name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Ordinal.le_cof_type | Mathlib.SetTheory.Cardinal.Cofinality.Ordinal | [
"Cardinal",
"Preorder.toLE",
"Cardinal.mk",
"Set.Elem",
"LE.le",
"Cardinal.instLE",
"Iff",
"Order.cof",
"IsCofinal",
"Order.le_cof_iff",
"Preorder",
"Set"
] | true |
_private.Lean.Compiler.LCNF.Simp.InlineCandidate.0.Lean.Compiler.LCNF.Simp.inlineCandidate?._sparseCasesOn_18 | Lean.Compiler.LCNF.Simp.InlineCandidate | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Compiler.LCNF.DeclValue.extern",
"Nat.hasNotBit",
"Lean.Compiler.LCNF.DeclValue.ctorIdx",
"instOfNatNat",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Code",
"Nat.land",
"Nat",
"Lean.ExternAttrData",
"Bool",
"Eq.refl",
"Lean.Compiler.LC... | false |
_private.Mathlib.Combinatorics.SimpleGraph.AdjMatrix.0.Matrix.compl_of_one_sub_one._simp_1_1 | Mathlib.Combinatorics.SimpleGraph.AdjMatrix | [
"AddGroup.toSubtractionMonoid",
"One",
"Equiv.instEquivLike",
"SimpleGraph.Top.adjDecidable",
"Matrix",
"Matrix.of",
"HSub.hSub",
"SimpleGraph.completeGraph",
"Equiv",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
... | false |
CliffordAlgebra.reverseOp | Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation | [
"CliffordAlgebra.ι",
"CommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"HMul.hMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"AlgHom",
"MulOpposite.opLinearEquiv",
"instAlgebraCliffordAlgebra",
"MulOpposite.instAlgebra",
"Mul... | true |
QuotientGroup.quotientKerEquivOfSurjective | Mathlib.GroupTheory.QuotientGroup.Basic | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Group",
"QuotientGroup.quotientKerEquivOfSurjective._proof_1",
"MulOne.toMul",
"QuotientGroup.instHasQuotientSubgroup",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"MonoidHom.ker",
"HasQuotient.Quotient",
"MulOne... | true |
IsContinuousRiemannianBundle | Mathlib.Topology.VectorBundle.Riemannian | [
"InnerProductSpace.toNormedSpace",
"Real",
"NormedSpace",
"FiberBundle",
"Real.denselyNormedField",
"Real.instRCLike",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"IsContinuousRiemannianBundle.mk",
"TopologicalSpace",
"VectorBundle",
"Seminorme... | true |
_private.Init.Data.String.Basic.0.String.Slice.Pos.offset_add_slice._proof_1_3 | Init.Data.String.Basic | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"String.Slice.Pos.offset",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Ome... | false |
CategoryTheory.Equivalence.instMonoidalInverseTrans._proof_22 | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Equivalence.instMonoidalInverseTrans._proof_8",
"CategoryTheory.Equivalence.instMonoidalInverseTrans._aux_1",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Equivalence.instMonoidalInverseTrans._proof_17",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Equiva... | false |
Std.RecursiveMutex._sizeOf_inst | Std.Sync.RecursiveMutex | [
"Std.RecursiveMutex._sizeOf_1",
"Std.RecursiveMutex",
"SizeOf.mk",
"SizeOf"
] | false |
Nat.le_step | Init.Data.Nat.Basic | [
"LE.le",
"instLENat",
"Nat.le.step",
"Nat",
"Nat.succ"
] | true |
Lean.Expr.ctorIdx | Lean.Expr | [
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.casesOn",
"List",
"Lean.MData",
"Nat",
"Bool",
"Lean.Name",
"Lean.BinderInfo"
] | false |
QuadraticAlgebra.instCommSemiring._proof_6 | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"HMul.hMul",
"QuadraticAlgebra",
"CommSemiring.toSemiring",
"NonAssocSemiring.toOne",
"NonUnitalNonAssocSemiring.toMul",
"CommSemiring",
"QuadraticAlgebra.instNonAssocSemiring",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonAssocSemiring.mul_one",
"One.toOfNat1",
"OfNat.ofNat",
"Semiring... | false |
_private.Lean.Meta.Tactic.Assert.0.Lean.MVarId.note.match_1 | Lean.Meta.Tactic.Assert | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Option.none",
