathlib.Tactic.Ring.Common.ExProd.mul",
"Lean.Literal.natVal",
"Qq.Quoted",
"Lean.Level.zero",
"Nat",
"Mathlib.Tactic.Ring.Common.ExProd",
"Mathlib.Tactic... | false |
InnerProductSpace.isSymmetric_rankOne_self._simp_1 | Mathlib.Analysis.InnerProductSpace.Symmetric | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"ContinuousLinearMap.topologicalAddGroup",
"ContinuousLinearMap.... | false |
Finset.sym.match_1 | Mathlib.Data.Finset.Sym | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Polynomial.natDegree_mul_le | Mathlib.Algebra.Polynomial.Degree.Defs | [
"Polynomial.degree_mul_le",
"WithBot.addMonoidWithOne",
"WithBot.instPreorder",
"Eq.mpr",
"WithBot.addRightMono",
"WithBot.addLeftMono",
"WithBot",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"covariant_swap_add_of_covariant_add",
"add_le_add",
"Preor... | true |
_private.Init.Data.Array.Lemmas.0.Array.back?_eq_none_iff._simp_1_1 | Init.Data.Array.Lemmas | [
"instOfNatNat",
"List.toArray",
"Array",
"Nat",
"propext",
"Array.size_eq_zero_iff",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Array.size",
"List.nil"
] | false |
CategoryTheory.Functor.pointwiseRightKanExtensionIsPointwiseRightKanExtension | Mathlib.CategoryTheory.Functor.KanExtension.Pointwise | [
"CategoryTheory.Functor.pointwiseRightKanExtensionCounit",
"CategoryTheory.Functor",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.limit.cone",
"CategoryTheory.Iso.refl",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.limit.isLimit",
"CategoryTheory.Functor.RightExtension.IsPointwiseR... | true |
CategoryTheory.CostructuredArrow.isoMk | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToIso",
"CategoryTheory.CostructuredArrow.hom",
"CategoryTheory.Comma.isoMk",
"CategoryTheory.CostructuredArrow",
"CategoryTheory.Iso",
"CategoryTheory.CostructuredArro... | true |
ofBoolAlg_bot | Mathlib.Algebra.Ring.BooleanRing | [
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"BooleanRing.toCommRing",
"AsBoolAlg",
"Equiv",
"Bot.bot",
"ofBoolAlg",
"CommRing.toCommSemiring",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"instBooleanAlgebraAsBoolAlg",
"rfl",
"BooleanAlgebra.toBot",
"BooleanRing",
"Mul... | true |
OpenPartialHomeomorph.EqOnSource.symm_eqOn_target | Mathlib.Topology.OpenPartialHomeomorph.IsImage | [
"PartialEquiv.target",
"OpenPartialHomeomorph.toFun'",
"Set.EqOn",
"TopologicalSpace",
"And.right",
"OpenPartialHomeomorph.eqOnSourceSetoid",
"HasEquiv.Equiv",
"instHasEquivOfSetoid",
"PartialEquiv.source",
"OpenPartialHomeomorph.EqOnSource.symm'",
"OpenPartialHomeomorph.toPartialEquiv",
"Eq",... | true |
List.inits._sunfold | Batteries.Data.List.Basic | [
"List.map",
"List.next?.match_1",
"List.cons",
"List",
"Unit",
"List.inits",
"List.nil"
] | false |
CategoryTheory.Limits.CategoricalPullback.instIsIsoFst | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"_private.Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic.0.CategoryTheory.Limits.CategoricalPullback.instIsIsoFst._proof_1",
"CategoryTheory.Limits.CategoricalPullback.fst",
"Catego... | true |
_private.Init.Data.Nat.Bitwise.Lemmas.0.Nat.mod_two_pow_shiftLeft_mod_two_pow._proof_1_2 | Init.Data.Nat.Bitwise.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"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.Omega.LinearCombo.eval"... | false |
