name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
RingHom.star_def | Mathlib.Algebra.Star.Basic | [
"CommSemiring.toSemiring",
"RingHom",
"CommSemiring",
"RingHom.comp",
"NonAssocSemiring",
"StarRing",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"RingHom.involutiveStar",
"InvolutiveStar.toStar",
"starRingEnd",
"Semiring.toNonAssocSemiring",
"Eq",
"rfl",
"Star.star"
] | true |
BitVec.toNat_umod | Init.Data.BitVec.Lemmas | [
"BitVec",
"Nat.instMod",
"instHMod",
"BitVec.toNat",
"HMod.hMod",
"Nat",
"Eq",
"BitVec.instMod",
"rfl"
] | true |
CategoryTheory.objUp_objDown | Mathlib.CategoryTheory.Category.ULift | [
"CategoryTheory.ULiftHom",
"CategoryTheory.ULiftHom.objUp",
"CategoryTheory.ULiftHom.objDown",
"Eq",
"rfl"
] | true |
ZNum.cast_bit1 | Mathlib.Data.Num.ZNum | [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"Eq.mpr",
"castZNum",
"NegZeroClass.toNeg",
"castPosNum",
"ZNum.bit1",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"ZNum.bit1.eq_2",
"AddMonoid.toAddSemigroup",
"ZNum.cast_neg",
"PosNum.pred'",
"AddGroupWithOne.to... | true |
Zsqrtd.linearOrder._proof_5 | Mathlib.NumberTheory.Zsqrtd.Basic | [
"LT.mk",
"Preorder.toLT",
"Preorder.toLE",
"Preorder.mk",
"Ordering",
"Preorder.le_refl",
"inferInstance",
"Int",
"compareOfLessAndEq",
"LE.le",
"Preorder.le_trans",
"Nat.cast",
"decidableLTOfDecidableLE",
"Preorder.lt_iff_le_not_ge",
"Zsqrtd.preorder",
"Nat",
"LT.lt",
"LE.mk",
"... | false |
eventually_norm_pow_le | Mathlib.Analysis.Normed.Ring.Basic | [
"Iff.mpr",
"Norm.norm",
"SeminormedRing.toNorm",
"Real.instLE",
"Real",
"Filter.Eventually",
"instArchimedeanNat",
"Preorder.toLE",
"SeminormedRing.toRing",
"instInhabitedNat",
"Exists",
"GE.ge",
"instOfNatNat",
"LE.le",
"instLENat",
"Monoid.toPow",
"Filter.atTop",
"Real.instMonoid... | true |
_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.ensureType.match_1 | Lean.Meta.LetToHave | [
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.ensureType._sparseCasesOn_1",
"Lean.Expr.ctorIdx"
] | false |
Lean.JsonRpc.MessageKind.noConfusion | Lean.Data.JsonRpc | [
"Lean.JsonRpc.MessageKind.ctorIdx",
"Lean.JsonRpc.MessageKind",
"noConfusionEnum",
"Nat",
"instDecidableEqNat",
"Lean.JsonRpc.MessageKind.noConfusionType",
"Eq"
] | false |
TopCat.isEmbedding_of_pullback | Mathlib.Topology.Category.TopCat.Limits.Pullbacks | [
"CategoryTheory.Limits.hasFiniteLimits_of_hasLimits",
"CategoryTheory.Limits.limit.π",
"Eq.mpr",
"CategoryTheory.Limits.pullback",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"HEq.refl",
"CategoryTheory.Limits.... | true |
Function.Injective.isCancelAdd | Mathlib.Algebra.Group.InjSurj | [
"IsRightCancelAdd",
"IsCancelAdd.toIsLeftCancelAdd",
"Function.Injective.isLeftCancelAdd",
"instHAdd",
"HAdd.hAdd",
"IsLeftCancelAdd",
"Function.Injective.isRightCancelAdd",
"IsCancelAdd",
"Function.Injective",
"Eq",
"IsCancelAdd.toIsRightCancelAdd",
"Add",
"IsCancelAdd.mk"
] | true |
Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two | Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | [
"Left.neg_pos_iff._simp_1",
"LinearIsometryEquiv.instEquivLike",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"Orientation",
"False",
"Real.partialOrder",
"Real",
"instHSMul",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalN... | true |
Lean.Firefox.instFromJsonProfile.fromJson | Lean.Util.Profiler | [
"Pure.pure",
"Lean.Firefox.Profile",
"Lean.Json",
"Lean.Firefox.ProfileMeta",
"Monad.toApplicative",
"String",
"Lean.Firefox.Profile.mk",
"Lean.Firefox.instFromJsonThread",
"Lean.Name.mkStr3",
"Lean.Json.getObjValAs?",
"Lean.instFromJsonArray",
"Applicative.toPure",
"ToString.toString",
"E... | true |