"Unit",
"Option"
] | false |
UInt32.mod | Init.Data.UInt.Basic | [
"UInt32.toBitVec",
"instOfNatNat",
"UInt32.ofBitVec",
"BitVec.umod",
"Nat",
"UInt32",
"OfNat.ofNat"
] | true |
Polynomial.ofFinsupp_single | Mathlib.Algebra.Polynomial.Basic | [
"Semiring.toModule",
"LinearMap.instFunLike",
"Polynomial.monomial",
"LinearMap",
"Polynomial",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Polynomial.semiring",
"Nat",
"eq_self",
"of_eq_true",
"Semiring",
"Polynomial.module",
"Polynomial.o... | true |
Finset.powerset.eq_1 | Mathlib.Data.Finset.Powerset | [
"Finset.powerset._proof_1",
"Finset.powerset._proof_2",
"Multiset.Nodup",
"Finset",
"Multiset.powerset",
"Multiset",
"Finset.val",
"Multiset.pmap",
"Finset.powerset",
"Eq.refl",
"Finset.mk",
"Eq"
] | true |
JoinedIn | Mathlib.Topology.Connected.PathConnected | [
"Real",
"Membership.mem",
"Exists",
"Set.Elem",
"TopologicalSpace",
"Path.instFunLike",
"Path",
"Set.instMembership",
"DFunLike.coe",
"unitInterval",
"Set"
] | true |
NoZeroDivisors.to_isDomain | Mathlib.Algebra.Ring.Basic | [
"Nontrivial",
"IsDomain",
"Ring.toNonAssocRing",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"IsCancelMulZero",
"NonAssocRing.toNonUnitalNonAssocRing",
"IsDomain.mk",
"instDistribOfSemiring",
"NoZeroDivisors",
"Distrib.toMul",
"NoZeroDivisor... | true |
HasDerivWithinAt.eventually_notMem | Mathlib.Analysis.Calculus.Deriv.Inverse | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst",
"le_r... | true |
Mathlib.Tactic.Linarith.Sum.pow._unsafe_rec | Mathlib.Tactic.Linarith.Parsing | [
"Nat.instAndOp",
"instOfNatNat",
"instHShiftRightOfShiftRight",
"Mathlib.Tactic.Linarith.Sum.mul",
"Unit",
"Nat.instShiftRight",
"Mathlib.Tactic.Linarith.Sum",
"HShiftRight.hShiftRight",
"Nat",
"Mathlib.Tactic.Linarith.Sum.one",
"instDecidableEqNat",
"Mathlib.Tactic.Linarith.Sum.pow._unsafe_re... | false |
CategoryTheory.Equivalence.induced._proof_1 | Mathlib.CategoryTheory.EqToHom | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"Equiv",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"Eq.trans",
"EquivLike.toFunLike"
] | false |
_private.Lean.Elab.PreDefinition.Structural.BRecOn.0.Lean.Elab.Structural.searchPProd._sparseCasesOn_5 | Lean.Elab.PreDefinition.Structural.BRecOn | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
Function.iterate_pred_comp_of_pos | Mathlib.Logic.Function.Iterate | [
"Eq.mpr",
"Nat.succ_pred_eq_of_pos",
"Function.iterate_succ",
"congrArg",
"Function.comp",
"id",
"instOfNatNat",
"Nat.iterate",
"Nat",
"LT.lt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Eq.symm",
"Nat.succ",
"Eq",
"Nat.pred"
] | true |
AlgebraicTopology.DoldKan.compatibility_Γ₂N₁_Γ₂N₂_natTrans | Mathlib.AlgebraicTopology.DoldKan.NCompGamma | [
"Eq.mpr",
"CategoryTheory.Functor",
"ChainComplex",
"HomologicalComplex.instCategory",
"CategoryTheory.Iso.app_inv",
"Opposite",
"CategoryTheory.Idempotents.Karoubi",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"AlgebraicTopology.DoldKan.Γ₂",
"Quiver.Hom",
"congrArg",
"CategoryT... | true |
Array.replicate_succ_ne_empty._simp_1 | Init.Data.Array.Lemmas | [
"False",
"eq_false",
"Array.replicate",
"instOfNatNat",
"List.toArray",
"Array",
"instHAdd",
"HAdd.hAdd",
"Array.replicate_succ_ne_empty",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq",
"List.nil"
] | false |
AddEquiv.congr_arg | Mathlib.Algebra.Group.Equiv.Defs | [
"AddEquiv",
"AddEquiv.instEquivLike",
"Eq",
"DFunLike.coe",
"Add",
"EquivLike.toFunLike",
"DFunLike.congr_arg"
] | true |
Lean.Meta.Grind.SplitInfo.ctorElimType | Lean.Meta.Tactic.Grind.Types | [
"cond",
"Lean.Meta.Grind.SplitInfo.default",
"Nat.ble",
"Lean.Expr",
"PULift",
"Lean.Meta.Grind.SplitInfo.imp",
"Bool.true",
"Lean.Meta.Grind.SplitSource",
"Nat",
"Lean.Meta.Grind.SplitInfo",
"Bool",
"Lean.Meta.Grind.SplitInfo.arg",
"Eq",
"Lean.Expr.isForall"
] | false |