bddBelow_empty._simp_1 | Mathlib.Order.Bounds.Basic | [
"Preorder.toLE",
"bddBelow_empty",
"True",
"BddBelow",
"eq_true",
"Set.instEmptyCollection",
"Nonempty",
"EmptyCollection.emptyCollection",
"Eq",
"Preorder",
"Set"
] | false |
RingHom.toOpposite_apply | Mathlib.Algebra.Ring.Opposite | [
"RingHom.toOpposite",
"MulOpposite",
"Commute",
"RingHom",
"Function.comp",
"instDistribOfSemiring",
"RingHom.instFunLike",
"Distrib.toMul",
"Semiring",
"Eq.refl",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"MulOpposite.instNonAssocSemiring",
"MulOpposite.op"
] | true |
WType.ofList.eq_def | Mathlib.Data.W.Constructions | [
"List.brecOn",
"Eq.mpr",
"List.brecOn.go",
"List.brecOn.eq",
"WType",
"congrArg",
"WType.ofList._f",
"WType.ofList",
"WType.Listβ",
"id",
"WType.Listα",
"List.rec",
"WType.ofList.match_1",
"WType.Listα.cons",
"PEmpty.elim",
"List.cons",
"List",
"WType.mk",
"Unit",
"PProd",
"P... | true |
_private.Init.Data.List.Nat.TakeDrop.0.List.lt_length_right_of_zipWith._proof_1_1 | Init.Data.List.Nat.TakeDrop | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"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.add_congr",
"Int.decLe",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lea... | false |
Filter.TendstoCofinite.mapDomain | Mathlib.Order.Filter.TendstoCofinite | [
"Filter.TendstoCofinite.finite_preimage_singleton",
"Set.instSingletonSet",
"AddCommMonoid",
"Set.preimage",
"Set.Finite.toFinset",
"Singleton.singleton",
"Filter.TendstoCofinite",
"Finset.sum",
"Set"
] | true |
Array.toList_mapIdxM | Init.Data.Array.MapIdx | [
"Eq.mpr",
"Array.mapIdxM",
"congrArg",
"Monad.toApplicative",
"List.mapIdxM",
"LawfulApplicative.toLawfulFunctor",
"id",
"LawfulMonad",
"Array.toList",
"List.toArray",
"Array",
"List",
"Nat",
"True",
"eq_self",
"id_map'",
"of_eq_true",
"Applicative.toFunctor",
"congrFun'",
"Law... | true |
CategoryTheory.FreeMonoidalCategory.normalizeObj_unitor | Mathlib.CategoryTheory.Monoidal.Free.Coherence | [
"CategoryTheory.FreeMonoidalCategory.instMonoidalCategory",
"CategoryTheory.FreeMonoidalCategory.normalizeObj",
"CategoryTheory.FreeMonoidalCategory.categoryFreeMonoidalCategory",
"CategoryTheory.FreeMonoidalCategory",
"CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject",
"CategoryTheory.MonoidalCat... | true |
MeasureTheory.UniformIntegrable.spec | Mathlib.MeasureTheory.Function.UniformIntegrable | [
"MeasureTheory.ae",
"Eq.mpr",
"Exists.choose_spec",
"Real",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"Set.indicator",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"PartialOrder.toPreorder",
"setOf",
"MeasureTheory.UniformIntegrable",
... | true |
Finset.mulETransformRight_snd | Mathlib.Combinatorics.Additive.ETransform | [
"instHSMul",
"instSMulOfMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Finset",
"Group",
"Group.toDivisionMonoid",
"Finset.mulETransformRight",
"DivisionMonoid.toDivInvOneMonoid",
"Finset.smulFinset",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Inter.inter",
"Group.toDivInvM... | true |
_private.Mathlib.Data.List.Sort.0.List.orderedInsert_erase._proof_1_3 | Mathlib.Data.List.Sort | [
"List.erase_nil",
"List.orderedInsert_nil",
"List.pairwise_cons_cons",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"List.Pairwise.cons",
"Lean.Grind.nestedProof",
"List.orderedInsert_cons",
"eq_false",
