name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Hindman.FS.below.tail' | Mathlib.Combinatorics.Hindman | [
"Hindman.FS.tail'",
"Hindman.FS.below",
"AddSemigroup",
"Stream'",
"Hindman.FS.below.tail'",
"Hindman.FS",
"Stream'.tail"
] | true |
_private.Init.Data.Format.Basic.0.Std.Format.SpaceResult.mk | Init.Data.Format.Basic | [
"_private.Init.Data.Format.Basic.0.Std.Format.SpaceResult",
"_private.Init.Data.Format.Basic.0.Std.Format.SpaceResult.mk",
"Nat",
"Bool"
] | true |
TypeVec.lastFun_appendFun | Mathlib.Data.TypeVec | [
"TypeVec.last",
"TypeVec.append1",
"TypeVec.lastFun",
"Nat",
"TypeVec.appendFun",
"TypeVec.Arrow",
"Eq",
"rfl",
"TypeVec"
] | true |
_private.Mathlib.Algebra.Polynomial.FieldDivision.0.Polynomial.remainder_lt_aux | Mathlib.Algebra.Polynomial.FieldDivision | [
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"WithBot",
"Preorder.toLT",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"Polynomial.degree_mul_leadingCoeff_inv",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"DivisionSemiring.toGroupWithZero",
"Ring... | true |
UInt16.xor_eq_zero_iff._simp_1 | Init.Data.UInt.Bitwise | [
"UInt16",
"UInt16.xor_eq_zero_iff",
"HXor.hXor",
"propext",
"instXorOpUInt16",
"OfNat.ofNat",
"Eq",
"UInt16.instOfNat",
"instHXorOfXorOp"
] | false |
_private.Mathlib.RingTheory.TensorProduct.DirectLimitFG.0.TensorProduct.Algebra.eq_of_fg_of_subtype_eq._simp_1_11 | Mathlib.RingTheory.TensorProduct.DirectLimitFG | [
"Set.subset_union_right",
"Set.instUnion",
"HasSubset.Subset",
"True",
"eq_true",
"Union.union",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
CategoryTheory.OverPresheafAux.OverArrows.yonedaArrow_val | Mathlib.CategoryTheory.Comma.Presheaf.Basic | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.OverPresheafAux.OverArrows.val",
"CategoryTheory.Functor.category",
"CategoryTheory.yoneda",
"CategoryTheory.Functor.map",
"CategoryTheory.OverPresheafAux.OverArrows.yonedaArrow",
"Opposit... | true |
SNum._aux_Mathlib_Data_Num_Bitwise___unexpand_SNum_bit_1 | Mathlib.Data.Num.Bitwise | [
"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 |
IO.instLTTaskState | Init.System.IO | [
"IO.TaskState",
"ltOfOrd",
"IO.instOrdTaskState",
"LT"
] | true |
Lean.Lsp.SnippetString.noConfusion | Lean.Data.Lsp.Basic | [
"Lean.Lsp.SnippetString.noConfusionType",
"String",
"Lean.Lsp.SnippetString",
"Lean.Lsp.SnippetString.casesOn",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | false |
Aesop.NormM.Context.rec | Aesop.Search.Expansion.Norm | [
"Aesop.NormM.Context.mk",
"Aesop.Options'",
"Aesop.LocalRuleSet",
"Aesop.NormM.Context",
"Aesop.NormSimpContext"
] | false |
Continuous.cexp | Mathlib.Analysis.SpecialFunctions.Exp | [
"Iff.mpr",
"NormedCommRing.toSeminormedCommRing",
"Continuous",
"ContinuousAt",
"ContinuousAt.cexp",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"Continuous.continuousAt",
"TopologicalSpace",
"Complex.exp",
"SeminormedCommRing.toSeminormedRing",
"SeminormedRing.toPseudoMetri... | true |
HomologicalComplex.hasExactColimitsOfShape | Mathlib.Algebra.Homology.GrothendieckAbelian | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.preservesColimitNatIso",
"CategoryTheory.Limits.Cone",
"HomologicalComplex.instCategory",
"CategoryTheory.HasExactColimitsOfShape",
"CategoryTheory.Limits.IsLimit.postcomposeHomEquiv",
... | true |
Lean.Meta.DiscrTree.Key.arrow | Lean.Meta.DiscrTree.Types | [
"Lean.Meta.DiscrTree.Key",
"Lean.Meta.DiscrTree.Key.arrow"
] | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.le_two_mul_toInt._proof_1_2 | Init.Data.BitVec.Lemmas | [
"instPowNat",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"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",
"Lean.Omega.LinearCombo.eval",
"Opti... | false |
IsRightUniformGroup.mk._flat_ctor | Mathlib.Topology.Algebra.IsUniformGroup.Defs | [
"UniformSpace",
"Continuous",
"ContinuousInv.mk",
"InvOneClass.toOne",