Submodule.sup_orthogonal_of_hasOrthogonalProjection | Mathlib.Analysis.InnerProductSpace.Projection.Submodule | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Submodule",
"Lattice.toSemilatticeSup",
"congrArg",
"inf_of_le_left",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"le_top._simp_2",
"Submodule.completeLattice",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"Preorder.toLE",
"NormedField.to... | true |
Lean.Quote.recOn | Init.Meta.Defs | [
"Lean.TSyntax",
"Lean.Quote.rec",
"Lean.Quote",
"List.cons",
"Lean.SyntaxNodeKind",
"Lean.Quote.mk",
"List.nil"
] | false |
WithZero.instAddMonoid._proof_9 | Mathlib.Algebra.Group.WithOne.Defs | [
"AddZeroClass.toAddZero",
"AddSemigroup",
"AddZero.toZero",
"WithZero.instAddZeroClass",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"WithZero",
"AddZeroClass.add_zero",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
Lean.Grind.CommRing.Poly.mul.eq_1 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.mul.go",
"Int",
"Lean.Grind.CommRing.Poly.mul",
"instOfNat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Grind.CommRing.Poly.num"
] | true |
CategoryTheory.ShortComplex.Hom.comm₁₂_assoc | Mathlib.Algebra.Homology.ShortComplex.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ShortComplex.Hom.comm₁₂",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.Hom.τ₁",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"Eq.mp",
... | true |
CategoryTheory.functorialSurjectiveInjectiveFactorizationData._proof_2 | Mathlib.CategoryTheory.MorphismProperty.Concrete | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Arrow.left",
"TypeCat.ofHom",
"id",
"Subtype",
"CategoryTheory.Arrow.hom",
"CategoryThe... | false |
CategoryTheory.EnrichedOrdinaryCategory.noConfusionType | Mathlib.CategoryTheory.Enriched.Ordinary.Basic | [
"Equiv.instEquivLike",
"CategoryTheory.EnrichedOrdinaryCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.CategoryStruct.id",
"Equiv",
"CategoryTheory.EnrichedCategory.Hom",
"Cate... | false |
Std.Iter.toList_flatMap | Init.Data.Iterators.Lemmas.Combinators.FlatMap | [
"Pure.pure",
"Std.Iter.flatMapAfter",
"Std.Iterators.Types.Flatten.instIterator",
"Std.Iter.toList_map",
"congrArg",
"Monad.toApplicative",
"List.map",
"Std.Iterators.Types.Map.instIterator",
"MonadLiftT.monadLift",
"instMonadLiftT",
"Std.Iterators.Finite",
"Std.Iter.toList_flatMapAfter",
"S... | true |
_private.Std.Data.DHashMap.Internal.Raw.0.Std.DHashMap.Raw.Const.get?.eq_1 | Std.Data.DHashMap.Internal.Raw | [
"Std.DHashMap.Internal.Raw₀.Const.get?",
"Std.DHashMap.Raw",
"instOfNatNat",
"dite",
"Subtype.mk",
"Option.none",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.Raw.Const.get?",
"Nat.decLt",
"Eq.refl",
"Std.DHashMap.Internal.AssocList",
"Hashable",
"instLTNat",
"OfNat.ofNat"... | true |
HasSubset.Subset.iscofinalfor | Mathlib.Order.Bounds.Basic | [
"IsCofinalFor",
"IsCofinalFor.of_subset",
"Preorder.toLE",
"HasSubset.Subset",
"Preorder",
"Set.instHasSubset",
"Set"
] | true |
Lean.Compiler.LCNF.FindUsed.Context._sizeOf_1 | Lean.Compiler.LCNF.ReduceArity | [
"Lean.Compiler.LCNF.Decl._sizeOf_inst",
"instSizeOfDefault",
"Lean.Compiler.LCNF.Decl",
"instOfNatNat",
"Lean.Compiler.LCNF.FindUsed.Context",
"Lean.Compiler.LCNF.Purity.pure",
"Lean.Compiler.LCNF.FindUsed.Context.rec",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.FVa... | false |
CategoryTheory.cosimplicialSimplicialEquiv | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"Opposite",
"CategoryTheory.CosimplicialObject",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.opUnopEquiv",
"CategoryTheory.CosimplicialObject.instCategory",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"SimplexCategory.smallCategory",
"Categor... | true |
AddSubgroup.isComplement'_top_right | Mathlib.GroupTheory.Complement | [
"AddSubgroup.instBot",
"Set.univ",