"instLawfulBEq",
"List.Pairwise",
"Lean.Grind.iff_eq",
"Std.Antisymm",
"congrArg",
... | false |
AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_eq | Mathlib.AlgebraicGeometry.GammaSpecAdjunction | [
"AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace",
"Opposite",
"AlgebraicGeometry.SheafedSpace",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"PrimeSpectrum.basicOpen",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
... | true |
TwoP.concreteCategory._proof_5 | Mathlib.CategoryTheory.Category.TwoP | [
"TwoP.concreteCategory._aux_1",
"CategoryTheory.ConcreteCategory.hom_ofHom._autoParam",
"TwoP.toBipointed",
"Bipointed.hasForget",
"TwoP",
"Bipointed.X",
"Bipointed.HomSubtype",
"autoParam",
"Bipointed",
"TwoP.concreteCategory._aux_3",
"Eq",
"Bipointed.instFunLikeHomSubtypeX",
"CategoryTheor... | false |
ContinuousLinearMap.opNorm_comp_le | Mathlib.Analysis.Normed.Operator.Basic | [
"ContinuousLinearMap.comp",
"Real.instIsOrderedRing",
"Norm.norm",
"Eq.mpr",
"mul_nonneg",
"Real.partialOrder",
"Real.instLE",
"Semigroup.toMul",
"Real",
"SeminormedAddCommGroup",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"NormedSpace",
"Real.instZero",
"congrArg",
"ContinuousLinearMa... | true |
_private.Mathlib.RingTheory.WittVector.Defs.0.term𝕎 | Mathlib.RingTheory.WittVector.Defs | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.Presentable.0.SSet.Finite.exists_epi_from_isCardinalPresentable._simp_1_2 | Mathlib.AlgebraicTopology.SimplicialSet.Presentable | [
"SSet.S.subcomplex",
"Lattice.toSemilatticeSup",
"Opposite",
"CompleteLattice.toLattice",
"iSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"SSet",
"CategoryTheory.instCompleteLatticeSubfunctor",
"OrderTop.to... | false |
ValuativeRel.instLinearOrderValueGroupWithZero._proof_2 | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"CommRing",
"Iff.rfl",
"LE.le",
"And",
"Iff",
"ValuativeRel.instLEValueGroupWithZero",
"ValuativeRel",
"Not",
"ValuativeRel.ValueGroupWithZero"
] | false |
Matrix.conjTransposeAlgEquiv_symm_apply | Mathlib.LinearAlgebra.Matrix.ConjTranspose | [
"Matrix.conjTransposeAlgEquiv",
"Matrix.instStar",
"Matrix.smul",
"Matrix.add",
"CommSemiring.toSemiring",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"MulOpposite",
"Algebra",
"Algebra.toSMul",
"StarAlgEquiv",
"Distrib.toAdd",
"StarAddMonoid.toInvolutiveStar",
"instDistribOfSemiri... | true |
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braiding._proof_5 | Mathlib.CategoryTheory.Monoidal.PushoutProduct | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Arrow.left",
"CategoryTheory.BraidedCategory.braiding_naturality_left",
"CategoryTheory.Arrow.hom",
"CategoryTheory.BraidedCategory",
"Categ... | false |
Lean.Macro.withIncRecDepth | Init.Prelude | [
"Lean.maxRecDepthErrorMessage",
"instMonadExceptOfMonadExceptOf",
"instMonadReaderOfReaderTOfMonad",
"MonadExcept.throw",
"EStateM.instMonad",
"Lean.Macro.Exception",
"MonadReader.read",
"Lean.Syntax",
"Lean.Macro.Exception.error",
"ReaderT.instMonad",
"Lean.Macro.Context.currRecDepth",
"Lean.... | true |
LieIdeal.incl_isIdealMorphism | Mathlib.Algebra.Lie.Ideal | [
"LieAlgebra.toModule",
"LieSubalgebra.lieAlgebra",
"LieSubmodule.instSetLike",
"Eq.mpr",
"LieHom.isIdealMorphism_def",
"CommRing",
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"congrArg",