"HMul.hMul",
"IsRightUniformGroup.mk",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"uniformity",
"instTopologicalSpaceProd",
"Group",
"IsTopologicalGroup.mk",
"Group.toDivisionMonoid",
"DivisionMonoid.toDiv... | false |
Language.reverse_zero | Mathlib.Computability.Language | [
"Language.reverse",
"Language.instZero",
"Zero.toOfNat0",
"Language",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
Nat.add_choose | Mathlib.Data.Nat.Choose.Basic | [
"Eq.mpr",
"Nat.add_sub_cancel_right",
"Nat.choose",
"instHDiv",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"Nat.le_add_left",
"id",
"HDiv.hDiv",
"instSubNat",
"instMulNat",
"Nat.mul_comm",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat.factorial",
"Nat",
"Nat.instDiv",
"instAddNat",
"E... | true |
CategoryTheory.Functor.FullyFaithful.preimage | Mathlib.CategoryTheory.Functor.FullyFaithful | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.FullyFaithful",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
AlgebraicGeometry.HasRingHomProperty.of_source_openCover | Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties | [
"AlgebraicGeometry.Scheme.Hom.opensFunctor",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.HasRingHomProperty",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"CommRing",
"AlgebraicGeometry.Scheme",
"Lattice.toSemilatticeSup",
"CategoryTheory.PreZeroHypercover... | true |
_private.Init.Grind.Ring.Basic.0.Lean.Grind.Ring.intCast_add._proof_1_6 | Init.Grind.Ring.Basic | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Om... | false |
Lean.Elab.Tactic.Doc.TacticDoc._sizeOf_inst | Lean.Elab.Tactic.Doc | [
"Lean.Elab.Tactic.Doc.TacticDoc._sizeOf_1",
"SizeOf.mk",
"Lean.Elab.Tactic.Doc.TacticDoc",
"SizeOf"
] | false |
GaloisInsertion.choice_eq | Mathlib.Order.GaloisConnection.Defs | [
"Preorder.toLE",
"LE.le",
"GaloisInsertion.choice",
"GaloisInsertion",
"Eq",
"Preorder"
] | true |
PrimeSpectrum.zeroLocusEquivIrreducibleCloseds | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"OrderDual.instLE",
"OrderDual.toDual",
"PrimeSpectrum.zeroLocus",
"PrimeSpectrum.instQuasiSoberElemZeroLocus",
"RelIso.mk",
"irreducibleSetEquivPoints",
"Equiv.trans",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.Elem",
"Equiv",
"OrderIso",
"LE.le",
"TopologicalSpa... | true |
CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesEIso_inv_τ₂ | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.ShortComplex.toCycles_comp_homologyπ",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.cokernelSequenceCyclesE",
"CategoryTheory.Abelian.SpectralObject.cycles",
"CategoryTheory.ShortComplex.homologyπ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",... | true |
Units.instStarMul._proof_4 | Mathlib.Algebra.Star.Basic | [
"Monoid",
"Units.val",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"Units.inv_val",
"StarMul",
"Units",
"MulOne.toMul",
"Units.instStarMul._proof_2",
"congr_arg",
"MulOneClass.toMulOne",
"Inv.inv",
"Units.mk",
"StarMul.toInvolutiveStar",
"StarMul.star_mul",
"One.toOfNat1",
... | false |
Lean.Parser.Term.noImplicitLambda._regBuiltin.Lean.Parser.Term.noImplicitLambda_1 | Lean.Parser.Term | [
"Lean.Parser.Term.noImplicitLambda",
"IO",
"Unit",
"Lean.Parser.addBuiltinLeadingParser",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
_private.Mathlib.Algebra.Homology.HomotopyCategory.MappingCone.0.CochainComplex.mappingCone.fst._proof_3 | Mathlib.Algebra.Homology.HomotopyCategory.MappingCone | [
"False",
"congrArg",
"Classical.byContradiction",
"False.casesOn",
"Int",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"True",
"eq_self",
"Int.instAdd",
"Lean.Grind.not_true",
"Lean.Grind.intro_with_eq",
"OfNat.ofNat",
"Eq",
"Not",
"Eq.trans"
] | false |
Orthonormal.basisTensorProduct | Mathlib.Analysis.InnerProductSpace.TensorProduct | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"SeminormedAddCommGroup",
