name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ZFSet.«_aux_Mathlib_SetTheory_ZFC_Basic___macroRules_ZFSet_term⋂₀__1» | Mathlib.SetTheory.ZFC.Basic | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad"... | false |
Nat.findGreatest_of_not | Mathlib.Data.Nat.Find | [
"eq_false",
"congrArg",
"instOfNatNat",
"Nat.findGreatest",
"instHAdd",
"HAdd.hAdd",
"DecidablePred",
"Nat",
"True",
"eq_self",
"of_eq_true",
"instAddNat",
"congrFun'",
"OfNat.ofNat",
"ite_cond_eq_false",
"Eq",
"Not",
"Eq.trans"
] | true |
DoubleCentralizer.toProdMulOppositeHom_apply | Mathlib.Analysis.CStarAlgebra.Multiplier | [
"instSMulOfMul",
"ContinuousLinearMap.semiring",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"MulOpposite",
"PseudoMetricSpace.to... | true |
Std.DTreeMap.Internal.Impl.getKey?_inter!_of_contains_eq_false_left | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Ord",
"congrArg",
"Std.TransOrd",
"id",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Std.DTreeMap.Internal.Impl.inter!",
"Option.none",
"Std.DTreeMap.Internal.Impl.contains",
"Std.DTreeMap.Internal.Impl.getKey?_inter_of_contains_eq_false_left",
"Std.DT... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.IsClique.of_induce._simp_1_3 | Mathlib.Combinatorics.SimpleGraph.Clique | [
"Exists",
"exists_and_right",
"And",
"propext",
"Eq"
] | false |
Aesop.RuleTerm.noConfusion | Aesop.RuleTac.RuleTerm | [
"Aesop.RuleTerm.casesOn",
"Aesop.RuleTerm.noConfusionType",
"Lean.Syntax.Term",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Aesop.RuleTerm",
"Eq"
] | false |
_private.Mathlib.Tactic.Algebraize.0.Mathlib.Tactic.Algebraize.addProperties.match_5 | Mathlib.Tactic.Algebraize | [
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"Prod.mk",
"_private.Mathlib.Tactic.Algebraize.0.Mathlib.Tactic.Algebraize.addProperties._sparseCasesOn_5",
"Prod",
"Prod.casesOn",
"Option"
] | false |
ContinuousMapZero.instR1Space | Mathlib.Topology.ContinuousMap.ContinuousMapZero | [
"ContinuousMapZero.isEmbedding_toContinuousMap",
"R1Space",
"Topology.IsInducing.r1Space",
"ContinuousMap",
"toContinuousMap",
"ContinuousMapZero",
"TopologicalSpace",
"ContinuousMapZero.instContinuousMapClass",
"ContinuousMapZero.instFunLike",
"Topology.IsEmbedding.toIsInducing",
"ContinuousMap... | true |
Even.natAbs | Mathlib.Algebra.Ring.Int.Parity | [
"Iff.mpr",
"Int",
"Nat",
"Even",
"Int.natAbs",
"Int.instAdd",
"instAddNat",
"Int.natAbs_even"
] | true |
MultilinearMap.fromDFinsuppEquiv._proof_7 | Mathlib.LinearAlgebra.Multilinear.DFinsupp | [
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.IsScalarTower.compatibleSMul",
"IsScalarTower.left",
"AddCommMonoid",
"instDistribOfSemiring",
"CommSemiring",
"AddZero.... | false |
AddCommGrpCat.preadditiveCoyonedaIso._proof_1 | Mathlib.CategoryTheory.Preadditive.Yoneda.Basic | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"AddEquiv.toAddCommGrpIso",
"id",
"CategoryTheory.Functor.map",
"AddCommGrpCat.homAddEquiv",
"AddCommGrpCat",
"AddCommGrpCat.coyoneda",... | false |
IsStrictOrderedRing.topologicalRing | Mathlib.Topology.Algebra.Order.Field | [
"OrderTopology",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"nhds_basis_abs_sub_lt",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"instNoMaxOrderOfNontrivial",
"AddGroupWithOne.toAddGroup",
"abs",
"congrArg",
"sub_zero",
"LinearOrder",
"covariant_swap_add_of_covariant_... | true |
Set.sub_nonempty._simp_1 | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Set.sub_nonempty",
"HSub.hSub",
"And",
"Set.Nonempty",
"instHSub",
"Set.sub",
"propext",
"Eq",
"Sub",
"Set"
] | false |
_private.Mathlib.RingTheory.Ideal.GoingUp.0.Ideal.comap_ne_bot_of_root_mem.match_1_1 | Mathlib.RingTheory.Ideal.GoingUp | [
"RingHom.instRingHomClass",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"RingHom",
"Membership.mem",
"Exists",
"Ne",
"Ideal",
"Polynomial",
"Polynomial.coeff",
"And.casesOn",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"And",
