name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Polynomial.smeval_at_natCast | Mathlib.Algebra.Polynomial.Smeval | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MonoidWithZero.toMulActionWithZero",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Pow",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap... | true |
Ideal.quotEquivPowQuotPowSuccEquiv | Mathlib.RingTheory.Ideal.IsPrincipalPowQuotient | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"IsDomain",
"Submodule.Quotient.addCommMonoid",
"Submodule.module._proof_1",
"CommRing",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Submodule.a... | true |
CochainComplex.singleFunctors._proof_7 | Mathlib.Algebra.Homology.HomotopyCategory.SingleFunctors | [
"CochainComplex.shiftFunctorZero_eq",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"CochainComplex.singleFunctors._proof_6",
"HomologicalComplex.Hom.isoOfComponents",
... | false |
_private.Mathlib.AlgebraicGeometry.Restrict.0.AlgebraicGeometry.Scheme.Opens.nonempty_iff._simp_1_1 | Mathlib.AlgebraicGeometry.Restrict | [
"Exists",
"Subtype",
"nonempty_subtype",
"propext",
"Nonempty",
"Eq"
] | false |
_private.Lean.Elab.Structure.0.Lean.Elab.Command.Structure.mkCtor | Lean.Elab.Structure | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.instMonadEnvOfMonadLift",
"Lean.instantiateMVars",
"Lean.mkNullNode",
"_private.Lean.Elab.Structure.0.Lean.Elab.Command.Structure.fieldNormalizeExpr",
"StateT.instMonadFunctor",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExc... | true |
MonoidHom.comp_noncommCoprod | Mathlib.GroupTheory.NoncommCoprod | [
"MonoidHom.noncommCoprod",
"Monoid",
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"MonoidHom.ext",
"Commute",
"Prod.instMulOneClass",
"MulOne.toMul",
"MonoidHom.comp",
"Prod.fst",
"map_mul",
"MulOneClass.toMulOne... | true |
_private.Init.PropLemmas.0.exists_and_self.match_1_3 | Init.PropLemmas | [
"Exists",
"Exists.casesOn",
"Exists.intro"
] | false |
Lean.Elab.Command.State.noConfusion | Lean.Elab.Command | [
"Lean.Elab.InfoState",
"Lean.NameSet",
"Lean.Language.SnapshotTree",
"Lean.Language.SnapshotTask",
"Array",
"List",
"Lean.DeclNameGenerator",
"Lean.TraceState",
"Lean.Elab.Command.State",
"Nat",
"Lean.Elab.Command.Scope",
"Eq.ndrec",
"Eq.refl",
"Lean.Elab.Command.State.noConfusionType",
... | false |
CategoryTheory.GrpObj.eq_lift_inv_left | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.GrpObj.inv",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.GrpObj.toMonObj",
"CategoryTheory.MonObj.lift_comp_one_left",
"CategoryTheory.CartesianMonoidalCategory.lift",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"Category... | true |
IndepMatroid.ofBddAugment_E | Mathlib.Combinatorics.Matroid.IndepAxioms | [
"Set.encard",
"ENat.instNatCast",
"Membership.mem",
"Exists",
"Insert.insert",
"HasSubset.Subset",
"LE.le",
"Nat.cast",
"instLEENat",
"And",
"Set.instInsert",
"IndepMatroid.ofBddAugment",
"Nat",
"ENat",
"LT.lt",
"Set.instEmptyCollection",
"instLTENat",
"EmptyCollection.emptyCollect... | true |
CategoryTheory.ObjectProperty.singleton_le_iff._simp_1 | Mathlib.CategoryTheory.ObjectProperty.Basic | [
"Prop.le",
"CategoryTheory.ObjectProperty.singleton",
"LE.le",
"Pi.hasLe",
"propext",
"CategoryTheory.CategoryStruct",
"CategoryTheory.ObjectProperty.singleton_le_iff",
"Eq",
"CategoryTheory.ObjectProperty"
] | false |
_private.Init.Prelude.0.Nat.le_trans.match_1_1 | Init.Prelude | [
"HEq.refl",
"LE.le",
"instLENat",
"Nat.le.step",
"Nat.le",
"Nat",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Nat.le.refl",
"Nat.le.casesOn",
"Eq.symm",
"Nat.succ",
"Eq"
] | false |
CategoryTheory.sheafify_hom_ext | Mathlib.CategoryTheory.Sites.Sheafification | [
"Eq.mpr",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.toSheafify",
"CategoryTheory.sheafifyLift_unique",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"id",