"Orthonormal",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"TensorProduct.addCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"TensorProduct.instNormedAddCommGroup",
"Algebra.id",
"Eq.casesOn",
"Module.Basis.in... | true |
instCoeTCBiheytingHomOfBiheytingHomClass._proof_3 | Mathlib.Order.Heyting.Hom | [
"BiheytingAlgebra",
"BiheytingHomClass.toHeytingHomClass",
"HeytingHomClass.map_himp",
"GeneralizedHeytingAlgebra.toHImp",
"BiheytingAlgebra.toHeytingAlgebra",
"HeytingAlgebra.toGeneralizedHeytingAlgebra",
"Eq",
"DFunLike.coe",
"FunLike",
"HImp.himp",
"BiheytingHomClass"
] | false |
HomologicalComplex₂.total.map | Mathlib.Algebra.Homology.TotalComplex | [
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex₂.toGradedObject",
"HomologicalComplex.Hom.mk",
"HomologicalComplex₂.toGradedObjectMap",
"HomologicalComplex₂.HasTotal",
"HomologicalComplex",
"ComplexShape",
"CategoryTheory.Preadditive",... | true |
CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategorySnd._proof_6 | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | [
"Eq.mpr",
"CategoryTheory.Over",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Over.homMk.congr_simp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Over.mk",
"CategoryTheory.MonoidalCategory.whiskerLeft_c... | false |
Height.logHeight_fun_mul_eq | Mathlib.NumberTheory.Height.Basic | [
"Real.log_mul._simp_1",
"Eq.mpr",
"Real.partialOrder",
"Real",
"HMul.hMul",
"Real.instZero",
"congrArg",
"Finite",
"PartialOrder.toPreorder",
"Height.mulHeight_pos",
"ne_of_gt",
"Height.AdmissibleAbsValues",
"id",
"Pi.instZero",
"Ne",
"Real.log",
"Field.toSemifield",
"Prod.fst",
... | true |
_private.Mathlib.NumberTheory.Rayleigh.0.Beatty.no_collision.match_1_3 | Mathlib.NumberTheory.Rayleigh | [
"Real",
"setOf",
"Membership.mem",
"Exists",
"Int",
"Exists.casesOn",
"Exists.intro",
"beattySeq'",
"Eq",
"Set.instMembership",
"Set"
] | false |
Std.PRange.Nat.size_Rio | Init.Data.Range.Polymorphic.NatLemmas | [
"Std.PRange.instHasSizeNat_1",
"Std.Rio.mk",
"Nat.size_rio",
"Nat",
"Std.PRange.instLeast?Nat",
"Eq",
"Std.Rio.size"
] | true |
PUnit.normedCommRing._proof_2 | Mathlib.Analysis.Normed.Ring.Basic | [
"PUnit.normedAddCommGroup",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddGroup",
"instHAdd",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"PUnit",
"NormedAddCommGroup.toAddCommGroup",
"SubNegMonoid.toAddMonoid",
"Eq",
"AddCommGroup.add_comm"
] | false |
SSet.horn₂₂.isPushout | Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SSet.horn₂₂.sq",
"Finset",
"instDecidableEqFin",
"CategoryTheory.Functor.category",
"CategoryTheory.CosimplicialObject.δ",
"Lattice.BicartSq.le₂₄",
"Ca... | true |
MeasureTheory.ComplexMeasure.re | Mathlib.MeasureTheory.Measure.Complex | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedSpace.toIsBoundedSMul",
"MeasureTheory.ComplexMeasure.re._proof_4",
"UniformContinuousConstSMul.to_continuousConstSMul",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"M... | true |
MonCat.Colimits.coconeMorphism._proof_1 | Mathlib.Algebra.Category.MonCat.Colimits | [
"MulOne.toOne",
"CategoryTheory.Functor",
"Quot.sound",
"MonCat.Colimits.colimitSetoid",
"Monoid.toMulOneClass",
"MonCat.Colimits.Prequotient",
"MonCat",
"MonCat.Colimits.Prequotient.of",
"MonCat.instCategory",
"MonCat.carrier",
"MonCat.Colimits.Relation.one",
"MulOneClass.toMulOne",
"MonCat... | false |
Qq.Impl.ExprBackSubstResult | Qq.Macro | [
"Qq.Impl.ExprBackSubstResult.quoted",
"Qq.Impl.ExprBackSubstResult.unquoted"
] | true |
Besicovitch.TauPackage.iUnionUpTo.eq_1 | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Preorder.toLT",
"Besicovitch.TauPackage",
"Besicovitch.TauPackage.iUnionUpTo",
"Ordinal.partialOrder",
"Besicovitch.TauPackage.index",
"PartialOrder.toPreorder",
"Besicovitch.BallPackage.r",
"Subtype",
"Metric.ball",
"Besicovitch.BallPackage.c",
"MetricSpace",
