name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ConcaveOn.mul_convexOn' | Mathlib.Analysis.Convex.Mul | [
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"ConcaveOn.smul_convexOn'",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"LinearOrder... | true |
Std.TreeMap.Raw.compare_maxKeyD_modify_eq | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.modify",
"Std.TreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.Const.compare_maxKeyD_modify_eq",
"Ordering",
"Ordering.eq",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw.maxKeyD",
"Std.TreeMap.Raw",
"Eq"
] | true |
AlgCat.limitSemiring._proof_7 | Mathlib.Algebra.Category.AlgCat.Limits | [
"Subalgebra.instSetLike",
"AddGroup.toSubtractionMonoid",
"AlgCat.instAlgebraObjForgetAlgHomCarrier",
"Equiv.ring._proof_3",
"CategoryTheory.Functor",
"CommRing",
"Equiv.instEquivLike",
"CategoryTheory.Limits.Types.Small.limitCone",
"AlgCat.limitSemiring._aux_4",
"AddMonoid.toAddSemigroup",
"Equ... | false |
Function.isFixedPt_piMap | Mathlib.Dynamics.PeriodicPts.Defs | [
"funext_iff",
"Pi.map",
"Iff",
"Function.IsFixedPt"
] | true |
Affine.Triangle.mem_circumsphere_of_two_zsmul_oangle_eq | Mathlib.Geometry.Euclidean.Angle.Sphere | [
"EuclideanGeometry.oangle",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Affine.Simplex.points",
"False",
"Real.partialOrder",
"Real",
"Collinear",
"instHSMul",
"Function.update",
"AffineIndependent",
"Affine.Triangle.circumsphere_eq_circumsphere_of_eq_of_eq_of_two_zsmul_oangle_eq",
"Affine... | true |
Lean.Server.FileWorker.Insertion.mk | Lean.Server.CodeActions.UnknownIdentifier | [
"Lean.Lsp.TextEdit",
"Lean.Server.FileWorker.Insertion.mk",
"Lean.Server.FileWorker.Insertion",
"Lean.Name"
] | true |
_private.Mathlib.Order.SuccPred.Basic.0.WithBot.succ_unbot.match_1_1 | Mathlib.Order.SuccPred.Basic | [
"WithBot.some",
"WithBot",
"Option.casesOn",
"Option.some",
"Ne",
"Bot.bot",
"Option.none",
"WithBot.bot"
] | false |
Lean.Lsp.TextDocumentPositionParams._sizeOf_inst | Lean.Data.Lsp.Basic | [
"Lean.Lsp.TextDocumentPositionParams._sizeOf_1",
"SizeOf.mk",
"Lean.Lsp.TextDocumentPositionParams",
"SizeOf"
] | false |
Partition.IsRepFun.forall_apply_eq_apply_iff | Mathlib.Order.Partition.Basic | [
"Eq.mpr",
"le_rfl",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"em",
"id",
"Iff.not",
"Partition.IsRepFun.apply_mem_iff",
"Partition.IsRepFun.apply_of_notMem",
"Partition",
"Iff",
"Iff.intro",
"Partition.IsRepFu... | true |
Vector.range'_eq_mk_range'._proof_1 | Init.Data.Vector.Range | [
"congrArg",
"Array.range'",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Array.size_range'",
"Eq",
"Array.size",
"Eq.trans"
] | false |
CategoryTheory.MorphismProperty.CodescendsAlong.mk._flat_ctor | Mathlib.CategoryTheory.MorphismProperty.Descent | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.CodescendsAlong",
"CategoryTheory.IsPushout",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.MorphismProperty.CodescendsAlong.mk",
"CategoryTheory.Category"
] | false |
Cubic.discr._proof_3 | Mathlib.Algebra.CubicDiscriminant | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
FirstOrder.Language.presburger.instSMulNatTerm | Mathlib.ModelTheory.Arithmetic.Presburger.Basic | [
"FirstOrder.Language.presburger",
"SMul",
"FirstOrder.Language.Term",
"SMul.mk",
"FirstOrder.Language.presburger.instZeroTerm",
"nsmulRec",
"Nat",
"FirstOrder.Language.presburger.instAddTerm"
] | true |
instLEOption | Init.Data.Option.Basic | [
"LE.le",
"LE",
"LE.mk",
"Option.le",
"Option"
] | true |
MulEquiv.rec | Mathlib.Algebra.Group.Equiv.Defs | [
"HMul.hMul",
"Mul",
"Equiv",
"Equiv.toFun",
"MulEquiv",
"Eq",