"CategoryTheory.sheafify",
"CategoryTheory.GrothendieckTopology",
"C... | true |
IsCyclotomicExtension.autEquivPow._proof_3 | Mathlib.NumberTheory.Cyclotomic.Gal | [
"Units.val",
"IsDomain",
"Nat.instMulZeroClass",
"CommRing",
"ZMod.commRing",
"CommSemiring.toSemiring",
"PowerBasis.gen",
"Algebra",
"Polynomial.cyclotomic",
"Field.toDivisionRing",
"IsPrimitiveRoot.pow_of_coprime",
"Units",
"Irreducible",
"Set.instSingletonSet",
"id",
"DivisionRing.t... | false |
Lean.Grind.LinarithConfig.locals._inherited_default | Init.Grind.Config | [
"id",
"Bool",
"Bool.false"
] | false |
PFunctor.Approx.CofixA._sizeOf_1 | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.A",
"PFunctor.B",
"instSizeOfDefault",
"PFunctor.Approx.CofixA.rec",
"instOfNatNat",
"instHAdd",
"PFunctor.Approx.CofixA",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"instSizeOfNat",
"OfNat.ofNat"
] | false |
CategoryTheory.leftDistributor_ext₂_left_iff | Mathlib.CategoryTheory.Monoidal.Preadditive | [
"CategoryTheory.leftDistributor_ext₂_left",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"Finite",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Limits.HasFiniteBiproducts",
"CategoryTheory.MonoidalPreadditive",
"Eq.c... | true |
PFunctor.MIntl.mk._flat_ctor | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.MIntl.mk",
"PFunctor.Approx.AllAgree",
"PFunctor.Approx.CofixA",
"Nat",
"PFunctor.MIntl"
] | false |
Lean.Elab.Tactic.Location.wildcard | Lean.Elab.Tactic.Location | [
"Lean.Elab.Tactic.Location.wildcard",
"Lean.Elab.Tactic.Location"
] | true |
Subsemiring.smul_def | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"instHSMul",
"Subsemiring.instSetLike",
"SMul",
"Subsemiring.smul",
"Membership.mem",
"Subtype",
"Subsemiring",
"NonAssocSemiring",
"HSMul.hSMul",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"rfl"
] | true |
QuadraticMap.map_sum | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"Eq.mpr",
"instDecidableNot",
"_private.Mathlib.LinearAlgebra.QuadraticForm.Basic.0.QuadraticMap.map_sum._simp_1_1",
"False",
"CommRing",
"Sym2.map",
"instDecidableTrue",
"SemilinearMapClass.distribMulActionSemiHomClass",
"AddMonoid.toAddSemigroup",
"outParam",
"Finset.sum_cons",
"Finset.cons_... | true |
EReal.le_mul_of_forall_lt | Mathlib.Data.EReal.Inv | [
"Preorder.toLT",
"Set.mem_Ioo",
"HMul.hMul",
"Or.imp_left",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Membership.mem",
"Exists",
"ne_of_gt",
"instTopEReal",
"LT.lt.le",
"Ne",
"instZeroEReal",
"LE.le",
"And.casesOn",
"instLinearOrderEReal",
"GT.gt",
"And",
"_private.... | true |
toLex_neg | Mathlib.Algebra.Order.Group.Synonym | [
"Equiv.instEquivLike",
"Lex",
"Equiv",
"Neg",
"instNegLex",
"Eq",
"DFunLike.coe",
"Neg.neg",
"rfl",
"EquivLike.toFunLike",
"toLex"
] | true |
Ring.multichoose_eq | Mathlib.RingTheory.Binomial | [
"Eq.mpr",
"AddCommMonoidWithOne.toAddCommMonoid",
"AddGroupWithOne.toAddGroup",
"Pow",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Eq.rec",
"id",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"AddMonoidWithOne.toNatCast",
"Ring.choose.eq_1",
"Non... | true |
SimpleGraph.Walk.firstDart.congr_simp | Mathlib.Combinatorics.SimpleGraph.Walk.Traversal | [
"SimpleGraph.Walk",
"Eq.rec",
"SimpleGraph.Dart",
"SimpleGraph",
"SimpleGraph.Walk.firstDart",
"SimpleGraph.Walk.Nil",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Not"
] | true |
QuotientGroup.coe_mk' | Mathlib.GroupTheory.QuotientGroup.Defs | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"QuotientGroup.mk",
"Group",
"QuotientGroup.instHasQuotientSubgroup",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"HasQuotient.Quotient",
"MulOneClass.toMulOne",
"QuotientGroup.mk'",
"QuotientGroup.Quotient.group"... | true |
CategoryTheory.GrothendieckTopology.recOn | Mathlib.CategoryTheory.Sites.Grothendieck | [
"Lattice.toSemilatticeSup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"CategoryTheory.GrothendieckTopo... | false |