_aux_Init_NotationExtra___macroRules_tacticFunext____1 | Init.NotationExtra | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.mkNullNode",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"Lean.Syntax.getArgs",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
... | false |
DividedPowers.SubDPIdeal.instBot._proof_1 | Mathlib.RingTheory.DividedPowers.SubDPIdeal | [
"Ideal.mem_bot",
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"Membership.mem",
"id",
"Ne",
"instOfNatNat",
"Bot.bot",
"Ideal",
"DividedPowers.dpow_eval_zero",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Submodule.instBot",
"NonAssocSemiring.t... | false |
HasFDerivAt.sqrt | Mathlib.Analysis.SpecialFunctions.Sqrt | [
"HasFDerivAt",
"Real",
"Algebra.to_smulCommClass",
"instHSMul",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsSemitopolo... | true |
CategoryTheory.Cat.HasLimits.homDiagram_map | Mathlib.CategoryTheory.Category.Cat.Limit | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Cat.HasLimits.homDiagram._proof_4",
"CategoryTheory.eqToHom",
"CategoryTheory.Cat.HasLimits.homDiag... | true |
CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso_inv | Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.StrictlyUnitaryLaxFunctor.map_id",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.LaxFunctor.toPrel... | true |
UniqueFactorizationMonoid.multiplicative_prime_power | Mathlib.RingTheory.UniqueFactorizationDomain.Multiplicative | [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"MulOne.toOne",
"Semigroup.toMul",
"Dvd.dvd",
"Finset.prod_insert",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"Finset.mem_insert_self",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"mul_assoc",
"semigroupDvd",
"Prime"... | true |
_private.Mathlib.Analysis.SpecialFunctions.Gamma.Basic.0.Complex.GammaAux._sunfold | Mathlib.Analysis.SpecialFunctions.Gamma.Basic | [
"instHDiv",
"Complex.GammaIntegral",
"Complex.instDivInvMonoid",
"HDiv.hDiv",
"instHAdd",
"Unit",
"_private.Mathlib.Analysis.SpecialFunctions.Gamma.Basic.0.Complex.GammaAux",
"HAdd.hAdd",
"Nat",
"DivInvMonoid.toDiv",
"_private.Mathlib.Analysis.SpecialFunctions.Gamma.Basic.0.Complex.GammaAux.matc... | false |
Subalgebra.map_le | Mathlib.Algebra.Algebra.Subalgebra.Basic | [
"Subalgebra.instSetLike",
"Subsemiring.instSetLike",
"AlgHom",
"AlgHom.funLike",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"RingHom",
"Subalgebra.toSubsemiring",
"LE.le",
"Subsemiring",
"CommSemiring",
"Subalgebra.map",
"Iff",
"RingHom.instFunLike",
"SetLike.coe",
"RingH... | true |
DirectLimit.instDistribSMulOfMulActionHomClass._proof_1 | Mathlib.Algebra.Colimit.DirectLimit | [
"MulActionHomClass",
"DirectLimit.setoid",
"Eq.mpr",
"instHSMul",
"DirectLimit.instSMulZeroClassOfMulActionHomClass",
"congrArg",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"id",
"DirectLimit.instZero",
"DistribSMul.toSMulZeroClass",
"AddMonoidHomClass",
"DirectLimit.add_def",
"LE.le",
"... | false |
IsCompactlyGenerated.BooleanGenerators.mk | Mathlib.Order.BooleanGenerators | [
"Lattice.toSemilatticeSup",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"IsCompactlyGenerated.BooleanGenerators.mk",
"id",
"HasSubset.Subset",
"LE.le",
"And",
"SetLike.... | true |
HolorIndex.cast_type | Mathlib.Data.Holor | [
"cast",
"Eq.rec",
"Subtype.mk",
"congr_arg",
"List",
"Nat",
"LT.lt",
"List.Forall₂",
"Eq.refl",
"instLTNat",
"Subtype.val",
"Eq",
"HolorIndex"
] | true |
IsTopologicalRing.toIsTopologicalSemiring | Mathlib.Topology.Algebra.Ring.Basic | [
"NonUnitalNonAssocRing",
"IsTopologicalSemiring",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"IsTopologicalRing",
"TopologicalSpace"
] | true |