"LieSubalgebra.incl",
"LieSubalgebra.incl_range",
"Membership.mem",
"LieHom.range",
"id",
... | true |
Lean.Meta.Grind.EMatch.Context.thm._default | Lean.Meta.Tactic.Grind.EMatch | [
"Inhabited.default",
"Lean.Meta.Grind.instInhabitedEMatchTheorem",
"Lean.Meta.Grind.EMatchTheorem",
"id"
] | false |
Std.Internal.IndexMultiMap.entries | Std.Internal.Http.Internal.IndexMultiMap | [
"Array",
"Hashable",
"Std.Internal.IndexMultiMap",
"Prod",
"BEq"
] | true |
Lean.Parser.getSyntaxKindOfParserAlias? | Lean.Parser.Extension | [
"Pure.pure",
"Lean.NameMap",
"IO.instMonadLiftSTRealWorldBaseIO",
"Monad.toApplicative",
"instMonadLiftT",
"IO",
"Lean.NameMap.find?",
"ST.Ref.get",
"IO.RealWorld",
"instMonadEIO",
"Applicative.toPure",
"Lean.Parser.parserAlias2kindRef",
"ST",
"Lean.Name",
"Monad.toBind",
"Bind.bind",
... | true |
CauSeq.inf_le_right | Mathlib.Algebra.Order.CauSeq.Basic | [
"AddGroupWithOne.toAddGroup",
"abs",
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Field.toDivisionRing",
"inf_le_right",
"SemilatticeInf.toPartialOrder",
"GE.ge",
"DistribLattice.toLattice",
"CauSeq.instLEAbs",
"DivisionRing.toRing",
"instOfNatNat",
... | true |
CategoryTheory.Abelian.SpectralObject.cokernelSequenceE._proof_2 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.SpectralObject.H_map_twoδ₂Toδ₁_toCycles_assoc",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.E",
"CategoryTheory.Abelian.SpectralObject.cycles",
"CategoryTheory.Abelian.SpectralObject.δToCycles_πE",
"CategoryTheory.Abelian.SpectralObject.δToCycles"... | false |
CategoryTheory.Pretriangulated.Triangle.shiftFunctorZero_inv_app_hom₁ | Mathlib.CategoryTheory.Triangulated.TriangleShift | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Functor.id",
"CategoryTheory.shiftFunctorZero",
"AddZeroCl... | true |
Polynomial.comp_eq_aeval | Mathlib.Algebra.Polynomial.AlgebraMap | [
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Algebra.id",
"Polynomial",
"CommSemiring",
"Polynomial.semiring",
"Polynomial.aeval",
"Eq",
"Polynomial.comp",
"DFunLike.coe",
"rfl"
] | true |
Std.Time.Year.Offset.Valid | Std.Time.Date.Unit.Year | [
"Std.Time.Month.Ordinal.days",
"Std.Time.Year.Offset.isLeap",
"LE.le",
"Std.Time.Year.Offset",
"Std.Time.Day.Ordinal",
"Std.Time.Day.instLEOrdinal",
"Std.Time.Month.Ordinal"
] | true |
Polynomial.coeff_natDegree_eq_zero_of_degree_lt | Mathlib.Algebra.Polynomial.Degree.Operations | [
"WithBot.instPreorder",
"WithBot",
"Preorder.toLT",
"Polynomial.degree",
"Polynomial.degree_le_natDegree",
"instNatCastNat",
"Nat.cast",
"Polynomial",
"Polynomial.coeff",
"Nat.instPreorder",
"WithBot.natCast",
"Nat",
"LT.lt",
"Semiring",
"Zero.toOfNat0",
"Polynomial.natDegree",
"OfNa... | true |
AddTorsor.nonempty | Mathlib.Algebra.AddTorsor.Defs | [
"outParam",
"AddGroup",
"AddTorsor",
"Nonempty"
] | true |
ModuleCat.exteriorPower.functor_obj | Mathlib.Algebra.Category.ModuleCat.ExteriorPower | [
"CommRing",
"ModuleCat",
"ModuleCat.exteriorPower.functor",
"ModuleCat.exteriorPower",
"Nat",
"ModuleCat.moduleCategory",
"Eq.refl",
"CommRing.toRing",
"Eq",
"CategoryTheory.Functor.obj"
] | true |
Ideal.symm_apply_mem_of_equiv_iff._simp_1 | Mathlib.RingTheory.Ideal.Maps | [
"Semiring.toModule",
"RingEquiv.instEquivLike",
"Membership.mem",
"Distrib.toAdd",
"Ideal.map",
"Ideal.symm_apply_mem_of_equiv_iff",
"Ideal",
"instDistribOfSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Submodule.setLik... | false |
_private.Mathlib.Tactic.NormNum.NatLog.0.Mathlib.Meta.NormNum.evalNatLog.match_1 | Mathlib.Tactic.NormNum.NatLog | [
"Lean.Expr.const",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Sigma.mk",
"Sigma.casesOn",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Sigma",
"List.nil"
] | false |
FirstOrder.Language.BoundedFormula.freeVarFinset.eq_1 | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.BoundedFormula.freeVarFinset",
"Finset",
"Finset.instEmptyCollection",
"FirstOrder.Language.BoundedFormula.falsum",
"Nat",
"Eq.refl",
"FirstOrder.Language",
"EmptyCollection.emptyCollection",
"Eq",
"DecidableEq"
] | true |
Profinite.NobelingProof.GoodProducts.SumEval | Mathlib.Topology.Category.Profinite.Nobeling.Successor | [
"Ordinal.instLinearOrder",
"Preorder.toLT",
"isWellOrder_lt",
"Pi.topologicalSpace",
"Ordinal.partialOrder",
"Profinite.NobelingProof.Products.eval",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"instTopologicalSpaceBool",
"Profinite.NobelingProof.π",
"Membership.mem",
"Semilat... | true |
_private.Mathlib.Probability.Moments.SubGaussian.0.ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul._simp_1_1 | Mathlib.Probability.Moments.SubGaussian | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
_private.Mathlib.Algebra.Module.StablyFree.FreeOfInvertible.0.exteriorPower.cofactorLinear.eq_1 | Mathlib.Algebra.Module.StablyFree.FreeOfInvertible | [
"AlternatingMap",
"CommRing",
"AlternatingMap.smulRight",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"LinearMap.snd",
"AddCommGroup.toAddCommMonoid",
"instDecidableEqFin",
"_private.Mathlib.Algebra.Module.Stabl... | true |
Lean.OpaqueVal._sizeOf_1 | Lean.Declaration | [
"Lean.ConstantVal",
"Lean.Expr",
"instOfNatNat",
"List",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Lean.OpaqueVal",
"Nat",
"List._sizeOf_inst",
"SizeOf.sizeOf",
"Bool",
"Lean.ConstantVal._sizeOf_inst",
"instAddNat",
"Lean.Name",
"Lean.OpaqueVal.rec",
"OfNat.ofNat",
"Bool._si... | false |
RootPairing.corootForm_apply_apply | Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Finset.univ",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RootPairing.flip",
"LinearMap.instFunLike",
"AddCommGroup",
"RootPa... | true |
Std.TreeMap.toList_roo | Std.Data.TreeMap.Slice | [
"Pure.pure",
"Std.Slice.toList",
"Std.TreeMap.instSliceableRooSlice",
"Monad.toApplicative",
"Std.Iterators.Types.Map.instIterator",
"MonadLiftT.monadLift",
"Std.TreeMap.toList_roo._auto_1",
"instMonadLiftT",
"Std.TreeMap.inner",
"Ord.mk",
"Std.DTreeMap.Internal.Impl.WF.ordered",
"Std.DTreeMap... | true |
localCohomology.SelfLERadical.inhabited | Mathlib.Algebra.Homology.LocalCohomology | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CommRing",
"localCohomology.SelfLERadical.inhabited._proof_1",
"Semiring.toModule",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Preorder.smallCategory",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"NonUnitalNo... | true |
_private.Mathlib.RingTheory.HahnSeries.Multiplication.0.HahnModule.coeff_smul_left._simp_1_1 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"And",
"propext",
"not_and'",
"Eq",
"Not"
] | false |
Lean.Grind.CommRing.SimpResult.mk.noConfusion | Lean.Meta.Tactic.Grind.Arith.CommRing.Poly | [