Std.Rxc.Iterator.pairwise_toList_upwardEnumerableLt | Init.Data.Range.Polymorphic.Lemmas | [
"Eq.mpr",
"Std.Rxc.Iterator",
"Exists.choose_spec",
"Decidable.casesOn",
"_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Rxc.Iterator.toList_eq_match.match_1.splitter",
"List.Pairwise.cons",
"Std.PRange.UpwardEnumerable.succMany?_add_one",
"Std.IterStep",
"Std.PRange.UpwardEnumerable",
"Std.Ite... | true |
Tactic.ComputeAsymptotics.Majorized.zero | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Majorized | [
"NormedCommRing.toSeminormedCommRing",
"Real.instPow",
"Real",
"Real.instZero",
"Asymptotics.isLittleO_zero",
"Real.instLT",
"Pi.instPow",
"Pi.instZero",
"Filter.atTop",
"GT.gt",
"HPow.hPow",
"Real.normedCommRing",
"NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing",
"Tactic.ComputeAsy... | true |
String.Slice.RevPosIterator.mk | Init.Data.String.Iterate | [
"String.Slice",
"String.Slice.RevPosIterator.mk",
"String.Slice.Pos",
"String.Slice.RevPosIterator"
] | true |
AlgebraicGeometry.pullbackRestrictIsoRestrict_inv_fst_assoc | Mathlib.AlgebraicGeometry.Restrict | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOr... | true |
_private.Mathlib.Algebra.Polynomial.RuleOfSigns.0.Polynomial.succ_signVariations_le_X_sub_C_mul._proof_1_1 | Mathlib.Algebra.Polynomial.RuleOfSigns | [
"instLawfulOrderLT_mathlib",
"Lean.Grind.Linarith.Expr.zero",
"Lean.Grind.Linarith.Expr",
"NegZeroClass.toNeg",
"of_eq_false",
"Lean.RArray.leaf",
"False",
"Lean.Grind.Linarith.Expr.neg",
"Preorder.toLT",
"Lean.Grind.Linarith.not_lt_norm",
"Polynomial.instNeg",
"eq_false",
"Lean.Grind.iff_eq... | false |
CategoryTheory.MorphismProperty.pushout_inr_iff | Mathlib.CategoryTheory.MorphismProperty.Descent | [
"CategoryTheory.IsPushout.of_hasPushout",
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.iff_of_isPushout",
"CategoryTheory.MorphismProperty.CodescendsAlong",
"CategoryTheory.MorphismProperty.IsStableUnderCobaseChange",
"Iff"... | true |
CommSemiring.toBialgebra | Mathlib.RingTheory.Bialgebra.Basic | [
"CommSemiring.toSemiring",
"CommSemiring.toCoalgebra",
"Algebra.id",
"CommSemiring",
"CommSemiring.toBialgebra._proof_4",
"CommSemiring.toBialgebra._proof_3",
"Bialgebra",
"CommSemiring.toBialgebra._proof_2",
"Bialgebra.mk",
"CommSemiring.toBialgebra._proof_1"
] | true |
Orthonormal.inner_left_finsupp | Mathlib.Analysis.InnerProductSpace.Orthonormal | [
"Finsupp.instFunLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"SeminormedAddCommGroup",
"Semiring.toModule",
"Finsupp.module",
"Orthonormal",
"Inner.inner",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"LinearMap.instFunLike",
"RingHo... | true |
_private.Mathlib.Topology.LocallyConstant.Basic.0.LocallyConstant.piecewise._simp_1 | Mathlib.Topology.LocallyConstant.Basic | [
"Decidable",
"dite_eq_right_iff",
"dite",
"propext",
"Eq",
"Not"
] | false |
Real.expPartialHomeomorph._proof_2 | Mathlib.Analysis.SpecialFunctions.Log.Basic | [
"Real",
"Set.Ioi",
"Real.instZero",
"Set.univ",
"Membership.mem",
"Real.log",
"Set.mem_univ",
"Zero.toOfNat0",
"OfNat.ofNat",
"Set.instMembership",
"Real.instPreorder",
"Set"
] | false |
AlgebraicGeometry.PresheafedSpace | Mathlib.Geometry.RingedSpace.PresheafedSpace | [
"AlgebraicGeometry.PresheafedSpace.mk",
"CategoryTheory.Category"
] | true |
Std.ExtHashSet.getD_inter_of_not_mem_right | Std.Data.ExtHashSet.Lemmas | [
"Std.ExtHashSet",
"Membership.mem",
"Std.ExtHashSet.getD",
"LawfulHashable",
"Inter.inter",
"Std.ExtHashSet.instInterOfEquivBEqOfLawfulHashable",
"Unit",
"EquivBEq",
"Std.ExtHashSet.inner",
"Hashable",
"Std.ExtHashSet.instMembershipOfEquivBEqOfLawfulHashable",
"Std.ExtHashMap.getKeyD_inter_of_... | true |
Orientation.definition._proof_7._@.Mathlib.Analysis.InnerProductSpace.TwoDim.1773570744._hygCtx._hyg.2 | Mathlib.Analysis.InnerProductSpace.TwoDim | [
"InnerProductSpace.toNormedSpace",
"Real",