Aesop.Stats._sizeOf_inst | Aesop.Stats.Basic | [
"Aesop.Stats._sizeOf_1",
"Aesop.Stats",
"SizeOf.mk",
"SizeOf"
] | false |
Turing.TM1to1.tr | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"List.Vector",
"Turing.Dir.left",
"Turing.TM1to1.trNormal",
"Turing.TM1to1.move",
"Turing.TM1to1.Λ'",
"Turing.TM1to1.write",
"Nat",
"Turing.TM1to1.tr.match_1",
"Bool",
"List.Vector.toList",
"Turing.TM1.Stmt"
] | true |
ZMod.instIsAddCyclic | Mathlib.GroupTheory.SpecificGroups.Cyclic | [
"RingHom.instRingHomClass",
"RingHomClass.toAddMonoidHomClass",
"ZMod.commRing",
"AddGroupWithOne.toAddGroup",
"instIsAddCyclicInt",
"RingHom",
"Int",
"CommRing.toNonAssocCommRing",
"ZMod",
"RingHom.instFunLike",
"AddGroup.toSubNegMonoid",
"Int.castRingHom",
"Nat",
"isAddCyclic_of_surjecti... | true |
Lean.Parser.Command.syntaxCat._regBuiltin.Lean.Parser.Command.syntaxCat_1 | Lean.Parser.Syntax | [
"Lean.Parser.Command.syntaxCat",
"IO",
"Unit",
"Lean.Parser.addBuiltinLeadingParser",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
AlgebraicGeometry.tilde.adjunction._proof_1 | Mathlib.AlgebraicGeometry.Modules.Tilde | [
"CategoryTheory.Functor.FullyFaithful.map_injective",
"CategoryTheory.Functor.op",
"Eq.mpr",
"RingHom.instRingHomClass",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme.Modules.fromTildeΓ",
"CategoryTheory.Functor",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"Lattice.to... | false |
_private.Qq.Match.0.Qq._aux_Qq_Match___macroRules_Lean_Parser_Term_match_1.match_3 | Qq.Match | [
"Lean.TSyntax",
"Unit.unit",
"Option.casesOn",
"Option.some",
"List.cons",
"Array",
"Option.none",
"Unit",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr1",
"List.nil",
"Option"
] | false |
Affine.Simplex.excenter | Mathlib.Geometry.Euclidean.Incenter | [
"InnerProductSpace.toNormedSpace",
"Nat.instMulZeroClass",
"Real",
"Real.instRCLike",
"Finset",
"NormedSpace.toModule",
"Affine.Simplex",
"Real.instRing",
"instOfNatNat",
"EuclideanGeometry.Sphere.center",
"instHAdd",
"NormedAddTorsor.toAddTorsor",
"MetricSpace",
"HAdd.hAdd",
"Nat",
"i... | true |
_private.Mathlib.Data.Nat.Log.0.Nat.clog_of_one_lt._proof_1_4 | Mathlib.Data.Nat.Log | [
"Lean.Grind.of_eq_eq_true",
"instPowNat",
"Nat.ToInt.pow_congr",
"Int.Linear.eq_of_core",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Int.Nonneg.toPoly",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.Poly",
"Lean.Gr... | false |
Lean.Server.Test.Runner.Client.MsgEmbed.below_4 | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.MsgEmbed.rec_4",
"String",
"Lean.Server.Test.Runner.Client.SubexprInfo",
"Lean.Server.Test.Runner.Client.InteractiveGoal",
"Lean.Server.Test.Runner.Client.WidgetInstance",
"Lean.Widget.TaggedText",
"Lean.Server.Test.Runner.Client.MsgEmbed",
"Array",
"Lean.Server.Test.... | false |
Int64.decEq._proof_2 | Init.Data.SInt.Basic | [
"False",
"Int64.noConfusion",
"Int64.ofUInt64",
"UInt64",
"Int64",
"absurd",
"Eq",
"Not"
] | false |
_private.Lean.Meta.Match.Basic.0.Lean.Meta.Match.Pattern.toExpr.visit | Lean.Meta.Match.Basic | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.instInhabitedMetaM",
"Bool",
"Lean.Meta.Match.Pattern"
] | true |
CategoryTheory.NatIso.mapHomologicalComplex._proof_2 | Mathlib.Algebra.Homology.Additive | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.NatTrans.mapHomologicalComplex_id",
"congrArg",
"CategoryTheory.Functor.category",
"_private.Mathlib.Algebra.Homology.Additiv... | false |
LinearEquiv.instZero._proof_1 | Mathlib.Algebra.Module.Equiv.Basic | [
"RingHom",
"LinearMap.toAddHom",
"AddHom.map_add'",
"LinearMap",
"AddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"Semiring",
"Zero.toOfNat0",
"LinearMap.instZero",