"MulEquiv.mk",
"instHMul"
] | false |
AddSubgroup.mem_goursatSnd._simp_1 | Mathlib.GroupTheory.Goursat | [
"AddGroup.toSubtractionMonoid",
"Membership.mem",
"Prod.mk",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddSubgroup",
"AddGroup",
"AddSubgroup.instSetLike",
"propext",
"Zero.toOfNat0",
"Prod",
"OfNat.ofNat",
"AddSubgroup.goursatSnd",
"NegZeroClass.toZero",
... | false |
_private.Mathlib.CategoryTheory.WithTerminal.Basic.0.CategoryTheory.WithInitial.id.match_1.eq_2 | Mathlib.CategoryTheory.WithTerminal.Basic | [
"Unit.unit",
"CategoryTheory.WithInitial.of",
"CategoryTheory.WithInitial",
"CategoryTheory.WithInitial.id.match_1",
"Unit",
"CategoryTheory.WithInitial.star",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Data.Set.Subsingleton.0.Set.not_subsingleton_iff._simp_1_3 | Mathlib.Data.Set.Subsingleton | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
instAddCommGroupFreeAbelianGroup._aux_1 | Mathlib.GroupTheory.FreeAbelianGroup | [
"Equiv.instEquivLike",
"HMul.hMul",
"Monoid.toMulOneClass",
"Additive",
"Additive.toMul",
"Equiv",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Additive.ofMul",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"FreeAbelianGroup",
"CommGroup.toGroup",
"Abelianization",
"DFunLike.coe",
"Free... | false |
CommRingCat.equalizer_ι_isLocalHom | Mathlib.Algebra.Category.Ring.Constructions | [
"CategoryTheory.Limits.limMap_π",
"CommRingCat.equalizerForkIsLimit",
"CategoryTheory.Limits.limit.π",
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CommRingCat.Hom.hom",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.... | true |
FirstOrder.Language.BoundedFormula.realize_rel₁ | Mathlib.ModelTheory.Semantics | [
"Eq.mpr",
"congrArg",
"FirstOrder.Language.Relations.boundedFormula",
"FirstOrder.Language.Term",
"Sum",
"id",
"FirstOrder.Language.BoundedFormula.Realize",
"Matrix.cons_val_fin_one",
"FirstOrder.Language.Relations.boundedFormula₁.eq_1",
"instOfNatNat",
"FirstOrder.Language.Structure.RelMap",
... | true |
Valuation.IsEquiv.valueGroup₀Fun._proof_1 | Mathlib.RingTheory.Valuation.Basic | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"ValuationClass.toMonoidWithZeroHomClass",
"CommMonoidWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero",
"LinearOrderedCommMonoidWithZero.toCommMonoidWithZero",
"MonoidWithZeroHomClass",
"Valuation.instValuationClass",
"ins... | false |
ModelWithCorners.continuous_invFun._autoParam | Mathlib.Geometry.Manifold.IsManifold.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.MorphismProperty.transfiniteCompositions_le | Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition | [
"CategoryTheory.MorphismProperty.IsStableUnderTransfiniteComposition",
"CategoryTheory.MorphismProperty",
"Preorder.toLT",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra... | true |
ContinuousAlternatingMap.ext | Mathlib.Topology.Algebra.Module.Alternating.Basic | [
"DFunLike.ext",
"AddCommMonoid",
"TopologicalSpace",
"ContinuousAlternatingMap.funLike",
"Semiring",
"Module",
"Eq",
"DFunLike.coe",
"ContinuousAlternatingMap"
] | true |
_private.Std.Data.ExtDTreeMap.Lemmas.0.Std.ExtDTreeMap.Const.insertManyIfNewUnit_list_eq_empty_iff._simp_1_2 | Std.Data.ExtDTreeMap.Lemmas | [
"Bool.true",
"List",
"List.isEmpty",
"List.isEmpty_iff",
"propext",
"Bool",
"Eq",
"List.nil"
] | false |
Finset.affineCombinationLineMapWeights_apply_left | Mathlib.LinearAlgebra.AffineSpace.Combination | [
"NegZeroClass.toNeg",
"False",
"instHSMul",
"instSMulOfMul",
"HMul.hMul",
"eq_false",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_neg_add",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"AddZeroClass.toAddZero",