"Semiring.toModule",
"Real.instRCLike",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instSMulCommClass",
"NormedSpace.toModule",
"Real.semiring",
"LinearMap",
"smulCommClass_self",
"LinearMa... | false |
CategoryTheory.instNontrivialEndOfSimple | Mathlib.CategoryTheory.Simple | [
"Nontrivial",
"CategoryTheory.End.one",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"nontrivial_of_ne",
"CategoryTheory.End",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.id_nonzero",
"One.toOfNat1",
"Zero.toOfNat0",
"Cate... | true |
Sum.elim_intCast_intCast | Mathlib.Data.Int.Cast.Pi | [
"Int.cast",
"Pi.instIntCast",
"IntCast",
"Sum",
"Int",
"Sum.elim_lam_const_lam_const",
"Eq",
"Sum.elim"
] | true |
ContDiffMapSupportedIn.structureMapLM._proof_1 | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | [
"Real",
"PseudoMetricSpace.toBornology",
"NormedSpace",
"Real.denselyNormedField",
"ContinuousMultilinearMap.instAddMonoid",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"ContinuousMultilinearMap.seminormedAddCommGroup'",
"PseudoMetricSpace.toUniformSpace",
... | false |
_private.Mathlib.Combinatorics.Enumerative.Composition.0.Composition.recOnSingleAppend.match_3._arg_pusher | Mathlib.Combinatorics.Enumerative.Composition | [
"Nat.instMulZeroClass",
"Composition.mk",
"HEq.refl",
"List.sum",
"Membership.mem",
"id",
"instOfNatNat",
"Composition",
"List",
"List.instMembership",
"_private.Mathlib.Combinatorics.Enumerative.Composition.0.Composition.recOnSingleAppend.match_3.splitter",
"Nat",
"LT.lt",
"eq_of_heq",
... | false |
FirstOrder.Language.Structure.funMap | Mathlib.ModelTheory.Basic | [
"FirstOrder.Language.Structure",
"Nat",
"FirstOrder.Language.Functions",
"FirstOrder.Language",
"Fin"
] | true |
String.intercalate_singleton | Init.Data.String.Lemmas.Intercalate | [
"String",
"List.cons",
"eq_self",
"of_eq_true",
"String.intercalate",
"Eq",
"List.nil"
] | true |
Std.HashMap.getKey!_ofList_of_contains_eq_false | Std.Data.HashMap.Lemmas | [
"Inhabited.default",
"List.map",
"List.contains",
"Std.HashMap.ofList",
"LawfulHashable",
"Prod.fst",
"Std.HashMap.getKey!",
"List",
"EquivBEq",
"Bool",
"Inhabited",
"Hashable",
"Std.DHashMap.Const.getKey!_ofList_of_contains_eq_false",
"Prod",
"Bool.false",
"BEq",
"Eq"
] | true |
CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom | Mathlib.CategoryTheory.IsomorphismClasses | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsIsomorphic",
"CategoryTheory.Groupoid.isoEquivHom",
"CategoryTheory.Groupoid",
"CategoryTheory.Iso",
"Iff",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"Equiv.nonempty_congr",
"CategoryTheory.Groupoid.toCategor... | true |
Multiset.rel_add_left | Mathlib.Data.Multiset.AddSub | [
"Eq.mpr",
"congrArg",
"Multiset.rel_zero_left._simp_1",
"Exists",
"exists_and_left._simp_1",
"Multiset",
"Multiset.cons",
"id",
"Multiset.induction_on",
"Multiset.cons_add",
"Multiset.zero_add",
"And.casesOn",
"iff_self",
"exists_eq_right'._simp_1",
"funext",
"instHAdd",
"And",
"_p... | true |
instULiftableId | Mathlib.Control.ULiftable | [
"Equiv",
"Id",
"ULiftable.mk",
"ULiftable"
] | true |
instFromJsonMessageActionItem | Lean.Data.Lsp.Window | [
"MessageActionItem",
"instFromJsonMessageActionItem.fromJson",
"Lean.FromJson",
"Lean.FromJson.mk"
] | true |
Metric.mem_closedEBall._simp_1 | Mathlib.Topology.EMetricSpace.Defs | [
"Metric.mem_closedEBall",
"Membership.mem",
"LE.le",
"PseudoEMetricSpace",
"PseudoEMetricSpace.toEDist",
"ENNReal.instLE",
"ENNReal",
"propext",
"Metric.closedEBall",
"EDist.edist",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.bmod_natAbs_add_one._proof_1_4 | Init.Data.Int.DivMod.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"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.add_congr",
"Int.decLe",
"Lean.Omega.Linear... | false |
Real.rpow_eq_const_mul_integral_rpowIntegrand₁₂ | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation | [
"MeasureTheory.ae",
"Real.integrableOn_rpowIntegrand₀₁_Ioi",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.instPow",
"instClosedIicTopology",
"Real.instLE",
"Real",
"MeasureTheory.ae_restrict_mem",
"Set.Ioi",
"Algebra.to_smulCom... | true |
Std.DTreeMap.Internal.Impl.ordered_insert | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.ordered_insertₘ",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.insert_eq_insertₘ",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.Ordered",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.s... | true |
Int.Linear.instBEqPoly.beq._sparseCasesOn_2 | Init.Data.Int.Linear | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Int.Linear.Poly.rec",
"Nat.hasNotBit",
"instOfNatNat",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.num",
"Int.Linear.Poly.add",
"Nat.land",
"Int.Linear.Poly.ctorIdx",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Int.Linear.Poly"
] | false |
Std.Roc.size_eq_match_roc | Init.Data.Range.Polymorphic.Lemmas | [
"Eq.mpr",
"Std.Roc.upper",
"Std.Rcc.lower",
"Std.PRange.UpwardEnumerable",
"congrArg",
"Std.Rxc.Iterator.toList_eq_match.match_1",
"Std.Rxc.HasSize",
"Std.Rxc.LawfulHasSize",
"id",
"instOfNatNat",
"LE.le",
"Std.PRange.UpwardEnumerable.succ?",
"LE",
"funext",
"instHAdd",
"DecidableLE",
... | true |
Mathlib.Tactic.RingNF.nat_rawCast_0 | Mathlib.Tactic.Ring.RingNF | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.rawCast",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"CommSemiring",
"AddZero.toZero",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Zer... | true |
fderiv_finset_prod | Mathlib.Analysis.Calculus.FDeriv.Mul | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NormedCommRing.toCommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedRing.toRing",
"NormedSpace",
"NormedCommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMon... | true |
Std.DTreeMap.Const.entryAtIdx | Std.Data.DTreeMap.Basic | [
"Std.DTreeMap",
"Ordering",
"Std.DTreeMap.inner",
"Std.DTreeMap.Const.getThenInsertIfNew?._proof_1",
"Std.DTreeMap.size",
"Nat",
"LT.lt",
"Std.DTreeMap.Internal.Impl.Const.entryAtIdx",
"instLTNat",
"Prod"
] | true |
Finsupp.sum_smul_index_semilinearMap' | Mathlib.LinearAlgebra.Finsupp.LSum | [
"Eq.mpr",
"Finsupp.smulZeroClass",
"instHSMul",
"Finsupp.sum_smul_index'",
"SemilinearMapClass.toMulActionSemiHomClass",
"outParam",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Finsupp.sum",
"RingHom",
"LinearMap.map_zero",
"AddZeroCl... | true |
Valuation.map_add_of_distinct_val | Mathlib.RingTheory.Valuation.Basic | [
"le_iff_eq_or_lt",
"Eq.mpr",
"False",
"Trans.trans",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"lt_irrefl",
"Classical.or_iff_not_imp_right",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Valuation.map_add",
"PartialOrder.toPreorder",
"HSub.hSub",
"LinearOrderedCom... | true |
CategoryTheory.AddGrp.toAddMon_X | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.AddGrp",
"CategoryTheory.AddGrp.toAddMon",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.AddMon.X",
"CategoryTheory.AddGrp.X",
"Eq.refl",
"Eq",
"CategoryTheory.Category",
"CategoryTheory.CartesianMonoi... | true |
_private.Mathlib.Algebra.QuadraticAlgebra.Basic.0.QuadraticAlgebra.norm_eq_zero_iff_eq_zero._proof_1_2 | Mathlib.Algebra.QuadraticAlgebra.Basic | [
"QuadraticAlgebra.re",
"NegZeroClass.toNeg",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.diseq_to_eq",
"instHDiv",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Divisi... | false |
LinearMap.rTensor_add | Mathlib.LinearAlgebra.TensorProduct.Map | [
"LinearMap.map_add",
"CommSemiring.toSemiring",
"LinearMap.rTensorHom",
"TensorProduct.addCommMonoid",
"LinearMap.instAdd",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"instHAdd",
"HAdd.hAdd",
"CommMonoid.toMonoid",
"TensorProduct.instSMul._proof... | true |