"AddCommSemigroup.toAddCommMagma",
"Module",
"OfNat.ofNat",
"AddCommMonoid.toAddCommSemigroup",
"Semiring.toNonAssocSemiring",
"... | false |
Lean.Widget.PanelWidgetInstance.mk.inj | Lean.Widget.UserWidget | [
"String",
"Lean.Widget.PanelWidgetInstance.mk.noConfusion",
"Lean.Widget.PanelWidgetInstance",
"Lean.Widget.PanelWidgetInstance.mk",
"Lean.Widget.WidgetInstance",
"And",
"And.intro",
"Lean.Lsp.Range",
"Eq",
"Option"
] | true |
CategoryTheory.Abelian.SpectralObject.descOpcycles.congr_simp | Mathlib.Algebra.Homology.SpectralObject.Cycles | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.descOpcycles",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Abelian",
"CategoryTheory.Com... | true |
Lean.Grind.Ring.OfSemiring.r_trans | Init.Grind.Ring.Envelope | [
"Std.Commutative",
"Eq.mpr",
"Lean.Data.AC.Expr.var",
"congrArg",
"Lean.Grind.Ring.OfSemiring.r",
"Lean.Data.AC.Variable",
"Lean.Data.AC.Context.mk",
"Option.some",
"Exists",
"Lean.Grind.Semiring.toAdd",
"Eq.mp",
"id",
"PLift",
"Prod.mk",
"instOfNatNat",
"Lean.Grind.Ring.OfSemiring.ins... | true |
cfcₙ_le_iff._auto_5 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
LinearMap.BilinForm.IsometryEquiv.toIsometry._proof_2 | Mathlib.LinearAlgebra.BilinearForm.IsometryEquiv | [
"instHSMul",
"LinearMap.BilinForm.IsometryEquiv.instEquivLike._proof_1",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.toAddHom",
"AddCommMonoid",
"L... | false |
_private.Mathlib.RingTheory.Localization.Away.Basic.0.IsLocalization.Away.map_surjective_iff._simp_1_4 | Mathlib.RingTheory.Localization.Away.Basic | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
_private.Std.Data.Iterators.Lemmas.Combinators.Zip.0.Std.Iter.atIdxSlow?_eq_match.match_1.eq_2 | Std.Data.Iterators.Lemmas.Combinators.Zip | [
"Std.Iter.atIdxSlow?_eq_match.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
RightCancelSemigroup.casesOn | Mathlib.Algebra.Group.Defs | [
"Semigroup",
"RightCancelSemigroup.rec",
"Semigroup.toMul",
"RightCancelSemigroup.mk",
"RightCancelSemigroup",
"IsRightCancelMul"
] | false |
Lean.Lsp.RefIdent.recOn | Lean.Data.Lsp.Internal | [
"String",
"Lean.Lsp.RefIdent.const",
"Lean.Lsp.RefIdent.rec",
"Lean.Lsp.RefIdent",
"Lean.Lsp.RefIdent.fvar"
] | false |
abs_mul_self | Mathlib.Algebra.Order.Ring.Abs | [
"HMul.hMul",
"IsOrderedRing",
"AddGroupWithOne.toAddGroup",
"abs",
"congrArg",
"LinearOrder",
"abs_mul",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"instDistribOfSemiring",
"Distrib.toMul",
"True",
"eq_self",
"of_eq_true",
"abs_mul_abs_self",
"congrFun'",
"Ring.toSe... | true |
CategoryTheory.MorphismProperty.IsInvertedBy.iff_of_iso | Mathlib.CategoryTheory.MorphismProperty.IsInvertedBy | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"id",
"CategoryTheory.Iso",
"CategoryTheory.MorphismProperty.IsInvertedBy",
"CategoryTheory.Functor.map",
... | true |
Finset.card_le_card_mul_self | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Finset.mul_empty",
"HMul.hMul",
"instReflLe",
"congrArg",
"Finset",
"IsLeftCancelMul",
"Mul",
"Std.le_refl._simp_1",
"_private.Mathlib.Algebra.Group.Pointwise.Finset.Basic.0.Finset.card_le_card_mul_self._simp_1_1",
"instOfNatNat",
"LE.le",
"instLENat",
"Finset.instEmptyCollection",
"Or.ca... | true |
Lean.Grind.CommRing.Expr.denoteS_toPolyS | Init.Grind.Ring.CommSemiringAdapter | [
"Lean.Grind.CommRing.Expr.toPolyS",
"instPowNat",
"Lean.Grind.Semiring.one_mul",
"Eq.mpr",
"Int.toNat_natCast",
"Lean.Grind.CommRing.Poly.NonnegCoeffs",
"False",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",... | true |
CochainComplex.HomComplex.Cochain.single_v_eq_zero | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"CochainComplex.HomComplex.Cochain._proof_1",