"Besicovitch.TauPackage.toBallPa... | true |
_private.Mathlib.LinearAlgebra.Semisimple.0.Module.End.IsSemisimple.of_mem_adjoin_pair._simp_1_2 | Mathlib.LinearAlgebra.Semisimple | [
"IsRadical",
"CommSemiring.toNonUnitalCommSemiring",
"CommSemiring.toSemiring",
"semigroupDvd",
"SemigroupWithZero.toSemigroup",
"Set.instSingletonSet",
"NonUnitalSemiring.toSemigroupWithZero",
"isRadical_iff_span_singleton",
"Monoid.toPow",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"CommSemi... | false |
ProbabilityTheory.Kernel.instIsFiniteKernelSectROfProd | Mathlib.Probability.Kernel.Composition.MapComap | [
"Eq.mpr",
"ProbabilityTheory.Kernel.comap",
"ProbabilityTheory.IsFiniteKernel",
"congrArg",
"inferInstance",
"id",
"Prod.mk",
"MeasurableSpace",
"ProbabilityTheory.Kernel.sectR.eq_1",
"ProbabilityTheory.Kernel.IsFiniteKernel.comap",
"ProbabilityTheory.Kernel.sectR._proof_1",
"ProbabilityTheory... | true |
_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.withAlts | Lean.Meta.Match.Match | [
"Lean.Meta.Match.AltParamInfo",
"Lean.Meta.Match.Alt",
"Lean.Meta.Match.AltLHS",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.Match.Overlaps",
"List.toArray",
"Array",
"List",
"_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.withAlts.loop",
"Lean.Meta.Match.DiscrInfo",
"List.nil",
"Option"
] | true |
Std.Rii.pairwise_toList_ne | Init.Data.Range.Polymorphic.Lemmas | [
"Std.PRange.UpwardEnumerable",
"List.Pairwise",
"Std.PRange.UpwardEnumerable.LT",
"Std.PRange.LawfulUpwardEnumerableLeast?",
"Std.Rxi.instIteratorIteratorIdOfUpwardEnumerable",
"Ne",
"Std.Rii.pairwise_toList_upwardEnumerableLt",
"Std.Rxi.IsAlwaysFinite",
"Std.Rii.toList",
"Std.Rxi.Iterator.instFin... | true |
CategoryTheory.PresheafOfGroups.OneCocycle.mk | Mathlib.CategoryTheory.Sites.NonabelianCohomology.H1 | [
"CategoryTheory.Functor",
"CategoryTheory.PresheafOfGroups.OneCocycle",
"GrpCat",
"Opposite",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"GrpCat.str",
"Monoid.toMulOneClass",
"CategoryTheory.PresheafOfGroups.OneCochain",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Cat... | true |
CategoryTheory.MonoidalCategory.«term_◁ᵢ_» | Mathlib.CategoryTheory.Monoidal.Category | [
"Lean.Name.mkStr3",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
hasFDerivAt_apply | Mathlib.Analysis.Calculus.FDeriv.Prod | [
"HasFDerivAt",
"NormedSpace",
"Pi.topologicalSpace",
"ContinuousLinearMap.hasFDerivAt",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Pi.module",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Field.toSemifield",
"ContinuousLinearMap.proj",
"Semifield.toDivisionSemiring... | true |
Filter.le_prod | Mathlib.Order.Filter.Prod | [
"SProd.sprod",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Filter.tendsto_prod_iff'",
"LE.le",
"Prod.fst",
"And",
"Iff",
"Filter.Tendsto",
"Prod",
"Filter.instSProd",
"Prod.snd",
"Filter",
"Filter.instPartialOrder"
] | true |
Multiset.union_comm | Mathlib.Data.Multiset.UnionInter | [
"Lattice.toSemilatticeSup",
"Multiset.instLattice",
"Multiset",
"sup_comm",
"Multiset.instUnion",
"Union.union",
"Eq",
"DecidableEq"
] | true |
skewAdjoint.instSMulSubtypeMemAddSubgroupOfStarModule | Mathlib.Algebra.Star.SelfAdjoint | [
"Monoid",
"skewAdjoint.instSMulSubtypeMemAddSubgroupOfStarModule._proof_1",
"instHSMul",
"DistribMulAction.toDistribSMul",
"SMul",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Subtype",
"DistribSMul.toSMulZeroClass",
"SMu... | true |
Lean.Lsp.TextDocumentChangeRegistrationOptions.mk._flat_ctor | Lean.Data.Lsp.TextSync | [
"Lean.Lsp.DocumentSelector",
"Lean.Lsp.TextDocumentSyncKind",
"Lean.Lsp.TextDocumentChangeRegistrationOptions.mk",
"Lean.Lsp.TextDocumentChangeRegistrationOptions",
"Option"
] | false |
_private.Qq.ForLean.Do.0.Lean.Elab.Term.extractBind.match_1 | Qq.ForLean.Do | [
"Lean.Expr",
"Nat.hasNotBit",
"_private.Qq.ForLean.Do.0.Lean.Elab.Term.extractBind._sparseCasesOn_1",