"Finset.weight... | true |
FirstOrder.Language.LHom.id_comp | Mathlib.ModelTheory.LanguageMap | [
"FirstOrder.Language.LHom.comp",
"FirstOrder.Language.LHom.id",
"Nat",
"FirstOrder.Language.Relations",
"FirstOrder.Language.Functions",
"Eq.ndrec",
"FirstOrder.Language.LHom",
"Eq.refl",
"FirstOrder.Language",
"FirstOrder.Language.LHom.casesOn",
"Eq.symm",
"Eq",
"FirstOrder.Language.LHom.mk... | true |
liminf_eq_top._simp_1 | Mathlib.Topology.Order.LiminfLimsup | [
"OrderTopology",
"Lattice.toSemilatticeSup",
"Filter.liminf",
"liminf_eq_top",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CoheytingAlgebra.toOrderTop",
"Filter.EventuallyEq",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"CompleteDistribLattice.toCoframe",
"FirstCountableT... | false |
toIcoMod_add_nsmul' | Mathlib.Algebra.Order.ToIntervalMod | [
"instHSMul",
"Preorder.toLT",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"AddMonoid.toNSMul",
"AddCommGroup.toAddGroup",
"cast",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"SubtractionMonoid.toSubNegZeroMonoid",
"... | true |
_private.Init.Data.Int.Linear.0.Int.Linear.le_of_le'._proof_1_3 | Init.Data.Int.Linear | [
"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",
"Option.some",
"Int... | false |
exp_neg_mul_sq_isLittleO_exp_neg | Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral | [
"Eq.mpr",
"Real.instPow",
"Real.partialOrder",
"Real",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Real.instZero",
"Real.instZeroLEOneClass",
"congrArg",
"instIsLeftCancelAddOfAddLeftReflectLE",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"... | true |
Set.Ioc.instMul._proof_1 | Mathlib.Algebra.Order.Interval.Set.Instances | [
"Set.Ioc",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"HMul.hMul",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"le_of_lt",
"Preorder.toLE",
"Membership.mem",
"PartialOrder",
"Set.Elem",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LE.le",
"instDistribOfSemiring",
"A... | false |
ProbabilityTheory.IsLocalizingSequence.mk._flat_ctor | Mathlib.Probability.Process.LocalProperty | [
"MeasureTheory.ae",
"MeasureTheory.IsStoppingTime",
"OrderTopology",
"MeasureTheory.Measure",
"WithTop.instPreorder",
"Filter.Eventually",
"Monotone",
"nhds",
"MeasureTheory.Filtration",
"ProbabilityTheory.IsLocalizingSequence.mk",
"ProbabilityTheory.IsPreLocalizingSequence._auto_1",
"autoPara... | false |
Lean.Compiler.LCNF.Probe.filterByFunDecl | Lean.Compiler.LCNF.Probing | [
"Lean.Compiler.LCNF.Decl",
"Lean.Compiler.LCNF.FunDecl",
"_private.Lean.Compiler.LCNF.Probing.0.Lean.Compiler.LCNF.Probe.filterByFunDecl.go",
"Lean.Compiler.LCNF.Decl.value",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.DeclValue.isCodeAndM",
"Lean.Compiler.LCNF.instMonadCompilerM",
"Lean.Compiler... | true |
Algebra.Generators.CotangentSpace.compEquiv.eq_1 | Mathlib.RingTheory.Kaehler.JacobiZariski | [
"Algebra.Generators.CotangentSpace.compEquiv._proof_5",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"Algebra.Extension.commRing",
"Algebra.Generators.CotangentSpace.compEquiv._proof_6",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Algebra.Generators.CotangentSpace.compEquiv",
"S... | true |
_aux_Mathlib_Data_Complex_Basic___macroRules_termℂ_1 | Mathlib.Data.Complex.Basic | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad",
"Lean.TSyntax.... | false |
QuotSMulTop.map_exact | Mathlib.RingTheory.QuotSMulTop | [
"Function.Exact",
"Submodule.pointwiseDistribMulAction",
"Submodule",
"Submodule.Quotient.instZeroQuotient",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"Function.Exact.iff_of_ladder_linearEquiv",