"Exists",
"AddSubgroup.isComplement_univ_right",
"Set.instSingletonSet",
"Bot.bot",
"AddSubgroup",
"AddSubgroup.coe_eq_singleton",
"AddGroup",
"Iff",
"SetLike.coe",
"AddSubgroup.instSetLike",
"Iff.trans",
"AddSubgroup.IsComplement",
"AddSubgroup.IsCompl... | true |
LinearEquiv.coe_toLinearMap | Mathlib.Algebra.Module.Equiv.Defs | [
"LinearMap.instFunLike",
"RingHom",
"LinearMap",
"AddCommMonoid",
"RingHomInvPair",
"LinearEquiv.toLinearMap",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike",
"Module",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
CanLift.prf | Mathlib.Tactic.Lift | [
"outParam",
"Exists",
"CanLift",
"Eq"
] | true |
Mathlib.Tactic.Ring.RatCoeff.casesOn | Mathlib.Tactic.Ring.Common | [
"Mathlib.Tactic.Ring.RatCoeff",
"Rat",
"Lean.Expr",
"Lean.Expr.sort",
"Lean.Level",
"Mathlib.Tactic.Ring.RatCoeff.rec",
"Qq.Quoted",
"Mathlib.Tactic.Ring.RatCoeff.mk",
"Lean.Level.succ",
"Option"
] | false |
Quaternion.star_mul_self | Mathlib.Algebra.Quaternion | [
"Quaternion.coe",
"Eq.mpr",
"NegZeroClass.toNeg",
"CommRing",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"IsStarNormal.star_comm_self",
"AddGroupWithOne.toAddMonoidWithOne",
"Quaternion.normSq",
"MonoidWithZeroHom.funLike",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZero... | true |
Equiv.heytingAlgebra._proof_2 | Mathlib.Order.Heyting.Basic | [
"Preorder.toLT",
"Equiv.instEquivLike",
"Iff.rfl",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Equiv",
"Iff",
"GeneralizedHeytingAlgebra.toLattice",
"LT.lt",
"HeytingAlgebra.toGeneralizedHeytingAlgebra",
"HeytingAlgebra",
"DFunLike.coe",
"Lattice.toSemilatticeInf",
"EquivL... | false |
_private.Lean.Meta.LazyDiscrTree.0.Lean.Meta.LazyDiscrTree.createImportedEnvironmentSeq.go._unary._proof_1 | Lean.Meta.LazyDiscrTree | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"InvImage",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_cong... | false |
_private.Aesop.Script.Util.0.Aesop.Script.findFirstStep?.match_1 | Aesop.Script.Util | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Prod.mk",
"Nat",
"_private.Aesop.Script.Util.0.Aesop.Script.findFirstStep?._sparseCasesOn_1",
"Prod",
"Prod.casesOn",
"Option"
] | false |
HomotopicalAlgebra.instWeakEquivalencePCofibrationsTrivialFibrations | Mathlib.AlgebraicTopology.ModelCategory.Instances | [
"Eq.mpr",
"CategoryTheory.MorphismProperty.MapFactorizationData.Z",
"HomotopicalAlgebra.fibrations",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.MapFactorizationData.p",
"id",
"_private.Mathlib.AlgebraicTopology.ModelCategory.Instances.0.HomotopicalAlgebra.... | true |
Lean.Lsp.LocationLink.noConfusion | Lean.Data.Lsp.Basic | [
"Lean.Lsp.LocationLink",
"Lean.Lsp.DocumentUri",
"Lean.Lsp.LocationLink.noConfusionType",
"Lean.Lsp.LocationLink.casesOn",
"Eq.ndrec",
"Eq.refl",
"Lean.Lsp.Range",
"Eq",
"Option"
] | false |
Matrix.transposeRingEquiv_symm_apply | Mathlib.Data.Matrix.Basic | [
"Matrix.add",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"Matrix.transposeRingEquiv",
"RingEquiv.instEquivLike",
"MulOpposite",
"CommMagma.toMul",
"CommMagma",
"AddCommMonoid",
"MulOpposite.instAdd",
"Fintype",
"Matrix.transpose",
"Eq.refl",
"MulOpposite.unop",
"AddCommSemigroup... | true |
WithZero.unzero | Mathlib.Algebra.Group.WithOne.Defs | [
"WithZero.unzero.match_1",
"Ne",
"WithZero.instZero",
"WithZero",
"WithZero.coe",
"Zero.toOfNat0",
"OfNat.ofNat"
] | true |
_private.Lean.Elab.BuiltinDo.Match.0.Lean.Elab.Do.elabPatterns | Lean.Elab.BuiltinDo.Match | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.Context.mayPostpone",
"Lean.Elab.Term.Context.inPattern",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.Context.checkDeprecated",
"Lean.Elab.Term.instMonadMacroAdapt... | true |
Equiv.piEquivPiSubtypeProd._proof_13 | Mathlib.Logic.Equiv.Prod | [
"Subtype",
"Prod.mk",
"Prod.fst",