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Int.instDecidableEq",
"id",
"Ne",
"HomologicalC... | true |
AbsoluteValue.IsAdmissible.mk | Mathlib.NumberTheory.ClassNumber.AdmissibleAbsoluteValue | [
"Int.cast",
"Real",
"instHSMul",
"Real.instZero",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"HSub.hSub",
"Real.instLT",
"Exists",
"SemilatticeInf.toPartialOrder",
"instHMod",
"Real.instAddGroup",
"Ne",
"Int",
"SubNegMonoid.toSub",
"HMod.hMod",
"CommRing.toCommSemiring"... | true |
Std.Time.Nanosecond.Ordinal.instTransOrdOfDay | Std.Time.Time.Unit.Nanosecond | [
"Std.TransOrd",
"Std.Time.Nanosecond.Ordinal.instOrdOfDay",
"_private.Std.Time.Time.Unit.Nanosecond.0.Std.Time.Nanosecond.Ordinal.instTransOrdOfDay._proof_1",
"Std.Time.Nanosecond.Ordinal.OfDay"
] | true |
CategoryTheory.ComposableArrows.Precomp.obj_one | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"instNeZeroNatHAdd_1",
"CategoryTheory.ComposableArrows",
"CategoryTheory.ComposableArrows.Precomp.obj",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"CategoryTheory.ComposableArrows.obj'",
"OfNat.ofNat",
"Fin",
"Eq",
"CategoryTheor... | true |
RingCat.Colimits.ColimitType.AddGroupWithOne | Mathlib.Algebra.Category.Ring.Colimits | [
"RingCat.Colimits.Prequotient.one",
"CategoryTheory.Functor",
"AddMonoidWithOne.mk",
"One.mk",
"AddMonoid.toAddSemigroup",
"RingCat.Colimits.ColimitType.AddGroupWithOne._proof_4",
"AddMonoid.toZero",
"RingCat.Colimits.ColimitType.AddGroupWithOne._proof_6",
"RingCat.Colimits.colimitSetoid",
"Catego... | true |
TopologicalSpace.IrreducibleCloseds.mk_singleton | Mathlib.Topology.Sets.Closeds | [
"Set.instSingletonSet",
"isIrreducible_singleton",
"TopologicalSpace.IrreducibleCloseds",
"TopologicalSpace",
"T1Space",
"Singleton.singleton",
"isClosed_singleton",
"Eq",
"TopologicalSpace.IrreducibleCloseds.instSingletonOfT1Space",
"rfl",
"TopologicalSpace.IrreducibleCloseds.mk",
"Set"
] | true |
CategoryTheory.Limits.pushout.instIsSplitMonoInl | Mathlib.CategoryTheory.Limits.Shapes.Diagonal | [
"CategoryTheory.Limits.pushout.codiagonal",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SplitMono.mk",
"Nonempty.intro",
"CategoryTheory.Limits.pushout.inl_codiagonal",
"CategoryTheory.IsSplitMono",
"CategoryTheory.Limits.pushout",
"CategoryTheory.Category.toCategoryStruc... | true |
Order.Ideal.sup_mem | Mathlib.Order.Ideal | [
"Order.Ideal.lower",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"SemilatticeSup.toMax",
"Order.Ideal.directed",
"LE.le",
"And",
"SetLike.coe",
"Max.max",
"_private.Mathlib.Order.Ideal.0.Order.Ideal.sup_mem.match_1_1",
"sup_le",
"SemilatticeSup.toPartialOrder",
... | true |
mem_algebraicClosure_iff | Mathlib.FieldTheory.AlgebraicClosure | [
"IsAlgebraic",
"IntermediateField",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"Iff",
"IsIntegral",
"Semifield.toDivisionSemiring",
"algebraicClosure",
"DivisionSemiring.toSemiring",
"IntermediateField.instSetLike",
... | true |
ModuleCat.injectiveDimension_le_injectiveDimension_of_isLocalizedModule | Mathlib.RingTheory.LocalProperties.InjectiveDimension | [
"WithBot.instPreorder",
"Eq.mpr",
"CommRing",
"WithBot.some",
"WithBot",
"instCompleteLinearOrderENat",
"ChainCompletePartialOrder.instOfCompleteLattice",
"ENat.instNatCast",
"LocalizedModule",
"LocalizedModule.instSubsingleton",
"ModuleCat",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCom... | true |
Finset.expect_neg_distrib | Mathlib.Algebra.BigOperators.Expect | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"NNRat.instInv",
"Finset.expect",
"congrArg",
"NNRat.instSemifield",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Finset",