"Submodule.Quotient.addCommGroup",
"CommSe... | true |
Sum.LiftRel.isRight_left | Mathlib.Data.Sum.Basic | [
"Sum.isRight",
"Sum.ctorIdx",
"HEq.refl",
"False.elim",
"Sum.LiftRel.inl",
"Sum.inr.noConfusion",
"noConfusion_of_Nat",
"Sum",
"Sum.inl",
"Sum.LiftRel.inr",
"Sum.LiftRel",
"Bool.true",
"Sum.inr",
"Bool",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"Sum.LiftRel... | true |
Polynomial.leadingCoeff_divByMonic_of_monic | Mathlib.Algebra.Polynomial.Div | [
"Nontrivial",
"WithBot.instPreorder",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"WithBot",
"Preorder.toLT",
"HMul.hMul",
"Polynomial.divByMonic_eq_zero_iff",
"congrArg",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Polynomial.monic_of_subsi... | true |
Module.Dual.eq_of_ker_eq_of_apply_eq | Mathlib.LinearAlgebra.Dual.Lemmas | [
"Submodule.span_eq_bot._simp_1",
"IsCompl.sup_eq_top",
"Eq.mpr",
"Submodule",
"False",
"instHSMul",
"IsDomain.to_noZeroDivisors",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"instSMulOfMul",
"SemilinearMapClass.toMulActionSemiHomClass",
"HMul.hMul",
"SemilinearMapClass.distribMulActionS... | true |
UniformSpace.hasBasis_nhds_prod | Mathlib.Topology.UniformSpace.Basic | [
"Filter.instMembership",
"Set.instSProd",
"UniformSpace",
"Eq.mpr",
"SetRel",
"SProd.sprod",
"congrArg",
"UniformSpace.ball_inter_right",
"uniformity",
"instTopologicalSpaceProd",
"Membership.mem",
"Exists",
"nhds",
"inferInstance",
"id",
"Prod.mk",
"HasSubset.Subset",
"Filter.inte... | true |
CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.tensor.elim | Mathlib.CategoryTheory.Monoidal.Free.Coherence | [
"PULift.up",
"CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.ctorIdx",
"CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.ctorElim",
"Nat",
"CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject",
"Eq.symm",
"Eq",
"CategoryTheory.FreeMonoidalCategory.NormalMonoidalObject.tensor"
] | false |
Fin.getElem?_fin | Init.GetElem | [
"GetElem?",
"Fin.val",
"Nat",
"GetElem?.getElem?",
"Fin",
"Eq",
"rfl",
"Fin.instGetElem?FinVal",
"Option"
] | true |
OrderIso.image_eq_preimage_symm | Mathlib.Order.Hom.Set | [
"OrderIso",
"LE.le",
"OrderIso.symm",
"LE",
"Equiv.image_eq_preimage_symm",
"instFunLikeOrderIso",
"Set.preimage",
"Set.image",
"RelIso.toEquiv",
"Eq",
"DFunLike.coe",
"Set"
] | true |
Set.FiniteExhaustion.mk.injEq | Mathlib.Data.Set.FiniteExhaustion | [
"Eq.propIntro",
"Finite",
"Set.Elem",
"HasSubset.Subset",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Set.FiniteExhaustion",
"Eq.ndrec",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Set.FiniteExhaustion.mk.inj",
"Eq",
"Set.iUnion",
"Set.FiniteExhaustion.mk",
"Set.instHasSubset",
... | true |
_private.Mathlib.Util.Export.0.Lean.Export.exportDef.defn._unsafe_rec | Mathlib.Util.Export | [
"Pure.pure",
"IO.println",
"Lean.Core.instMonadLiftIOCoreM",
"StateT.instMonadLift",
"instForInOfForIn'",
"Monad.toApplicative",
"String",
"instMonadLiftT",
"IO",
"inferInstance",
"Lean.Expr",
"EIO",
"Lean.Export.exportName",
"liftM",
"ForIn.forIn",
"Applicative.toPure",
"ToString.to... | false |
_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.upShadow_compls._simp_1_1 | Mathlib.Combinatorics.SetFamily.Shadow | [
"Finset.shadow",
"Finset",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"propext",
"Finset.mem_shadow_iff",
"Finset.erase",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.contains_maxKeyD._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
OrderHom.le_prevFixed | Mathlib.Order.FixedPoints | [
"Iff.mpr",
"OrderHom.prevFixed",
"ChainCompletePartialOrder.instOfCompleteLattice",