"dite",
"Subtype.mk",
"_private.Mathlib.Logic.Equiv.Prod.0.Equiv.piEquivPiSubtypeProd._proof_7",
"Prod.ext",
"DecidablePred",
"Function.RightInverse",
"_private.Mathlib.Logic.Equiv.Prod.0.Equiv.piEquivPiSubtypeProd._proof_12",
"Prod",
"Prod.casesOn",
"Subtyp... | false |
_private.Mathlib.Order.Cover.0.Prod.mk_covBy_mk_iff_right._simp_1_3 | Mathlib.Order.Cover | [
"Preorder.toLT",
"Prod.mk",
"Prod.mk_lt_mk_iff_right",
"LT.lt",
"propext",
"Prod.instPreorder",
"Prod",
"Eq",
"Preorder"
] | false |
Std.DTreeMap.Internal.Const.RoiSliceData.treeMap | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"Std.DTreeMap.Internal.Const.RoiSliceData",
"Std.DTreeMap.Internal.Impl"
] | true |
_private.Mathlib.Analysis.Calculus.LogDeriv.0.logDeriv_fun_zpow._simp_1_7 | Mathlib.Analysis.Calculus.LogDeriv | [
"False",
"eq_false",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CharZero",
"Nat.cast_add_one_ne_zero",
"AddMonoidWithOne.toOne",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"On... | false |
_private.Init.Data.Array.Lemmas.0.Array.foldrM_start_stop._proof_1_3 | Init.Data.Array.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Int.decLe",
"Lean.Omega.Li... | false |
Order.Frame.recOn | Mathlib.Order.CompleteBooleanAlgebra | [
"Order.Frame.rec",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"Compl.compl",
"OrderBot.toBot",
"HImp",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Bot.bot",
"SemilatticeInf.toMin",
"LE.le",
"SemilatticeInf.mk",
"Iff",
"BoundedOrder.toOrder... | false |
_private.Mathlib.Topology.TietzeExtension.0.BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_isClosedEmbedding._simp_1_1 | Mathlib.Topology.TietzeExtension | [
"funext_iff",
"propext",
"Eq"
] | false |
max_sub_sub_right | Mathlib.Algebra.Order.Group.MinMax | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Lattice.toSemilatticeSup",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"sub_eq_add_neg",
"HSub.hSub",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"S... | true |
CategoryTheory.MonoOver.liftIso | Mathlib.CategoryTheory.Subobject.MonoOver | [
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Mono",
"CategoryTheory.Functor.fullyFaithfulCancelRight",
"CategoryTheory.Functor.category",
"CategoryTheory.Iso",
"CategoryTheory.instCategoryOver",
"CategoryTheory.Over.left",
"CategoryTheory.Functor.isoWhiskerLeft",
"CategoryTheor... | true |
CategoryTheory.instCategoryTransportEnrichment._aux_1 | Mathlib.CategoryTheory.Enriched.Ordinary.Basic | [
"CategoryTheory.TransportEnrichment",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalCategory",
"Quiver",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.LaxMonoidal",
"CategoryTheory.Category"
] | false |
StieltjesFunction.measure_botSet | Mathlib.MeasureTheory.Measure.Stieltjes | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"False",
"Exists.choose_spec",
"OrderTopology",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"eq_false",
"sub_self",
"ENNReal.ofReal",
"congrArg",
"StieltjesFunction.measure_singleton",
"Real.instSub",
"SecondCountableTopology",
"LinearOrder... | true |
CategoryTheory.RelCat.rel_iso_iff | Mathlib.CategoryTheory.Category.RelCat | [
"Iff.mpr",
"Set.ext",
"CategoryTheory.IsIso",
"SetRel",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.RelCat.Hom",
"TypeCat.instFunLikeFun",
"CategoryTheory.IsIso.inv_hom_id",
"Membership.mem",
"Exists",
"Category... | true |
Int.negSucc_mul_ofNat | Init.Data.Int.Lemmas | [
"HMul.hMul",
"Int.instNegInt",
"instMulNat",
"Int",
"Nat.cast",
"Int.instMul",
"Nat",
"instNatCastInt",
"Int.negSucc",
"Nat.succ",
"Eq",
"Neg.neg",
"rfl",
"instHMul"
] | true |
_private.Mathlib.Order.BooleanSubalgebra.0.BooleanSubalgebra.mem_closure_iff_sup_sdiff.match_1_1 | Mathlib.Order.BooleanSubalgebra | [
"BooleanAlgebra",
"Lattice.toSemilatticeSup",
"Compl.compl",