"Lean.Expr.app",
"Lean.Expr.ctorIdx"
] | false |
Rat.mul_eq_mkRat | Mathlib.Data.Rat.Defs | [
"Rat.normalize_eq_mkRat",
"Eq.mpr",
"Rat.mul_def",
"Rat.instMul",
"Rat.num",
"HMul.hMul",
"Nat.mul_ne_zero",
"congrArg",
"Rat",
"Rat.den",
"id",
"instMulNat",
"Int",
"Rat.normalize",
"Int.instMul",
"Rat.den_nz",
"mkRat",
"Nat",
"Eq.refl",
"Eq",
"instHMul"
] | true |
CategoryTheory.Localization.SmallShiftedHom.equiv | Mathlib.CategoryTheory.Localization.SmallShiftedHom | [
"CategoryTheory.Iso.homToEquiv",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.Localization.SmallHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Equiv.trans",
"CategoryTheory.Localization.SmallHom.equiv",
"CategoryTheory.Functor.comp",
"CategoryTheory.... | true |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.toArray_rcc_ne_empty_iff._simp_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"LE.le",
"instLENat",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Nat.succ_le_iff",
"Nat.succ",
"Eq"
] | false |
CategoryTheory.Limits.isColimitOfConeUnopOfCocone | Mathlib.CategoryTheory.Limits.Opposites | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Opposite",
"CategoryTheory.Limits.coneUnopOfCocone",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Functor.unop",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Category.opposite",
"CategoryTheory.Limits.isColimitCoconeOfConeUnop",
... | true |
Lean.Lsp.Hover.mk.inj | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.Hover.mk",
"Lean.Lsp.Hover",
"Lean.Lsp.MarkupContent",
"Lean.Lsp.Hover.mk.noConfusion",
"And",
"And.intro",
"Lean.Lsp.Range",
"Eq",
"Option"
] | true |
Int.neg_neg | Init.Data.Int.Lemmas | [
"_private.Init.Data.Int.Lemmas.0.Int.neg_neg.match_1_1",
"Int.instNegInt",
"Int",
"Nat.cast",
"Unit",
"instOfNat",
"Nat",
"instNatCastInt",
"Int.negSucc",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Neg.neg",
"rfl"
] | true |
CategoryTheory.ShortComplex.leftRightHomologyComparison'_fac | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.leftHomologyData",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.ShortComplex.HomologyData.iso",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ShortComplex.ri... | true |
AffineEquiv.mk.inj | Mathlib.LinearAlgebra.AffineSpace.AffineEquiv | [
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Equiv",
"AffineEquiv.mk",
"AffineEquiv.mk.noConfusion",
"HVAdd.hVAdd",
"AddAction.toAddSemigroupAction",
"And",
"AddSemigroupAction.toVAdd",
"AddGroup.toSubNegMonoid... | true |
RootPairing.Base.cartanMatrix_apply_eq_zero_iff_symm | Mathlib.LinearAlgebra.RootSystem.CartanMatrix | [
"IsDomain",
"RootPairing.pairing",
"CommRing",
"CharZero.NeZero.two",
"congrArg",
"CommSemiring.toSemiring",
"RootPairing.pairing_eq_zero_iff",
"RootPairing.Base",
"AddCommGroup.toAddCommMonoid",
"Finset",
"Module.IsReflexive",
"AddGroupWithOne.toAddMonoidWithOne",
"RootPairing.IsCrystallogr... | true |
_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.Result.mk.inj | Lean.Meta.LetToHave | [
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.Result.mk",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.Result.mk.noConfusion",
"Lean.Expr",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.Result",
"And",
"And.intro",
"Eq",
"Option"
] | true |
Mathlib.TacticAnalysis.Config.mk._flat_ctor | Mathlib.Tactic.TacticAnalysis | [
"Mathlib.TacticAnalysis.Config",
"Mathlib.TacticAnalysis.Config.mk",
"Array",
"Unit",
"Lean.Elab.Command.CommandElabM",
"Mathlib.TacticAnalysis.TacticNode"
] | false |
_private.Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions.0.CategoryTheory.Localization.exists_leftFraction₂.match_1_1 | Mathlib.CategoryTheory.Localization.CalculusOfFractions.Fractions | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Exists",
"CategoryTheory.MorphismProperty.LeftFraction.map",
"CategoryTheory.MorphismProperty.LeftFraction",