"PartialOrder.toPreorder",
"Function.fixedPoints",
"Preorder.toLE",
"Membership.mem",
"Set.Elem",
"LE.le",
"ChainCompletePartialOrder.toPartialOrder",
"OrderHom.instFunLike",
"OrderHom.le_prevFixed_iff",
"Com... | true |
Aesop.UnorderedArraySet.singleton | Aesop.Util.UnorderedArraySet | [
"_private.Aesop.Util.UnorderedArraySet.0.Aesop.UnorderedArraySet.mk",
"List.toArray",
"List.cons",
"Aesop.UnorderedArraySet",
"BEq",
"List.nil"
] | true |
IsLocalHomeomorph.apply_self_mem_localInverseAt_source | Mathlib.Topology.IsLocalHomeomorph | [
"Eq.mpr",
"IsLocalHomeomorph.self_mem_localInverseAt_target",
"congrArg",
"IsLocalHomeomorph.localInverseAt",
"Membership.mem",
"id",
"OpenPartialHomeomorph.toFun'",
"OpenPartialHomeomorph.map_target",
"TopologicalSpace",
"IsLocalHomeomorph.localInverseAt_symm",
"congrFun",
"PartialEquiv.sourc... | true |
AddGroup.fintypeOfDomOfCoker._proof_1 | Mathlib.GroupTheory.QuotientGroup.Finite | [
"AddGroup.toSubtractionMonoid",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.range",
"Membership.mem",
"QuotientAddGroup.Quotient.addGroup",
"AddZeroClass.toAddZero",
"QuotientAddGroup.mk",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddSubgroup",
"AddSubgroup.Normal... | false |
CategoryTheory.Under.liftCocone._proof_4 | Mathlib.CategoryTheory.Comma.Over.Basic | [
"Eq.mpr",
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Under.liftCocone._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Under.homMk",
"CategoryTheory.Functor.category",
"CategoryTheory... | false |
Finsupp.toAList_lookupFinsupp | Mathlib.Data.Finsupp.AList | [
"Iff.mpr",
"Finsupp.instFunLike",
"Eq.mpr",
"False",
"Finsupp.mem_toAlist._simp_1",
"Finsupp.ext",
"Prod.toSigma",
"congrArg",
"Option.instMembership",
"Finset",
"List.map",
"Option.getD",
"Prod.exists._simp_1",
"Classical.propDecidable",
"heq_eq_eq",
"Option.some",
"Membership.mem",... | true |
FirstOrder.Language.FGEquiv.symm | Mathlib.ModelTheory.PartialEquiv | [
"FirstOrder.Language.PartialEquiv.symm",
"FirstOrder.Language.FGEquiv",
"FirstOrder.Language.PartialEquiv.dom",
"FirstOrder.Language.FGEquiv.symm._proof_1",
"Subtype.mk",
"FirstOrder.Language.Substructure.FG",
"FirstOrder.Language.Structure",
"FirstOrder.Language",
"FirstOrder.Language.PartialEquiv"... | true |
HurwitzZeta.hasSum_expZeta_of_one_lt_re | Mathlib.NumberTheory.LSeries.HurwitzZeta | [
"mul_div",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"HasSum.add",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.pi",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"Complex.cos",
"IsTopologicalRin... | true |
LinearMap.IsPerfectCompl.left_top_iff | Mathlib.LinearAlgebra.PerfectPairing.Basic | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommG... | true |
Std.DHashMap.Internal.Raw₀.diff | Std.Data.DHashMap.Internal.Defs | [
"Bool.not",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Raw",
"instOfNatNat",
"LE.le",
"Std.DHashMap.Internal.Raw₀.filter",
"instLENat",
"Id",
"Std.DHashMap.Raw.instForInSigmaOfMonad",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.Internal.AssocList",
"Id.instMonad",
... | true |
_private.Mathlib.LinearAlgebra.Reflection.0.Module.preReflection_apply_self._abel_1_1 | Mathlib.LinearAlgebra.Reflection | [
"Mathlib.Tactic.Abel.term_atomg",
"NegZeroClass.toNeg",
"Mathlib.Meta.NormNum.isNat_add",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Mathlib.Tactic.Abel.term_neg",
"AddCommGroup.toAddGroup",
"Mathlib... | false |
Std.Http.Internal.Char.isValidDomainNameChar | Std.Internal.Http.Internal.Char | [
"Bool.true",
"Unit",
"Std.Http.Internal.Char.isValidDomainNameChar.match_1",
"Bool",
"Bool.or",