"Finset",
"Membership.mem",
"Exists",
"BooleanAlgebra.toCompl",
"Set.Elem",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"Prod.fst",
"BooleanAlgebra.toBiheytingAlgebra",
"BooleanAlgebra.toSDiff",
"S... | false |
RingOfIntegers.ZModXQuotSpanEquivQuotSpanPair._proof_9 | Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind | [
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"AddGroupWithOne.toAddMonoidWithOne",
"SemilatticeSup.toMax",
"Algebra.id",
"Set.instSingletonSet",
"Ideal.IsTwoSided",
"AddMonoidWithOne.toNatCast",
"Int",
"Ideal"... | false |
_private.Init.Data.Range.Polymorphic.Map.0.Std.PRange.LawfulUpwardEnumerableLT.ofMap._simp_1_1 | Init.Data.Range.Polymorphic.Map | [
"Std.PRange.UpwardEnumerable",
"Std.PRange.LawfulUpwardEnumerableLT",
"Std.PRange.UpwardEnumerable.LT",
"LT.lt",
"propext",
"Std.PRange.LawfulUpwardEnumerableLT.lt_iff",
"Eq",
"LT"
] | false |
Lean.PrettyPrinter.categoryParenthesizerAttribute | Lean.PrettyPrinter.Parenthesizer | [
"Classical.ofNonempty",
"Lean.PrettyPrinter.CategoryParenthesizer",
"Lean.KeyedDeclsAttribute",
"Lean.instNonemptyKeyedDeclsAttribute"
] | true |
_private.Mathlib.Topology.Spectral.ConstructibleTopology.0.compactSpace_withConstructibleTopology._proof_16 | Mathlib.Topology.Spectral.ConstructibleTopology | [
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"eq_false",
"Lean.Grind.iff_eq",
"Set.subset_def",
"Set.union_subset_iff",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"setOf",
"Maximal.prop",
"Set.Finite",
"Membership.mem",
"Exist... | false |
_private.Lean.PrettyPrinter.Delaborator.TopDownAnalyze.0.Lean.PrettyPrinter.Delaborator.TopDownAnalyze.analyze.analyzeLet | Lean.PrettyPrinter.Delaborator.TopDownAnalyze | [
"Inhabited.default",
"Lean.PrettyPrinter.Delaborator.TopDownAnalyze.State",
"Lean.PrettyPrinter.Delaborator.TopDownAnalyze.AnalyzeM",
"instInhabitedOfMonad",
"instInhabitedPUnit",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.PrettyPrinter.Delaborator.TopDownAnalyze.Context",
"Unit",
"Lean.Meta.instMon... | true |
_private.Mathlib.Analysis.Normed.Algebra.GelfandMazur.0.NormedAlgebra.Complex.norm_sub_eq_norm_sub_of_isMinOn._simp_1_1 | Mathlib.Analysis.Normed.Algebra.GelfandMazur | [
"Monoid",
"HMul.hMul",
"Monoid.toMulOneClass",
"MulOne.toMul",
"instOfNatNat",
"Monoid.toPow",
"instHAdd",
"MulOneClass.toMulOne",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"instAddNat",
"instHPow",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"pow_succ'",
"instHMul"
] | false |
CategoryTheory.GrothendieckTopology.W.isLocallySurjective | Mathlib.CategoryTheory.Sites.LocallyBijective | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.GrothendieckTopology.W",
"CategoryTheory.ConcreteCategory",
"And",
"And.right",
"CategoryTheory.GrothendieckTopology",
"Iff.mp",
"CategoryTheory.Grot... | true |
CategoryTheory.ShiftedHom.map_smul | Mathlib.CategoryTheory.Shift.ShiftedHom | [
"CategoryTheory.Functor",
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.Linear",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Linear",
"CategoryTheory.Functor.category",
... | true |
Module.End.instDivisionRing._proof_2 | Mathlib.RingTheory.SimpleModule.Basic | [
"Module.End.instRing",
"Mul.mk",
"LinearEquiv.symm",
"Semigroup.toMul",
"One.mk",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"IsSimpleModule",
"Int",
"npowRec",
"dite",
"One.one",
"LinearEquiv.toLinearMap",
"instOfNat",
"Inv.mk",
"Mul.mul",
"RingHomInvPair.ids",
"Semiring.toMo... | false |
Lean.Grind.CommRing.Mon.denote_concat | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Power",
"Lean.Grind.Semiring.one_mul",
"Eq.mpr",
"Lean.Grind.CommRing.Mon.mult",
"HMul.hMul",
"congrArg",
"Lean.Grind.CommRing.Mon.concat",
"id",
"Lean.Grind.Semiring.toMul",
"Lean.Grind.CommRing.Mon.denote",
"Lean.Grind.Semiring.mul_assoc",