Lean.Meta.Grind.SimpGoalResult.noConfusion | Lean.Meta.Sym.Grind | [
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.SimpGoalResult",
"Eq.ndrec",
"Lean.Meta.Grind.SimpGoalResult.noConfusionType",
"Eq.refl",
"Eq",
"Lean.Meta.Grind.SimpGoalResult.casesOn"
] | false |
Sbtw.angle₂₃₁_eq_zero | Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine | [
"InnerProductSpace.toNormedSpace",
"Real.partialOrder",
"Real",
"Real.instZero",
"Real.instRCLike",
"NormedSpace.toModule",
"Real.instRing",
"NormedAddTorsor.toAddTorsor",
"MetricSpace",
"Wbtw.angle₂₃₁_eq_zero_of_ne",
"Sbtw.wbtw",
"Zero.toOfNat0",
"NormedAddCommGroup.toAddCommGroup",
"Metr... | true |
_private.Mathlib.Data.Fin.Tuple.Reflection.0.FinVec.exists_iff._simp_1_8 | Mathlib.Data.Fin.Tuple.Reflection | [
"instNeZeroNatHAdd_1",
"Fin.succ",
"Fin.cons",
"Exists",
"Fin.exists_fin_succ_pi",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"propext",
"instAddNat",
"OfNat.ofNat",
"Fin",
"Eq"
] | false |
Polynomial.degree_gcd_le_right | Mathlib.RingTheory.Polynomial.Content | [
"WithBot.instPreorder",
"Eq.mpr",
"CommRing",
"WithBot",
"Polynomial.degree_gcd_le_left",
"congrArg",
"CommSemiring.toSemiring",
"NormalizedGCDMonoid",
"Preorder.toLE",
"CommSemiring.toCommMonoidWithZero",
"Polynomial.normalizedGcdMonoid",
"id",
"Ne",
"Polynomial.degree",
"LE.le",
"Pol... | true |
Matroid.closure_closure_union_closure_eq_closure_union | Mathlib.Combinatorics.Matroid.Closure | [
"cond",
"Eq.mpr",
"Matroid.closure_iUnion_closure_eq_closure_iUnion",
"congrArg",
"Set.instUnion",
"apply_ite",
"id",
"instDecidableEqBool",
"eq_comm",
"Bool.true",
"funext",
"congr",
"True",
"eq_self",
"propext",
"Matroid.closure",
"Bool",
"of_eq_true",
"congrFun'",
"Union.uni... | true |
_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic.0.CFC.sqrt_ringInverse._proof_1_11 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"False",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Lean.Grind.not_or",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Lean.Grind.and_eq_of_eq_true_left",
"IsUnit",
"Preorder.toLE",
"PartialOrder",
"Eq.mp",
"id",
"LE.le",
"And.casesOn",
"IsStrictlyP... | false |
List.length_inits | Mathlib.Data.List.Infix | [
"congrArg",
"List.map",
"List.length_reverse",
"List.inits_eq_tails",
"instOfNatNat",
"List",
"instHAdd",
"Nat.add_left_cancel_iff._simp_1",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"List.reverse",
"List.length_map",
"of_eq_true",
"instAddNat",
"congrFun'",
"OfNat.ofNat",
"Eq",
"... | true |
NonUnitalSubsemiring.range_snd | Mathlib.RingTheory.NonUnitalSubsemiring.Basic | [
"NonUnitalRingHom.srange",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Prod.instNonUnitalNonAssocSemiring",
"Zero.instNonempty",
"NonUnitalRingHom.instFunLike",
"NonUnitalRingHom.instNonUnitalRingHomClass",
"NonUnitalRingHom.srange_eq_top_of_surjective",
"NonUnitalSubsemiring.instTop",
"NonUnitalSu... | true |
Std.Format.ctorElimType | Init.Data.Format.Basic | [
"cond",
"Std.Format.nil",
"Std.Format.align",
"Nat.ble",
"String",
"Std.Format.line",
"Std.Format.group",
"Std.Format.tag",
"Int",
"PULift",
"Nat",
"Std.Format",
"Bool",
"Std.Format.append",
"Std.Format.FlattenBehavior",
"Std.Format.nest",
"Std.Format.text"
] | false |
DirichletCharacter.Odd.not_even | Mathlib.NumberTheory.DirichletCharacter.Basic | [
"DirichletCharacter.Even",
"CommRing",
"CommSemiring.toSemiring",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"CommSemiring.toCommMonoidWithZero",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"And",
"CommRing.toCommSemiring",
"DirichletCharacter.not_even_and_odd",
"Na... | true |
CategoryTheory.ShortComplex.RightHomologyMapData._sizeOf_inst | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.RightHomologyMapData._sizeOf_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomologyData",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instCategory",
"SizeOf.mk",
"Ca... | false |