"Std.Http.Internal.Char.isAsciiAlphaNumChar",
"Char",
"Bool.false"
] | true |
PseudoMetricSpace.induced._proof_3 | Mathlib.Topology.MetricSpace.Pseudo.Constructions | [
"Real.instLE",
"Real",
"PseudoMetricSpace.dist_triangle",
"LE.le",
"Real.instAdd",
"instHAdd",
"PseudoMetricSpace",
"HAdd.hAdd",
"Dist.dist",
"PseudoMetricSpace.toDist"
] | false |
CategoryTheory.Functor.PreservesLeftHomologyOf.congr_simp | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex",
"Eq.rec",
"CategoryTheory.Functor.PreservesLeftHomologyOf",
"Eq.ndrec",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.PreservesZeroMorphisms",
"CategoryTheory.Category"
] | true |
Lean.Server.RefInfo.noConfusion | Lean.Server.References | [
"Lean.Server.RefInfo.noConfusionType",
"Lean.Server.RefInfo.casesOn",
"Lean.Server.Reference",
"Array",
"Eq.ndrec",
"Eq.refl",
"Lean.Server.RefInfo",
"Eq",
"Option"
] | false |
Lean.Meta.Grind.Arith.Cutsat.LeCnstr.pp | Lean.Meta.Tactic.Grind.Arith.Cutsat.Util | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.MessageData",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"String",
"Lean.Meta.Sym.Context",
"Lean.MessageData.instAppend",
"ReaderT.instMonad",
"Lean.Meta.Grind.Context",
"Lean.Meta.MetaM",
"... | true |
Std.Sat.AIG.Fanin.invert_flip | Std.Sat.AIG.Basic | [
"instDecidableNot",
"False",
"Nat.instXorOp",
"Bool.not_false",
"Bool.not",
"instDecidableTrue",
"congrArg",
"Decidable.decide.congr_simp",
"Std.Sat.AIG.Fanin.val",
"_private.Std.Sat.AIG.Basic.0.Std.Sat.AIG.Fanin.invert_eq_testBit",
"Bool.toNat",
"iff_true",
"Std.Sat.AIG.Fanin.flip",
"Std.... | true |
Lean.Data.AC.Expr.brecOn | Init.Data.AC | [
"Lean.Data.AC.Expr.brecOn.go",
"Lean.Data.AC.Expr",
"Lean.Data.AC.Expr.below"
] | false |
_private.Init.Data.Subtype.Order.0.Subtype.instLawfulOrderLT._simp_1 | Init.Data.Subtype.Order | [
"Std.LawfulOrderLT.lt_iff",
"LE.le",
"Std.LawfulOrderLT",
"LE",
"And",
"LT.lt",
"propext",
"Eq",
"Not",
"LT"
] | false |
Real.strictMonoOn_rpow_Ici_of_exponent_pos | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Real.instPow",
"Real",
"Preorder.toLT",
"Set.Ici",
"Real.instZero",
"Real.instLT",
"Membership.mem",
"Real.rpow_lt_rpow",
"HPow.hPow",
"LT.lt",
"Zero.toOfNat0",
"instHPow",
"StrictMonoOn",
"OfNat.ofNat",
"Set.instMembership",
"Real.instPreorder",
"Set"
] | true |
NonUnitalSubsemiringClass.subtype_injective | Mathlib.RingTheory.NonUnitalSubsemiring.Defs | [
"SetLike",
"Membership.mem",
"NonUnitalSubsemiringClass.subtype",
"Subtype",
"NonUnitalRingHom.instFunLike",
"Subtype.coe_injective",
"NonUnitalSubsemiringClass.toNonUnitalNonAssocSemiring",
"Function.Injective",
"NonUnitalRingHom",
"NonUnitalSubsemiringClass",
"NonUnitalNonAssocSemiring",
"DF... | true |
AlgebraicGeometry.Scheme.Cover.sigma | Mathlib.AlgebraicGeometry.Cover.Sigma | [
"CategoryTheory.PreZeroHypercover.mk",
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"UnivLE",
"AlgebraicGeometry.IsZariskiLocalAtSource",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.I₀",
"AlgebraicGeometry.Scheme.Cov... | true |
Lean.Elab.MacroStackElem.before | Lean.Elab.Util | [
"Lean.Syntax",
"Lean.Elab.MacroStackElem"
] | true |
Lean.Lsp.InlayHintClientCapabilities.resolveSupport?._default | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.ResolveSupport",
"id",
"Option.none",
"Option"
] | false |
CategoryTheory.Functor.HomObj.mk.inj | Mathlib.CategoryTheory.Functor.FunctorHom | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.HomObj.mk",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"autoParam",
"CategoryTheory.Functor.map",
"TypeCat.Fun",
"CategoryTheory.Functor.HomObj.mk.noConfusion",
"Catego... | true |