"Lean.Grind.CommRing.Poly",
"id",
"Int",
"Lean.Grind.CommRing.SimpResult.mk",
"Lean.Grind.CommRing.SimpResult",
"Lean.Grind.CommRing.SimpResult.noConfusion",
"Eq",
"Lean.Grind.CommRing.Mon"
] | false |
Homeomorph.Quot.congrLeft._proof_1 | Mathlib.Topology.Homeomorph.Quotient | [
"congrArg",
"iff_self",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Iff",
"Homeomorph.symm",
"congr",
"True",
"Homeomorph",
"of_eq_true",
"Homeomorph.symm_apply_apply",
"DFunLike.coe",
"Eq.trans",
"EquivLike.toFunLike"
] | false |
_private.Init.Data.Int.Order.0.Int.sign.match_1.eq_3 | Init.Data.Int.Order | [
"Int.ofNat",
"instOfNatNat",
"Int",
"Unit",
"Nat",
"Eq.refl",
"Int.negSucc",
"OfNat.ofNat",
"Int.sign.match_1",
"Nat.succ",
"Eq"
] | true |
_private.Lean.Meta.Match.Basic.0.Lean.Meta.Match.Alt.toMessageData.match_1 | Lean.Meta.Match.Basic | [
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
AddAction.ofEndHom | Mathlib.Algebra.Group.Action.End | [
"Function.End",
"Monoid.toMulOneClass",
"Additive",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Additive.addZeroClass",
"AddAction",
"AddAction.compHom",
"instMonoidEnd",
"AddMonoid",
"Additive.addMonoid",
"AddMonoidHom",
"Function.End.applyAddAction"
] | true |
Real.Angle.abs_toReal_neg_coe_eq_self_iff | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"abs_neg",
"Real.partialOrder",
"Real.instLE",
"Real",
"Real.pi",
"Real.lattice",
"Real.Angle",
"Real.Angle.coe",
"Real.Angle.abs_toReal_le_pi",
"Real.instZero",
"abs",
"congrArg",
"Real.Angle.toReal_pi",
"c... | true |
_private.Mathlib.MeasureTheory.Measure.Haar.NormedSpace.0.MonoidHom.exists_nhds_isBounded._simp_1_4 | Mathlib.MeasureTheory.Measure.Haar.NormedSpace | [
"Set.instInter",
"Inter.inter",
"Set.inter_iUnion",
"Eq.symm",
"Eq",
"Set.iUnion",
"Set"
] | false |
CategoryTheory.Idempotents.toKaroubi_comp_karoubiFunctorCategoryEmbedding | Mathlib.CategoryTheory.Idempotents.FunctorCategories | [
"CategoryTheory.Idempotents.Karoubi.Hom.f",
"CategoryTheory.Functor",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"CategoryTheory.Functor.ext",
"congrArg",
"CategoryTheory.Idempotents.Karoubi.eqToHom_f",
"CategoryThe... | true |
Std.Do.Spec.forIn_iter._proof_4 | Std.Do.Triple.SpecLemmas | [
"congrArg",
"Id",
"List.append_nil",
"Std.Iterator",
"instHAppendOfAppend",
"List",
"Std.Iter",
"Std.Iter.toList",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"List.instAppend",
"Eq",
"HAppend.hAppend",
"Eq.trans",
"List.nil"
] | false |
Int.ModEq.instIsTrans | Mathlib.Data.Int.ModEq | [
"IsTrans.mk",
"Int.ModEq.trans",
"Int",
"IsTrans",
"Int.ModEq"
] | true |
SSet.Subcomplex.Pairing.RankFunction.Cell._sizeOf_1 | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | [
"SSet.Subcomplex.Pairing.RankFunction.rank",
"SSet.Subcomplex.Pairing.RankFunction.Cell.rec",
"LinearOrder",
"instSizeOfDefault",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"SSet.Subcomplex.N",
"Set.Elem",
"DistribLattice.toLattice",
"instOfNatNat",
"SSet",
"SSet.Subcomplex.Pairing",
... | false |
Uniformity.term𝓤 | Mathlib.Topology.UniformSpace.Defs | [
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"OfNat.ofNat"
] | true |
Quot.mk | Init.Prelude | [
"Quot"
] | true |
TemperedDistribution.delta._proof_3 | Mathlib.Analysis.Distribution.TemperedDistribution | [
"Complex.instNormedField",