Asymptotics.isLittleO_neg_left._simp_1 | Mathlib.Analysis.Asymptotics.Defs | [
"NegZeroClass.toNeg",
"SeminormedAddCommGroup",
"Norm",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"SeminormedAddCommGroup.toNorm",
"SeminormedAddCommGroup.toAddCommGroup",
"Asymptotics.isLittleO_neg_left",
"propext",
"... | false |
NonUnitalSubring.coe_prod._simp_1 | Mathlib.RingTheory.NonUnitalSubring.Basic | [
"Set.instSProd",
"NonUnitalNonAssocRing",
"NonUnitalSubring.instSetLike",
"SProd.sprod",
"NonUnitalSubring.prod",
"NonUnitalSubring",
"SetLike.coe",
"Prod",
"Prod.instNonUnitalNonAssocRing",
"Eq.symm",
"Eq",
"NonUnitalSubring.coe_prod",
"Set"
] | false |
Std.Internal.List.getEntry?_of_mem | Std.Data.Internal.List.Associative | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"False",
"Std.Internal.List.getEntry?_cons_of_true",
"congrArg",
"HEq.refl",
"False.elim",
"Option.some",
"Membership.mem",
"Eq.mp",
"Sigma.mk.noConfusion",
"Eq.casesOn",
"id",
"Std.Internal.List.assoc_induction",
"Sigma.fst",
"List.not_mem_n... | true |
_private.Mathlib.Algebra.Polynomial.PartialFractions.0.Polynomial.mul_prod_pow_inverse_eq_quo_add_sum_rem_mul_pow_inverse._proof_1_1 | Mathlib.Algebra.Polynomial.PartialFractions | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"of_decide_eq_true",
"Int.Linear.norm_le",
"Lean.Grind.ToInt.toInt",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Option.some",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",... | false |
Equiv.Perm.signBijAux | Mathlib.GroupTheory.Perm.Sign | [
"Equiv.instEquivLike",
"Sigma.fst",
"dite",
"Fin.decLt",
"Equiv.Perm",
"Nat",
"LT.lt",
"instLTFin",
"Sigma.mk",
"Sigma.snd",
"Fin",
"DFunLike.coe",
"Not",
"Sigma",
"EquivLike.toFunLike"
] | true |
CategoryTheory.Limits.Multifork.IsLimit.mk | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.Multifork.IsLimit.mk._proof_2",
"CategoryTheory.Limits.IsLimit.mk",
"CategoryTheory.Limits.Multifork.IsLimit.mk._proof_1",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategor... | true |
CategoryTheory.CostructuredArrow.liftQuotient | Mathlib.CategoryTheory.Subobject.Comma | [
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Functor",
"CategoryTheory.Subobject.underlying",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"PartialOrder.toPreorder",
"Quiver.Hom.unop",
"CategoryTheory.CostructuredArrow.hom",
"CategoryTheory.Costructur... | true |
Std.DHashMap.Const.mem_ofList._simp_1 | Std.Data.DHashMap.Lemmas | [
"List.map",
"List.contains",
"Membership.mem",
"Std.DHashMap.instMembership",
"LawfulHashable",
"Prod.fst",
"Bool.true",
"List",
"EquivBEq",
"Std.DHashMap.Const.mem_ofList",
"Std.DHashMap.Const.ofList",
"propext",
"Bool",
"Hashable",
"Prod",
"BEq",
"Eq",
"Std.DHashMap"
] | false |
Set.inter_singleton_nonempty._simp_1 | Mathlib.Data.Set.Insert | [
"Membership.mem",
"Set.instSingletonSet",
"Set.instInter",
"Inter.inter",
"Set.Nonempty",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set.inter_singleton_nonempty",
"Set"
] | false |
NonUnitalStarSubalgebra.topologicalClosure._proof_5 | Mathlib.Topology.Algebra.NonUnitalStarAlgebra | [
"ContinuousStar.continuous_star",
"CommSemiring.toSemiring",
"ContinuousStar",
"map_mem_closure",
"Membership.mem",
"StarMemClass.star_mem",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"TopologicalSpace",
"NonUnitalStarSubalgebra.... | false |
Filter.atTop | Mathlib.Order.Filter.AtTopBot.Defs | [
"iInf",
"Set.Ici",
"Filter.instInfSet",
"Filter.principal",
"Filter",
"Preorder"
] | true |
CategoryTheory.Limits.biproduct.lift_map_assoc | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.HasBiproduct",
"CategoryTheory.Limits.biproduct.lift_map",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.biproduct.lift",
"CategoryTheory.Limits.biproduct.ma... | true |
ContinuousCohomology.homogeneousCochains._proof_2 | Mathlib.Algebra.Category.ContinuousCohomology.Basic | [