_private.Mathlib.AlgebraicGeometry.ColimitsOver.0.AlgebraicGeometry.Scheme.Cover.ColimitGluingData.transitionMap_comp._simp_1_1 | Mathlib.AlgebraicGeometry.ColimitsOver | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.Functor.map_comp_assoc",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheor... | false |
Std.ExtTreeMap.getD_map_of_getKey?_eq_some | Std.Data.ExtTreeMap.Lemmas | [
"Option.getD",
"Std.ExtTreeMap.getKey?",
"Option.some",
"Membership.mem",
"Ordering",
"Std.ExtTreeMap.getD",
"Std.TransCmp",
"Option.map",
"Std.ExtTreeMap",
"Std.ExtTreeMap.inner",
"Std.ExtDTreeMap.Const.getD_map_of_getKey?_eq_some",
"Inhabited",
"Std.ExtTreeMap.map",
"Std.ExtTreeMap.instG... | true |
PresheafOfModules.Sheafify.zero_smul | Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify | [
"CategoryTheory.Presheaf.imageSieve",
"Eq.mpr",
"RingHom.instRingHomClass",
"AddMonoidHom.map_zero",
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"instHSMul",
"CategoryTheory.hasSheafCompose_of_preservesMulticospan",
"AddMonoidHom.instAddMonoidHomClass",
"Opposite",... | true |
NumberField.mixedEmbedding.negAt_symm | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearEquiv.ext",
"ContinuousLinearEquiv.symm",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModu... | true |
Submodule.starProjection_orthogonal' | Mathlib.Analysis.InnerProductSpace.Projection.Basic | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Submodule",
"NormedRing.toRing",
"Submodule.starProjection",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Submodule.HasOrthogonalProjection",
"... | true |
List.map_append_flatMap_perm | Mathlib.Data.List.Perm.Basic | [
"List.flatMap_append_perm",
"congrArg",
"List.map",
"Eq.mp",
"List.Perm",
"List.cons",
"instHAppendOfAppend",
"List",
"congrFun'",
"List.instAppend",
"HAppend.hAppend",
"List.flatMap",
"_private.Mathlib.Data.List.Perm.Basic.0.List.map_append_flatMap_perm._simp_1_1",
"List.nil"
] | true |
CategoryTheory.Under.mapId_inv_app_right | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Under.mapId",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Unde... | true |
MeasureTheory.SimpleFunc.instInf | Mathlib.MeasureTheory.Function.SimpleFunc | [
"MeasureTheory.SimpleFunc.seq",
"Min.mk",
"MeasureTheory.SimpleFunc",
"Min",
"MeasurableSpace",
"Min.min",
"MeasureTheory.SimpleFunc.map"
] | true |
Lean.IR.IRType.brecOn.go | Lean.Compiler.IR.Basic | [
"Lean.IR.IRType.below_1",
"Lean.IR.IRType.float",
"PProd.mk",
"Lean.IR.IRType.uint16",
"Lean.IR.IRType.below_2",
"Lean.IR.IRType.union",
"Lean.IR.IRType.float32",
"Lean.IR.IRType.usize",
"Lean.IR.IRType.uint32",
"List.cons",
"Array",
"List",
"PProd",
"PUnit",
"Lean.IR.IRType",
"Lean.IR... | true |
CategoryTheory.instMonoidalCategoryHom._proof_6 | Mathlib.CategoryTheory.Bicategory.End | [
"CategoryTheory.instCategoryEndMonoidal",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.Bicategory.whiskerLeft_id",
"True",
"eq_self",
"CategoryThe... | false |
Lean.Elab.Command.initFn._@.Lean.Elab.MutualInductive.3413988523._hygCtx._hyg.2 | Lean.Elab.MutualInductive | [
"IO",
"Lean.Elab.Command.InductiveElabDescr",
"Lean.KeyedDeclsAttribute",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.inductiveElabAttr.unsafe_impl_2"
] | false |
CategoryTheory.Functor.Fiber.fiberInclusion_mk | Mathlib.CategoryTheory.FiberedCategory.Fiber | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.Fiber.fiberInclusion",
"CategoryTheory.Functor.Fiber",
"CategoryTheory.Functor.Fiber.fiberCategory",
"CategoryTheory.Functor.Fiber.mk",
"Eq",
"CategoryTheory.Functor.obj",
"rfl",
"CategoryTheory.Category"
] | true |