"CategoryTheory.Functor.IsLocalization",
"Exists.casesOn",
"Exists.intr... | false |
_private.Mathlib.Topology.ContinuousOn.0.continuousOn_prod_of_discrete_right._simp_1_3 | Mathlib.Topology.ContinuousOn | [
"ContinuousWithinAt",
"DiscreteTopology",
"setOf",
"instTopologicalSpaceProd",
"Membership.mem",
"continuousWithinAt_prod_of_discrete_right",
"Prod.mk",
"Prod.fst",
"TopologicalSpace",
"propext",
"Prod",
"Eq",
"Set.instMembership",
"Prod.snd",
"Set"
] | false |
Filter.commMonoid._proof_5 | Mathlib.Order.Filter.Pointwise | [
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"MulOneClass.mul_one",
"Filter.mulOneClass",
"MulOne.toMul",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"CommMonoid",
"Filter",
"instHMul"
] | false |
SSet.homotopyEquivNormalizedChainComplex_hom | Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | [
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"HomologicalComplex",
"SSet.normalizedChainComplex",
"Nat.instAddCancelCommMonoid",
"SSet",
"CategoryTheor... | true |
_private.Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol.0.fastJacobiSym._proof_6 | Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | [
"instHDiv",
"Nat.instIsOrderedAddMonoid",
"AddMonoid.toAddSemigroup",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Nat.instZeroLEOneClass",
"HDiv.hDiv",
"IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono",
"Nat.div_lt_self",
"instOfNatNat",
"Nat.instAddMonoidWithOne",
"AddSemigroup.toAdd",
"Nat.in... | false |
Std.DTreeMap.Internal.RoiSliceData._sizeOf_inst | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"Std.DTreeMap.Internal.RoiSliceData._sizeOf_1",
"Std.DTreeMap.Internal.RoiSliceData",
"SizeOf.mk",
"SizeOf"
] | false |
FractionalIdeal.spanFinset_coe | Mathlib.RingTheory.FractionalIdeal.Operations | [
"Submodule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"IsFractionRing",
"Finset",
"Algebra",
"nonZeroDivisors",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"FractionalIdeal.spanFinset",
... | true |
SemiRingCat.limitπRingHom._proof_2 | Mathlib.Algebra.Category.Ring.Limits | [
"SemiRingCat.instConcreteCategoryRingHomCarrier",
"CategoryTheory.Functor",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"AddCommMonCat.instCategory",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.comp",
"RingHom",
"AddCommMonCat",
"AddZeroClass.toAddZero",
"Set.Elem",
"SemiRingCat... | false |
WithTop.lt_untop_iff | Mathlib.Order.WithBot | [
"congrArg",
"Exists",
"Ne",
"WithTop.some",
"iff_self",
"WithTop.untop",
"WithTop.coe_lt_coe",
"Iff",
"Exists.casesOn",
"WithTop.top",
"WithTop.canLift",
"WithTop.instLT",
"LT.lt",
"True",
"propext",
"of_eq_true",
"Eq.ndrec",
"Top.top",
"Eq",
"Eq.trans",
"LT",
"WithTop",
... | true |
_private.Mathlib.Data.List.Forall2.0.List.rel_flatten.match_1_8 | Mathlib.Data.List.Forall2 | [
"List.Forall₂.cons",
"Unit.unit",
"False",
"_private.Mathlib.Data.List.Forall2.0.List.rel_flatten._sparseCasesOn_1_1",
"HEq.refl",
"False.elim",
"Nat.shiftRight",
"noConfusion_of_Nat",
"Nat.hasNotBit",
"instOfNatNat",
"List.Forall₂.below",
"List.Forall₂.nil",
"List.cons",
"Bool.true",
"N... | false |
AugmentedSimplexCategory.equivAugmentedSimplicialObject_inverse_obj_map | Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithInitial.of",
"CategoryTheory.WithTerminal.id.match_1",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"Cat... | true |
_private.Mathlib.Data.Finset.Update.0.Function.updateFinset_updateFinset._simp_1_3 | Mathlib.Data.Finset.Update | [
"False",
"True",
"propext",
"not_false_iff",
"Eq",
"Not"
] | false |
_private.Mathlib.Data.Rat.Cast.Order.0.Mathlib.Meta.Positivity.evalRatCast._proof_5 | Mathlib.Data.Rat.Cast.Order | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr",
"Lean.Expr.sort",
"Lean.Level",
"Prod.fst",
"List.cons",
"Qq.Quoted",
"Qq.Quoted.unsafeMk",
"Bool",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Prod",