"Lean.Grind.CommRing.Mon.rec",
... | true |
TrivialStar.isStarNormal | Mathlib.Algebra.Star.SelfAdjoint | [
"Eq.mpr",
"IsStarNormal.mk",
"IsStarNormal",
"congrArg",
"StarMul",
"Mul",
"Commute",
"TrivialStar.star_trivial",
"id",
"Commute.refl",
"StarMul.toInvolutiveStar",
"TrivialStar",
"InvolutiveStar.toStar",
"Eq",
"Star.star"
] | true |
OpenNormalAddSubgroup.instInfOpenNormalAddSubgroup | Mathlib.Topology.Algebra.OpenSubgroup | [
"OpenAddSubgroup.instInfOpenAddSubgroup",
"Min.mk",
"OpenNormalAddSubgroup.instInfOpenNormalAddSubgroup._proof_1",
"OpenNormalAddSubgroup.toOpenAddSubgroup",
"Min",
"TopologicalSpace",
"OpenAddSubgroup",
"AddGroup",
"OpenNormalAddSubgroup.mk",
"OpenNormalAddSubgroup",
"Min.min"
] | true |
linearOrderOfSTO._proof_2 | Mathlib.Order.RelClasses | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"IsStrictTotalOrder",
"Unit",
"partialOrderOfSO",
"IsStrictTotalOrder.toIsStrictOrder",
"Or.inl",
"Or",
"trichotomous_of",
"Eq",
"IsStrictTotalOrder.toTrichotomous",
"Or.inr",
"rfl",
"linearOrderOfSTO.match_1"
] | false |
CategoryTheory.Under.eqToHom_right | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.instCategoryUnder",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Under.eqToHom_right._proof_1",
"CategoryTheory.eqToHom",
"Eq.rec",
"CategoryTheory.Under.right",
"CategoryTheory.Under",
"CategoryTheory.Under.Hom.right",
"Eq.refl",
"CategoryTheory.Catego... | true |
_private.Mathlib.Geometry.Euclidean.Circumcenter.0.EuclideanGeometry.existsUnique_dist_eq_of_insert._proof_1_2 | Mathlib.Geometry.Euclidean.Circumcenter | [
"instLawfulOrderLT_mathlib",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Submodule",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"Lean.Grind.CommRing.Mon.mu... | false |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedFields | Lean.Elab.StructInst | [
"Lean.NameMap",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedField"
] | true |
associatedPrimes | Mathlib.RingTheory.Ideal.AssociatedPrime.Basic | [
"IsAssociatedPrime",
"CommSemiring.toSemiring",
"setOf",
"Ideal",
"AddCommMonoid",
"CommSemiring",
"Module",
"Set"
] | true |
preNormEDS'.eq_4 | Mathlib.NumberTheory.EllipticDivisibilitySequence | [
"CommRing",
"instOfNatNat",
"Nat",
"Eq.refl",
"preNormEDS'",
"OfNat.ofNat",
"Eq"
] | true |
Std.ExtDHashMap.isSome_getKey?_iff_mem._simp_1 | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.ExtDHashMap.isSome_getKey?_iff_mem",
"Membership.mem",
"LawfulHashable",
"Std.ExtDHashMap.getKey?",
"Bool.true",
"EquivBEq",
"propext",
"Std.ExtDHashMap",
"Bool",
"Hashable",
"Option.isSome",
"BEq",
"Eq"
] | false |
_private.Mathlib.Data.List.AList.0.AList.union_assoc._simp_1_1 | Mathlib.Data.List.AList | [
"not_or",
"And",
"propext",
"Or",
"Eq",
"Not"
] | false |
LinearOrderedCommGroup.closure_equiv_closure._simp_5 | Mathlib.GroupTheory.ArchimedeanDensely | [
"eq_comm",
"propext",
"Eq"
] | false |
CategoryTheory.Limits.IndObjectPresentation.yoneda_I | Mathlib.CategoryTheory.Limits.Indization.IndObject | [
"CategoryTheory.Limits.IndObjectPresentation.I",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.IndObjectPresentation.yoneda",
"CategoryTheory.Functor.category",
"CategoryTheory.yoneda",
"PUnit",
"CategoryTheory.types",
"CategoryTheory.Category.opposite",
"Eq.refl",
"Eq",
"Catego... | true |
DirectLimit.Ring.of._proof_2 | Mathlib.Algebra.Colimit.DirectLimit | [
"HMul.hMul",
"MulHom.map_mul'",
"Preorder.toLE",
"LE.le",
"DirectLimit",
"MulHom.toFun",
"NonAssocSemiring",
"RingHomClass.toNonUnitalRingHomClass",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalRingHom.toMulHom",
"IsDirectedOrder",
"NonUnitalNonAssocSemiring.toD... | false |
Seminorm.ext | Mathlib.Analysis.Seminorm | [
"Real",
"DFunLike.ext",
"SMul",
"Seminorm",
"Seminorm.instFunLike",
"AddGroup",
"Eq",
"DFunLike.coe",
"SeminormedRing"
] | true |