Lean.CollectMVars.State._sizeOf_1 | Lean.Util.CollectMVars | [
"Lean.Expr.instBEq",
"Lean.MVarId",
"Lean.Expr",
"instOfNatNat",
"Lean.ExprSet",
"Std.HashSet._sizeOf_inst",
"Array._sizeOf_inst",
"Array",
"Lean.MVarId._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.CollectMVars.State",
"instAddNat",
"Lean.Expr.instHashable",
... | false |
AlgebraicGeometry.Scheme.IdealSheafData.subschemeCover._proof_2 | Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme | [
"AlgebraicGeometry.Scheme.GlueData.ι",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CommRingCat",
"PartialOrder.toPreorder",
"AlgebraicG... | false |
CompactlyCoherentSpace | Mathlib.Topology.Compactness.CompactlyCoherentSpace | [
"CompactlyCoherentSpace.mk",
"TopologicalSpace"
] | true |
LinearMap.mapMatrixModule_comp_apply | Mathlib.LinearAlgebra.Matrix.Module | [
"Pi.addCommMonoid",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"LinearMap.instFunLike",
"AddCommGroup",
"Matrix.Module.matrixModule",
"LinearMap.mapMatrixModule",
"LinearMap",
"Matrix.nonAssocSemiring",
"LinearMap.comp",
"LinearMap.mapMatrixModule_comp",
"Fintype",
"True",
"eq... | true |
DoubleCentralizer.mk.noConfusion | Mathlib.Analysis.CStarAlgebra.Multiplier | [
"instSMulOfMul",
"HMul.hMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"HEq.refl",
"IsScalarTower",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
... | false |
CategoryTheory.ComposableArrows.isIso_iff₂ | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"CategoryTheory.Functor",
"Fintype.elems",
"CategoryTheory.IsIso",
"Nat.le_refl",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HEq.refl",
"Finset",
"List.Mem.tail",
"False.elim",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.c... | true |
ProbabilityTheory.IsGaussianProcess | Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Def | [
"Real",
"MeasureTheory.Measure",
"ProbabilityTheory.IsGaussianProcess._auto_1",
"ProbabilityTheory.IsGaussianProcess.mk",
"Real.semiring",
"autoParam",
"AddCommMonoid",
"MeasurableSpace",
"TopologicalSpace",
"Module"
] | true |
instHashableInt64 | Init.Data.SInt.Basic | [
"Int64",
"Hashable.mk",
"Hashable",
"Int64.toUInt64"
] | true |
Nat.findX._proof_4 | Mathlib.Data.Nat.Find | [
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"And",
"HAdd.hAdd",
"Nat",
"And.intro",
"instAddNat",
"OfNat.ofNat",
"Eq",
"Not",
"rfl"
] | false |
Metric.hausdorffEDist_le_of_infEDist | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"Eq.mpr",
"Metric.hausdorffEDist_def",
"congrArg",
"iSup",
"CompletelyDistribLattice.toCompleteLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"id",
"ENNReal.instMax",
"LE.le",
"Metric.infEDist",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Ps... | true |
SimpleGraph.toSubgraph | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"SimpleGraph.Subgraph.mk",
"SimpleGraph.Subgraph",
"Set.univ",
"SimpleGraph.Adj",
"LE.le",
"SimpleGraph.symm",
"SimpleGraph",
"Set.mem_univ",
"SimpleGraph.instLE"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getD_filterMap._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
_private.Init.Data.SInt.Lemmas.0.Int32.le_total._simp_1_1 | Init.Data.SInt.Lemmas | [
"instLEInt32",
"Int",
"LE.le",
"Int32.toInt",
"Int32.le_iff_toInt_le",
"propext",
"Eq",
"Int32",
"Int.instLEInt"
] | false |
_private.Mathlib.MeasureTheory.Measure.LevyProkhorovMetric.0.MeasureTheory.LevyProkhorov.continuous_ofMeasure_probabilityMeasure._simp_1_9 | Mathlib.MeasureTheory.Measure.LevyProkhorovMetric | [
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.mem_compl_iff",
"Set"
] | false |
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