"NormedField.toField",
"RingHomCompTriple",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Complex",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring",
"Complex.instSemiring"
] | false |
Submodule.instModuleQuotientIdealSpanSingletonSetSubtypeMemTorsionBy._proof_5 | Mathlib.Algebra.Module.Torsion.Basic | [
"Submodule.instModuleQuotientIdealSpanSingletonSetSubtypeMemTorsionBy._proof_3",
"Submodule",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.torsion... | false |
ContinuousMap.HomotopyWith.prop | Mathlib.Topology.Homotopy.Basic | [
"Real",
"ContinuousMap.HomotopyWith.prop'",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMap.Homotopy.curry",
"Membership.mem",
"Set.Elem",
"ContinuousMap.HomotopyWith",
"TopologicalSpace",
"ContinuousMap.HomotopyWith.toHomotopy",
"Real.pseudoMetricSpace",
"instTopologicalSp... | true |
arrowAddAction._proof_2 | Mathlib.Algebra.Group.Action.Basic | [
"NegZeroClass.toNeg",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"VAdd.mk",
"HVAdd.hVAdd",
... | false |
locallyConnectedSpace_iff_isTopologicalBasis_isOpen_isPreconnected | Mathlib.Topology.Connected.LocallyConnected | [
"IsConnected",
"setOf",
"Membership.mem",
"nhds",
"id",
"LocallyConnectedSpace.mk",
"TopologicalSpace",
"TopologicalSpace.IsTopologicalBasis.isOpen_isPreconnected",
"And",
"Iff",
"Iff.intro",
"TopologicalSpace.IsTopologicalBasis",
"_private.Mathlib.Topology.Connected.LocallyConnected.0.local... | true |
_private.Mathlib.NumberTheory.DirichletCharacter.Basic.0.DirichletCharacter.factorsThrough_one_iff.match_1_1 | Mathlib.NumberTheory.DirichletCharacter.Basic | [
"Dvd.dvd",
"MonoidHom.instFunLike",
"DirichletCharacter.FactorsThrough",
"ZMod.commRing",
"MonoidHom",
"Monoid.toMulOneClass",
"Exists",
"DivInvMonoid.toMonoid",
"instOfNatNat",
"ZMod",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Exists.casesOn",
"Nat.instDvd",
"CommMonoidWithZero",... | false |
CategoryTheory.Limits.CoproductDisjoint | Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct | [
"CategoryTheory.Limits.CoproductDisjoint.mk",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Tactic.Widget.LibraryRewrite.0.Mathlib.Tactic.LibraryRewrite.getBinderInfos.match_3 | Mathlib.Tactic.Widget.LibraryRewrite | [
"MProd.casesOn",
"Lean.Expr",
"MProd.mk",
"Array",
"Nat",
"MProd",
"Lean.BinderInfo"
] | false |
_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.truncatedSup_union_left._simp_1_2 | Mathlib.Combinatorics.SetFamily.AhlswedeZhang | [
"Finset",
"Membership.mem",
"SetLike.coe",
"Finset.instSetLike",
"propext",
"Eq",
"Set.instMembership",
"Finset.mem_coe",
"SetLike.instMembership",
"Set"
] | false |
ByteArray.mapMUnsafe.loop | Batteries.Data.ByteArray | [
"Pure.pure",
"Monad.toApplicative",
"ByteArray.mapMUnsafe.loop",
"ByteArray.usize",
"lcProof",
"Applicative.toPure",
"ByteArray.uget",
"instHAdd",
"HAdd.hAdd",
"USize.toNat",
"Nat",
"LT.lt",
"instLTUSize",
"Monad.toBind",
"Bind.bind",
"ByteArray.uset",
"instLTNat",
"ByteArray",
"... | true |
QuotientAddGroup.quotientInfEquivSumNormalizerQuotient._proof_4 | Mathlib.GroupTheory.QuotientGroup.Basic | [
"AddMonoidHom.normal_ker",
"AddSubgroup.instCompleteLattice",
"Lattice.toSemilatticeSup",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"QuotientAddGroup.quotientInfEquivSumNormalizerQuotient._proof_1",