"AddMonoid.toAddZeroClass",
"AddCommG... | true |
_private.Mathlib.Data.Set.NAry.0.Set.Nonempty.image2.match_1_1 | Mathlib.Data.Set.NAry | [
"Membership.mem",
"Set.Nonempty",
"Exists.casesOn",
"Exists.intro",
"Set.instMembership",
"Set"
] | false |
Lean.Compiler.LCNF.ToLCNF.State.shouldCache | Lean.Compiler.LCNF.ToLCNF | [
"Lean.Compiler.LCNF.ToLCNF.State",
"Bool"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.getD_union._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 |
Finset.val_toFinset | Mathlib.Data.Finset.Dedup | [
"Multiset.toFinset",
"Eq.mpr",
"congrArg",
"Finset",
"Iff.rfl",
"Finset.ext",
"Membership.mem",
"Multiset",
"id",
"Finset.val",
"Multiset.instMembership",
"Iff",
"Finset.instSetLike",
"propext",
"Eq.symm",
"Eq",
"SetLike.instMembership",
"Multiset.mem_toFinset",
"Finset.mem_def",... | true |
CategoryTheory.Functor.inr_biprodComparison' | Mathlib.CategoryTheory.Limits.Preserves.Shapes.Biproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasBinaryBiproduct",
"CategoryTheory.Limits.biprod.inr_desc",
"CategoryTheory.Limits.biprod",
"CategoryTheory.Functor.map",
"CategoryTheory.Limits.biprod... | true |
WithTop.instSemiring._proof_3 | Mathlib.Algebra.Order.Ring.WithTop | [
"Nontrivial",
"WithTop.instMonoidWithZero",
"Semigroup.toMul",
"HMul.hMul",
"instDistribOfSemiring",
"NoZeroDivisors",
"Distrib.toMul",
"Monoid.toSemigroup",
"Semiring",
"One.toOfNat1",
"Monoid.toOne",
"Monoid.mul_one",
"OfNat.ofNat",
"Eq",
"MonoidWithZero.toMonoid",
"MulZeroClass.toZe... | false |
HomologicalComplex.truncLE'ToRestriction._proof_1 | Mathlib.Algebra.Homology.Embedding.TruncLE | [
"ComplexShape",
"ComplexShape.Embedding.instIsTruncGEOpOfIsTruncLE",
"ComplexShape.Embedding.op",
"ComplexShape.Embedding",
"ComplexShape.symm",
"ComplexShape.Embedding.IsRelIff",
"ComplexShape.Embedding.IsTruncLE",
"ComplexShape.Embedding.IsTruncGE.toIsRelIff"
] | false |
WithLp.toLp.noConfusion | Mathlib.Analysis.Normed.Lp.WithLp | [
"WithLp",
"WithLp.noConfusion",
"WithLp.toLp",
"id",
"heq_of_eq",
"ENNReal",
"Eq.refl",
"HEq",
"Eq"
] | false |
Lean.Meta.Grind.NewRawFact.generation | Lean.Meta.Tactic.Grind.Types | [
"Nat",
"Lean.Meta.Grind.NewRawFact"
] | true |
_private.Lean.Meta.Basic.0.Lean.initFn._@.Lean.Meta.Basic.2682336532._hygCtx._hyg.2 | Lean.Meta.Basic | [
"Lean.Name.mkNum",
"IO",
"Lean.Name.mkStr3",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.registerTraceClass",
"instMonadEIO",
"Lean.Name.anonymous",
"Unit",
"Nat",
"Lean.Name.mkStr2",
"Monad.toBind",
"Bind.bind",
"IO.Error",
"OfNat.ofNat",
"Bool.false"
] | false |
CategoryTheory.Localization.homEquiv_comp | Mathlib.CategoryTheory.Localization.HomEquiv | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Localization.homEquiv",
"Equiv",
"CategoryTheory.Functor.IsLocalization",
"CategoryTheory.LocalizerMorphism.homMap_comp",
"CategoryTheory.Loca... | true |
normalizedGCDMonoidOfGCD._proof_4 | Mathlib.Algebra.GCDMonoid.Basic | [
"Iff.mpr",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"Dvd.intro",
"NormalizationMonoid",
"semigroupDvd",
"MonoidWithZeroHom.funLike",
"SemigroupWithZero.toSemigroup",
"CommMonoidWithZero.toMonoidWithZero",
"MonoidWithZero.toSemigroupWithZero",
"MonoidWithZeroHom",
"MonoidWithZero.toMulZeroO... | false |
Subalgebra.centralizer_le | Mathlib.Algebra.Algebra.Subalgebra.Basic | [
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"HasSubset.Subset",
"LE.le",
"Set.centralizer_subset",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"Subalgebra.instPartialOrder",
"Semiring",
"Subalgebra.centralizer",
"Subalgebra",
"Set.instHasSubset",
"Set"
] | true |
Subgroup.fintypeQuotientOfFiniteIndex | Mathlib.GroupTheory.Index | [