"Lean.Name.mkStr1",
"Prod.snd",
"Qq.QuotedDefEq.unsafeIntro",
"List.... | false |
Lean.Elab.Structural.IndGroupInst.recOn | Lean.Elab.PreDefinition.Structural.IndGroupInfo | [
"Lean.Elab.Structural.IndGroupInst.mk",
"Lean.Elab.Structural.IndGroupInfo",
"Lean.Elab.Structural.IndGroupInst.rec",
"Lean.Expr",
"Lean.Level",
"Array",
"List",
"Lean.Elab.Structural.IndGroupInst"
] | false |
_private.Mathlib.RingTheory.SimpleModule.Isotypic.0.Submodule.le_linearEquiv_of_sSup_eq_top.match_1_5 | Mathlib.RingTheory.SimpleModule.Isotypic | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Membership.mem",
"Exists",
"AddCommGroup",
"Subtype",
"Submodule.module",
"Nonempty.intro",
"Exists.casesOn",
"Submodule.addCommGroup",
"RingHomInvPair.ids",
"Nonempty.casesOn",
"Submodule.setLike",
"LinearEquiv",
... | false |
Lean.Elab.Term.applyResult | Lean.Elab.Term.TermElabM | [
"Pure.pure",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"instMonadExceptOfMonadExceptOf",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.MonadError.toMonadExceptOf",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"MonadExcept.throw",
"Lean.Elab.Term.... | true |
CategoryTheory.Adjunction.unit | Mathlib.CategoryTheory.Adjunction.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Adjunction",
"CategoryTheory.Category"
] | true |
FreeGroup.of | Mathlib.GroupTheory.FreeGroup.Basic | [
"Prod.mk",
"List.cons",
"Bool.true",
"FreeGroup.mk",
"Bool",
"Prod",
"FreeGroup",
"List.nil"
] | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.CompStruct.0._auto_80 | Mathlib.AlgebraicTopology.SimplicialSet.CompStruct | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
NumberField.ComplexEmbedding.conjugate_comp | Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings | [
"NumberField.ComplexEmbedding.conjugate",
"RingHom",
"Field.toSemifield",
"RingHom.comp",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Complex",
"Semiring.toNonAssocSemiring",
"Eq",
"Field",
"rfl",
"Complex.instSemiring"
] | true |
normalizedGCDMonoidOfExistsLCM._proof_4 | Mathlib.Algebra.GCDMonoid.Basic | [
"Dvd.dvd",
"NormalizationMonoid",
"semigroupDvd",
"MonoidWithZeroHom.funLike",
"Exists",
"SemigroupWithZero.toSemigroup",
"CommMonoidWithZero.toMonoidWithZero",
"MonoidWithZero.toSemigroupWithZero",
"And",
"MonoidWithZeroHom",
"Iff",
"MonoidWithZero.toMulZeroOneClass",
"CommMonoidWithZero",
... | false |
UInt8.le_total | Init.Data.UInt.Lemmas | [
"instOfNatNat",
"LE.le",
"UInt8.toBitVec",
"Nat",
"BitVec.le_total",
"Or",
"OfNat.ofNat",
"UInt8",
"instLEUInt8"
] | true |
CategoryTheory.MorphismProperty.toSet_max | Mathlib.CategoryTheory.MorphismProperty.Basic | [
"CategoryTheory.MorphismProperty",
"Lattice.toSemilatticeSup",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CompleteLattice.toLattice",
"Set.instUnion",
"SemilatticeSup.toMax",
"CategoryTheory.MorphismProperty.toSet",
"Max.max",
"CompleteBooleanAlgebra.toCompleteLattice",
"Catego... | true |
_private.Init.Data.BitVec.Bitblast.0.BitVec.addRecAux_eq_of._proof_1_2 | Init.Data.BitVec.Bitblast | [
"instDecidableNot",
"Int.instDiv",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"instHDiv",
"HMul.hMul",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Int.natCast_ediv",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HS... | false |
NonUnitalAlgHom.coe_comp | Mathlib.Algebra.Algebra.NonUnitalHom | [
"Monoid",
"MonoidHom",
"Monoid.toMulOneClass",
"NonUnitalAlgHom.comp",
"Function.comp",
"NonUnitalAlgHom.instFunLike_1",
"MonoidHom.CompTriple",
"NonUnitalAlgHom",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"MulOneClass.toMulOne",
"DistribMulAction",
"AddCommMonoid.toAddMonoid",
"NonUnital... | true |
Std.DTreeMap.Internal.Impl.getKey?_insertMany_empty_list_of_mem | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.getKey?_insertMany_list_of_mem",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"List.Pairwise",