"Preorder.toLE",
"AddSubgroup.inclusion",
"AddSubgroup... | false |
_private.Mathlib.Tactic.Translate.GuessName.0.Mathlib.Tactic.GuessName.fixAbbreviationAux._unary.eq_def | Mathlib.Tactic.Translate.GuessName | [
"Eq.mpr",
"String.join",
"congrArg",
"String",
"invImage",
"List.instGetElem?NatLtLength",
"_private.Mathlib.Tactic.Translate.GuessName.0.PSigma.casesOn._arg_pusher",
"_private.Mathlib.Tactic.Translate.GuessName.0.Mathlib.Tactic.GuessName.fixAbbreviationAux.match_3._arg_pusher",
"Mathlib.Tactic.Gues... | false |
FreeAddMonoid.mem_of_self | Mathlib.Algebra.FreeMonoid.Basic | [
"FreeAddMonoid.of",
"List.mem_singleton_self",
"FreeAddMonoid.instMembership",
"Membership.mem",
"FreeAddMonoid"
] | true |
AlgebraicGeometry.Scheme.image_preimage_eq_of_isPullback | Mathlib.AlgebraicGeometry.PullbackCarrier | [
"Eq.mpr",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"and_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
"CategoryTheory.IsPullback",
"Set.i... | true |
GradedTensorProduct.instRing._proof_14 | Mathlib.LinearAlgebra.TensorProduct.Graded.Internal | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"SubNegMonoid.zsmul_succ'",
"GradedTensorProduct",
"CommRing",
"AddMonoid.toAddSemigroup",
"Ring.toNonAssocRing",
"instAddCommGroupWithOneGradedTensorProduct",
"CommSemiring.toSemiring",
"Algebra",
"AddCommGroup.toAddGroup",
"Algebra.toMo... | false |
_private.Lean.Meta.Tactic.Grind.Order.Assert.0.Lean.Meta.Grind.Order.propagatePending.getOriginal? | Lean.Meta.Tactic.Grind.Order.Assert | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Sym.ExprPtr.mk",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Grind.Order.State.termMapInv",
"Lean.Meta.Sym.Context",
"ReaderT.instMonad",
"Lean.Meta.Grind.Context",
"Lean.Expr",
... | true |
Prod.noConfusion | Init.Prelude | [
"HEq.refl",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Prod",
"Prod.casesOn",
"Prod.noConfusionType",
"Eq"
] | false |
LE.le.absolutelyContinuous | Mathlib.MeasureTheory.Measure.AbsolutelyContinuous | [
"MeasureTheory.Measure",
"PartialOrder.toPreorder",
"Preorder.toLE",
"MeasureTheory.Measure.AbsolutelyContinuous",
"LE.le",
"MeasurableSpace",
"MeasureTheory.Measure.instPartialOrder",
"MeasureTheory.Measure.absolutelyContinuous_of_le"
] | true |
Mathlib.Tactic.MkIff.mkOrList | Mathlib.Tactic.MkIffOfInductiveProp | [
"Lean.Expr",
"Lean.Level",
"Lean.mkConst",
"List",
"Mathlib.Tactic.MkIff.mkOpList",
"Lean.Name.mkStr1",
"List.nil"
] | true |
Algebra.TensorProduct.map_comp_includeLeft | Mathlib.RingTheory.TensorProduct.Maps | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"AlgHom.algHomClass",
"congrArg",
"CommSemiring.toSemiring",
"Algebra.TensorProduct.map",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"Algebra",
"Algebra.toSMul",
"MonoidHomClass.toOneHomClass",
"Algebra.toModule",
"RingHomClass.toMonoidWithZeroHom... | true |
AddSubgroup.quotientiInfEmbedding.eq_1 | Mathlib.GroupTheory.Coset.Basic | [
"AddSubgroup.instCompleteLattice",
"iInf",
"AddSubgroup.quotientMapOfLE",
"AddSubgroup.quotientiInfEmbedding",
"AddSubgroup.instInfSet",
"Function.Embedding.mk",
"AddSubgroup.quotientiInfEmbedding._proof_1",
"Function.Embedding",
"AddSubgroup",
"CompleteLattice.toCompleteSemilatticeInf",
"HasQuo... | true |
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