"Subgroup.FiniteIndex",
"Group",
"Subgroup.fintypeOfIndexNeZero",
"Subgroup.FiniteIndex.index_ne_zero",
"QuotientGroup.instHasQuotientSubgroup",
"Subgroup",
"HasQuotient.Quotient",
"Fintype"
] | true |
instMonadBaseIO._aux_1 | Init.System.IO | [
"Function.comp",
"IO.RealWorld",
"ST",
"ST.bind",
"ST.pure",
"BaseIO"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.get!_alter._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 |
Int32.toInt_sub_of_le | Init.Data.SInt.Lemmas | [
"Eq.mpr",
"Int.ofNat_sub",
"instLEInt32",
"congrArg",
"HSub.hSub",
"Int32.sub_nonneg_of_le",
"id",
"instSubNat",
"Int32.toNatClampNeg_sub_of_le",
"Int",
"LE.le",
"Int32.toInt",
"instSubInt32",
"Nat.cast",
"Int32.toNatClampNeg",
"instHSub",
"Int32.le_trans",
"Int32.toInt_eq_toNatCla... | true |
NumberField.InfinitePlace.even_finrank_of_not_isUnramified | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | [
"IsGalois.card_aut_eq_finrank",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Even.zero",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Algebra",
"Classical.propDecidable",
"Nat.instAddMonoid",
"NumberField.InfinitePlace.even_card_aut_of_not_isUnr... | true |
_private.Mathlib.Data.PEquiv.0.PEquiv.trans_eq_none._simp_1_1 | Mathlib.Data.PEquiv | [
"Option.instMembership",
"Membership.mem",
"Option.none",
"propext",
"Option.eq_none_iff_forall_not_mem",
"Eq",
"Not",
"Option"
] | false |
IsCoveringMap.monodromy._proof_1 | Mathlib.Topology.Homotopy.Lifting | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"Membership.mem",
"Real.semiring",
"Set.Elem",
"Set.instSingletonSet",
"TopologicalSpace",
"Set.preimage",
"Path.instFunLike",
"Path",
"Path.source",
"Zero.toOfNat0",
"Singleton.singleton",
"OfNat.ofNat",
"Eq.... | false |
CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso_inv_app_f | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Coalgebra.instCategory",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.i... | true |
NNRat.nndist_eq | Mathlib.Topology.Instances.Rat | [
"NNDist.nndist",
"Rat",
"PseudoMetricSpace.toNNDist",
"NNRat.instMetricSpace",
"NNRat",
"NNReal",
"Rat.instNNRatCast",
"MetricSpace.toPseudoMetricSpace",
"Rat.instMetricSpace",
"NNRat.cast",
"Eq",
"rfl"
] | true |
_private.Batteries.Data.List.Count.0.List.idxToSigmaCount_sigmaCountToIdx._proof_1_20 | Batteries.Data.List.Count | [
"Lean.Grind.Nat.lt_eq",
"Sigma.fst",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"List",
"instHAdd",
"BEq.beq",
"List.count",
"HAdd.hAdd",
"Nat",
"List.filter",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Sigma.snd",
"Fin",
"BEq",
"List.length",
... | false |
CharacterModule.eq_zero_of_ofSpanSingleton_apply_self | Mathlib.Algebra.Module.CharacterModule | [
"Int.instAddCommGroup",
"LinearMap.toAddMonoidHom",
"CharacterModule.intSpanEquivQuotAddOrderOf._proof_2",
"LinearMap.toAddMonoidHom_coe",
"Rat.instOfNat",
"Int.cast",
"AddCircle.coe_eq_zero_iff",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Submodule.Quotient.addCommMonoid",
"instHS... | true |
BoundedContinuousFunction.instAddMonoid | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"BoundedContinuousFunction.instAddMonoid._proof_2",
"instHSMul",
"PseudoMetricSpace.toBornology",
"BoundedContinuousFunction.instAdd",
"ContinuousMap.mk",
"AddMonoid.toAddZeroClass",
"BoundedContinuousFunction.instAddMonoid._proof_1",
"AddMonoid.toNSMul",
"PseudoMetricSpace.toUniformSpace",
"AddMo... | true |
_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic.0.Path.Homotopic.Quotient.refl_trans._simp_1_2 | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"Path.Homotopic.Quotient",
"Path.Homotopic.Quotient.refl",