Topology.CWComplex.OneSkeletonGraph.not_exists_isLoopAt_iff_nontrivial | Mathlib.Topology.CWComplex.Classical.Graph | [
"Set.not_subsingleton_iff",
"Graph.IsLoopAt",
"Topology.CWComplex",
"Topology.RelCWComplex.cellFrontier",
"Topology.CWComplex.instRelCWComplex",
"Exists",
"Iff.not",
"instOfNatNat",
"Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iff_subsingleton",
"TopologicalSpace",
"Iff",
"Nat",
"Top... | true |
CategoryTheory.Presieve.Arrows.pullbackCompatible_iff | Mathlib.CategoryTheory.Sites.IsSheafFor | [
"CategoryTheory.Presieve.HasPairwisePullbacks",
"Eq.mpr",
"CategoryTheory.Limits.pullback",
"CategoryTheory.op_comp",
"CategoryTheory.Presieve.instHasPullbackOfHasPairwisePullbacksOfArrows",
"CategoryTheory.Functor",
"Opposite",
"Quiver.opposite",
"CategoryTheory.Limits.pullback.lift",
"CategoryTh... | true |
Algebra.PreSubmersivePresentation.isUnit_jacobian_iff_aevalDifferential_bijective | Mathlib.RingTheory.Extension.Presentation.Submersive | [
"Eq.mpr",
"Pi.Function.module",
"CommRing",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Module.End.instMonoid",
"Semiring.toModule",
"Pi.addCommMonoid",
"CommRing.toNonUnitalCommRing",
"MonoidHom",
"congrArg",
"CommSemiring.toSemiring",
"LinearMap.isUnit_iff_is... | true |
BialgEquiv.noConfusion | Mathlib.RingTheory.Bialgebra.Equiv | [
"CoalgebraStruct",
"HMul.hMul",
"CoalgHom.toLinearMap",
"CommSemiring.toSemiring",
"HEq.refl",
"BialgEquiv",
"Algebra",
"BialgEquiv.noConfusionType",
"Algebra.toModule",
"LinearMap.toAddHom",
"instDistribOfSemiring",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Distrib.toM... | false |
CategoryTheory.Subobject.le_of_comm | Mathlib.CategoryTheory.Subobject.Basic | [
"Eq.mpr",
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Subobject.underlying",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HEq.refl",
"PartialOrder.toPreorder",
"CategoryTheory.Subobject.mk_le_mk_of_comm",
"Preorder.toLE",
"Eq.casesOn",
"CategoryTheory.Subobject.ar... | true |
ZFSet.coeEquiv | Mathlib.SetTheory.ZFC.Class | [
"Equiv.instEquivLike",
"ZFSet",
"Membership.mem",
"Equiv.mk",
"ZFSet.coeEquiv.match_1",
"Set.Elem",
"Equiv",
"Subtype",
"Quotient.out",
"ZFSet.coeEquiv._private_3",
"ZFSet.mk",
"PSet.mk",
"PSet",
"Subtype.mk",
"PSet.setoid",
"SetLike.coe",
"Shrink",
"ZFSet.coeEquiv._private_5",
"... | true |
CategoryTheory.Mon.EquivLaxMonoidalFunctorPUnit.monToLaxMonoidal_laxMonoidalToMon_obj_mul | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"PUnit.addCommGroup",
"CategoryTheory.Functor.comp",
"AddCommGroup.toAddGroup",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Mon",
"CategoryTheory.discreteCategory",
"AddGroup.toSubNegMonoid",
"Cate... | true |
Lean.Meta.Grind.Arith.Cutsat.CooperSplitPred.recOn | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.mul",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.coreToInt",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.core0",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.ofLeGe",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.neg",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.r... | false |
MulAction.selfEquivSigmaOrbitsQuotientStabilizer'.eq_1 | Mathlib.GroupTheory.GroupAction.Quotient | [
"Function.LeftInverse",
"Trans.trans",
"Equiv.trans",
"MulAction.orbitRel.Quotient.orbit",
"MulAction.selfEquivSigmaOrbitsQuotientStabilizer'",
"Equiv.setCongr",
"Group",
"MulAction.orbitEquivQuotientStabilizer",
"Quotient.mk''",
"Set.Elem",
"Equiv",
"QuotientGroup.instHasQuotientSubgroup",
... | true |
Primrec₂.unpaired' | Mathlib.Computability.Primrec.Basic | [
"Nat.Primrec",
"Primrec₂.unpaired",
"Primcodable.ofDenumerable",
"Primrec",
"Iff",
"Primrec.nat_iff",
"Nat",
"Nat.unpaired",
"Iff.trans",
"Denumerable.nat",
"Iff.symm",
"Primrec₂"
] | true |
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