"TopModuleCat.instCategory",
"CommRing",
"Group",
"Action.instPreadditive",
"ContinuousCohomology.instAdditiveActionTopModuleCatInvariants",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"TopologicalSpace",
"TopModuleCat",
"CategoryTheory.Functor.preservesZeroMorphisms_of_additive",
"Action",... | false |
ContinuousInv₀.mk | Mathlib.Topology.Algebra.GroupWithZero | [
"Inv",
"ContinuousInv₀.mk",
"ContinuousAt",
"ContinuousInv₀",
"Ne",
"TopologicalSpace",
"Inv.inv",
"Zero.toOfNat0",
"OfNat.ofNat",
"Zero"
] | true |
hasDerivAt_exp_of_mem_ball | Mathlib.Analysis.SpecialFunctions.Exponential | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"Semiring.toModule",
"NormedRing.toRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"IsTopologicalSemiring.toContinuousMul",
"NormedSpace.exp",
"IsTopologicalD... | true |
Lean.Server.GoToContext.rec | Lean.Server.GoTo | [
"Lean.Elab.InfoTree",
"Lean.Server.GoToContext",
"Lean.PersistentArray",
"Lean.Server.DocumentMeta",
"Lean.Server.GoToKind",
"Lean.Elab.Info",
"Lean.Server.GoToContext.mk",
"Option"
] | false |
Lean.Elab.Tactic.Omega.Context.recOn | Lean.Elab.Tactic.Omega.OmegaM | [
"Lean.Meta.Omega.OmegaConfig",
"Lean.Elab.Tactic.Omega.Context",
"Lean.Elab.Tactic.Omega.Context.rec",
"Lean.Elab.Tactic.Omega.Context.mk"
] | false |
Pi.seminormedCommRing._proof_19 | Mathlib.Analysis.Normed.Ring.Lemmas | [
"Semiring.toNatCast",
"Ring.toNeg",
"SeminormedCommRing",
"IntCast.intCast",
"SeminormedRing.toRing",
"instOfNatNat",
"Nat.cast",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Pi.ring",
"SeminormedCommRing.toSeminormedRing",
"Ring.intCast_negSucc",
"instAddNat",
"Int.negSucc",
"Ring.toIntCast",
"... | false |
Monoid.Coprod.range_eq | Mathlib.GroupTheory.Coprod.Basic | [
"Eq.mpr",
"Monoid.Coprod.range_inl_sup_range_inr",
"MonoidHom.range",
"Subgroup.map_sup",
"Lattice.toSemilatticeSup",
"MonoidHom",
"CompleteLattice.toLattice",
"Subgroup.map",
"Monoid.toMulOneClass",
"congrArg",
"MonoidHom.map_range",
"MonoidHom.range_eq_map",
"Group",
"SemilatticeSup.toMa... | true |
TwoSidedIdeal.matrix_ringCon | Mathlib.LinearAlgebra.Matrix.Ideal | [
"NonUnitalNonAssocRing",
"Matrix.add",
"TwoSidedIdeal",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"RingCon.matrix",
"RingCon",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Fintype",
"Distrib.toMul",
"TwoSidedIde... | true |
Std.Iter.flatMap.eq_1 | Init.Data.Iterators.Lemmas.Combinators.FlatMap | [
"Pure.pure",
"Std.Iter.flatMapAfter",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"instMonadLiftT",
"Std.Iter.toIterM",
"Id",
"Std.Iter.flatMap",
"Applicative.toPure",
"Std.Iterator",
"Option.none",
"Std.Iterators.instMonadPostconditionT",
"Std.Iter",
"Std.Iterators.Types.Map",
"Appli... | true |
singleton_add_closedBall_zero | Mathlib.Analysis.Normed.Group.Pointwise | [
"Real",
"SeminormedAddCommGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"Set.instSingletonSet",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"instHAdd",
"Set.add",
... | true |
_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Proof.0.Lean.Meta.Grind.Arith.CommRing.getContext | Lean.Meta.Tactic.Grind.Arith.CommRing.Proof | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.CommRing.ProofM.Context",
"Lean.Meta.Grind.Arith.CommRing.RingM",
"Lean.Meta.Grind.Arith.CommRing.RingM.Context",
"instMonadReaderOfReaderTOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.Context",
... | true |
CochainComplex.HomComplex.instAddCommGroupCochain._proof_20 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"CochainComplex.HomComplex.Cochain._proof_1",
"AddMonoid.toAddSemigroup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Add.mk",
"CochainComplex.HomComplex.instAddCommGroupCochain._aux_8",
"AddGroupWithOne.toAddMonoidWithOne",
"CochainComplex.HomComplex.instAddCommGroupCochain._aux_4",
"A... | false |
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