"TopologicalSpace",
"Eq.symm",
"Path.refl",
"Eq",
"Path.Homotopic.Quotient.mk_refl",
"Path.Homotopic.Quotient.mk"
] | false |
Aesop.GlobalRuleSetMember.base.noConfusion | Aesop.RuleSet.Member | [
"id",
"Aesop.GlobalRuleSetMember",
"Aesop.GlobalRuleSetMember.base",
"Aesop.BaseRuleSetMember",
"Eq",
"Aesop.GlobalRuleSetMember.noConfusion"
] | false |
CategoryTheory.Join.isoMkFunctor._proof_2 | Mathlib.CategoryTheory.Join.Basic | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Join.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Join.mkFunctor_edgeTransform",
"CategoryTheory.Functor.category",
"CategoryTheory.Join.mkFunctorLeft",
"Cate... | false |
CategoryTheory.IsUniversalColimit.isPullback_of_isColimit_left | Mathlib.CategoryTheory.Limits.VanKampen | [
"CategoryTheory.Limits.Cofan.IsColimit.desc",
"Eq.mpr",
"CategoryTheory.Limits.IsColimit.fac",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.IsUniversalColimit.nonempty_isColimit_of_isPullback_left",
"Cate... | true |
AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen' | Mathlib.AlgebraicGeometry.AffineScheme | [
"Eq.mpr",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Lattice.toSemilatticeSup",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
... | true |
Vector.unzip_snd | Init.Data.Vector.Zip | [
"Vector",
"Vector.unzip_mk._proof_1",
"congrArg",
"Array.unzip",
"Vector.casesOn",
"Array.map",
"Vector.map_mk._proof_1",
"Vector.unzip_mk._proof_2",
"Prod.mk",
"Prod.fst",
"Vector.map",
"Array",
"Vector.mk",
"Nat",
"congr",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl... | true |
_private.Mathlib.Analysis.Normed.Group.SemiNormedGrp.0.SemiNormedGrp.Hom.ext.match_1 | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"NormedAddGroupHom",
"SemiNormedGrp.Hom",
"SemiNormedGrp.Hom.casesOn",
"SemiNormedGrp.carrier",
"SemiNormedGrp.Hom.mk",
"SemiNormedGrp.str",
"SemiNormedGrp"
] | false |
_private.Mathlib.RingTheory.WittVector.Basic.0.Int.castDef.match_1.splitter | Mathlib.RingTheory.WittVector.Basic | [
"Int.ofNat",
"Int",
"Nat",
"Int.negSucc",
"Int.castDef.match_1"
] | true |
CategoryTheory.Sheaf.instMonoidalFunctorOppositePresheafToSheaf._aux_3 | Mathlib.CategoryTheory.Sites.Monoidal | [
"CategoryTheory.Localization.Monoidal.leftUnitor_hom_app",
"CategoryTheory.Functor",
"CategoryTheory.Functor.CoreMonoidal.μIso",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.IsMonoidal",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functo... | false |
MeasureTheory.ComplexMeasure.equivSignedMeasure._proof_1 | 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... | false |
TypeVec.append1Cases | Mathlib.Data.TypeVec | [
"Eq.mpr",
"TypeVec.last",
"TypeVec.append1",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"TypeVec.drop",
"TypeVec.append1Cases._proof_1",
"TypeVec"
] | true |
Polynomial.splits_of_splits_of_dvd | Mathlib.Algebra.Polynomial.Splits | [
"IsDomain",
"CommRing",
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"semigroupDvd",
"SemigroupWithZero.toSemigroup",
"Ne",
"NonUnitalSemiring.toSemigroupWithZero",
"Polynomial",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"CommRing.toCommSemiring",
"NonUnitalCommRi... | true |
CStarAlgebra.norm_le_norm_of_nonneg_of_le._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Filter.NeBot.nonneg_sub | Mathlib.Order.Filter.Pointwise | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"congrArg",
"Filter.NeBot",
"Filter.instCompleteLatticeFilter",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"Disjoint",
"CompleteLattice.toBoundedOrder",
"Filter.neBot_iff",
"id",
"Ne",
"SubtractionMonoid.toSubNegZe... | true |
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