"Ord",
"congrArg",
"instForInOfForIn'",
"List.map",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.Balanced",
"Option.some",
"Membership.mem",
"Ordering",... | true |
nonempty_orderEmbedding_of_finite_infinite | Mathlib.Data.Finset.Sort | [
"Infinite.exists_subset_card_eq",
"Fintype.ofFinite",
"Finset.orderEmbOfFin",
"OrderIso.toOrderEmbedding",
"Finset",
"LinearOrder",
"Finite",
"PartialOrder.toPreorder",
"Fintype.orderIsoFinOfCardEq",
"Preorder.toLE",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"F... | true |
Filter.map_inr_inf_map_inl | Mathlib.Order.Filter.Map | [
"Eq.mpr",
"CompleteLattice.toLattice",
"congrArg",
"Filter.map",
"Filter.instCompleteLatticeFilter",
"Sum",
"id",
"Filter.map_inl_inf_map_inr",
"Sum.inl",
"Bot.bot",
"SemilatticeInf.toMin",
"Filter.instInf",
"inf_comm",
"Sum.inr",
"Eq.refl",
"Eq",
"Filter",
"Min.min",
"Lattice.to... | true |
CategoryTheory.Subfunctor.Subpresheaf.toRange_app_val | Mathlib.CategoryTheory.Subfunctor.Image | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"TypeCat.instFunLikeFun",
"Membership.mem",
"CategoryTheory.Subfunctor.obj",
"CategoryTheory.Subfunctor.toFunctor",
"TypeCat.Fun",
"Category... | true |
CategoryTheory.Abelian.SpectralObject.SpectralSequence.pageD._proof_9 | Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | [
"CategoryTheory.Abelian.SpectralObject.SpectralSequence.pageX._proof_2",
"Int",
"LE.le",
"ComplexShape",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore",
"Int.instAdd",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.deg",
"O... | false |
Module.Basis.mk_coord_apply_ne | Mathlib.LinearAlgebra.Basis.Basic | [
"Set.mem_range_self",
"Finsupp.instFunLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"False",
"Semiring.toModule",
"Finsupp.module",
"eq_false",
"Module.Basis.coord",
"congrArg",
"LinearIndependent.repr_eq_single",
"Submodule.addCommMonoid",
"PartialOrder.toPreorder",
"Line... | true |
le_or_lt_of_mul_le_mul | Mathlib.Algebra.Order.Monoid.Unbundled.MinMax | [
"Eq.mpr",
"Preorder.toLT",
"HMul.hMul",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Mul",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"MulLeftMono",
"id",
"LE.le",
"not_or._simp_2",
"Mathlib.Tactic.Contrapose.contrapose₁",
"not_lt._simp_1",
... | true |
CategoryTheory.PreGaloisCategory.instHasFiniteLimits | Mathlib.CategoryTheory.Galois.Basic | [
"CategoryTheory.PreGaloisCategory",
"CategoryTheory.PreGaloisCategory.hasPullbacks",
"CategoryTheory.Limits.HasFiniteLimits",
"CategoryTheory.PreGaloisCategory.hasTerminal",
"CategoryTheory.Limits.hasFiniteLimits_of_hasTerminal_and_pullbacks",
"CategoryTheory.Category"
] | true |
Int.Linear.Poly.renameVars._f | Lean.Meta.Tactic.Grind.Arith.Cutsat.VarRename | [
"Option.getD",
"Membership.mem",
"instOfNatNat",
"Int",
"Std.HashMap",
"Int.Linear.Var",
"instHashableNat",
"Int.Linear.Poly.num",
"instBEqOfDecidableEq",
"Lean.Meta.Grind.VarRename.map",
"Lean.Meta.Grind.Var",
"Int.Linear.Poly.add",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.VarRename.0.... | false |
binomialSeries_eq_ordinaryHypergeometricSeries | Mathlib.Analysis.Analytic.Binomial | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"one_pow",
"IsSemitopologicalRing.toIsTopologicalAddGroup",
"Distrib.leftDistribClass",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"Polynomial.eval",
"GroupWithZero.toMonoidWithZero",
"not_exists._simp_1",
"NegZeroClass.toNeg",
"NonAssocSemiring.to... | true |
Lean.Elab.Term.ToDepElimPattern.TopSort.State._sizeOf_1 | Lean.Elab.Match | [
"instSizeOfDefault",
"Lean.Expr",
"instOfNatNat",
"Lean.MVarIdSet",
"Array._sizeOf_inst",
"Array",
"instHAdd",
"Lean.Elab.Term.ToDepElimPattern.TopSort.State.rec",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.FVarIdSet",
"OfNat.ofNat",
"Lean.Elab.Term.ToDepElimPattern.TopSort... | false |
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