"CommRing.toCommSemiring",
"RingHom.instFun... | false |
List.disjoint_cons_right._simp_1 | Batteries.Data.List.Lemmas | [
"Membership.mem",
"List.Disjoint",
"List.cons",
"List",
"And",
"List.instMembership",
"propext",
"Eq",
"Not",
"List.disjoint_cons_right"
] | false |
ContinuousLinearMapWOT.algebraMapCLM_apply | Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | [
"instHSMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"ContinuousLinearMapWOT.instRing",
"SMul",
"AddMonoid.toAddZeroClass",
"ContinuousLinearMapWOT.instFunLike",
"ContinuousLinearMapWOT",
"AddCommGroup.... | true |
Equiv.divLeft._proof_2 | Mathlib.Algebra.Group.Units.Equiv | [
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"DivisionMonoid.toInvolutiveInv",
"div_eq_mul_inv... | false |
_private.Mathlib.LinearAlgebra.Dimension.Torsion.Basic.0.rank_quotient_eq_of_le_torsion._simp_1_6 | Mathlib.LinearAlgebra.Dimension.Torsion.Basic | [
"Submodule",
"Submodule.Quotient.instZeroQuotient",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"Submodule.hasQuotient",
"Membership.mem",
"AddCommGroup",
"HasQuotient.Quotient",
"Submodule.setLike",
"propext",
"Zero.toOfNat0",
"Module",
"OfNat.ofNat",
"Ring.toSemiring",
"Eq... | false |
MvPolynomial.rename_comp_toMvPolynomial | Mathlib.Algebra.MvPolynomial.Equiv | [
"Polynomial.toMvPolynomial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"congrArg",
"CommSemiring.toSemiring",
"MvPolynomial.ext",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Polynomial.algebraOfAlgebra",
"Finsupp.instAddMonoid",
"MvPolynomial.X",
"Nat.instAddMonoid",
... | true |
CategoryTheory.MonoidalCategory.MonoidalRightAction.actionOfMonoidalFunctorToEndofunctor_actionHom | Mathlib.CategoryTheory.Monoidal.Action.End | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.MonoidalCategory.MonoidalRightAction.toMonoidalRightActionStruct",
"CategoryTheory.Functor.map",
"CategoryTheory.NatTrans.naturality",... | true |
PEquiv.mem_ofSet_self_iff | Mathlib.Data.PEquiv | [
"PEquiv.instFunLikeOption",
"Eq.mpr",
"False",
"eq_false",
"PEquiv.ofSet",
"Option.ctorIdx",
"congrArg",
"Option.instMembership",
"False.elim",
"noConfusion_of_Nat",
"Option.some",
"Membership.mem",
"id",
"if_pos",
"dite",
"iff_self",
"Option.none",
"Iff",
"DecidablePred",
"Opt... | true |
Algebra.FinitePresentation.baseChange | Mathlib.RingTheory.FiniteStability | [
"Eq.mpr",
"AlgEquiv.instEquivLike",
"RingHom.instRingHomClass",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"AlgHom.algHomClass",
"AlgHom.toMonoidHom'._proof_2",
"IsScalarTowe... | true |
IsUltrametricDist.nnnorm_div_eq_max_of_nnnorm_div_ne_nnnorm_div | Mathlib.Analysis.Normed.Group.Ultra | [
"Eq.mpr",
"Real",
"instHDiv",
"congrArg",
"NNNorm.nnnorm",
"SeminormedGroup",
"SeminormedGroup.toGroup",
"SeminormedGroup.toPseudoMetricSpace",
"Function.Injective.ne",
"SemilatticeSup.toMax",
"NNReal.instSemilatticeSup",
"id",
"HDiv.hDiv",
"NNReal",
"Ne",
"Group.toDivInvMonoid",
"Re... | true |
CommRingCat.Colimits.cocone_naturality | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CommRingCat.hom_ext",
"CommRingCat.Hom.hom",
"CommRingCat.carrier",
"Quot.sound",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"CommRingCat",
"RingHom",
"CommRingCat.Colimits.colimit",
"CommRingCat.instCategory",
"CategoryTheor... | true |
_private.Mathlib.CategoryTheory.Sites.Sieves.0.CategoryTheory.Presieve.instHasPullbacksOfArrowsOfHasPullback.match_1 | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve.ofArrows.mk",
"HEq.refl",
"eq_of_heq",
"Eq.ndrec",
"CategoryTheory.Presieve.ofArrows.casesOn",
"Eq.refl",
"HEq",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"CategoryTheory.Presieve.ofArrows",
... | false |
Sym2.fromRel_bot_iff | Mathlib.Data.Sym.Sym2 | [
"Eq.mpr",
"False",
"iff_false",
"Symmetric",
"Set.mem_empty_iff_false._simp_1",
"Sym2.mk",
"congrArg",
"Membership.mem",
"Eq.mp",
"id",
"Pi.instBotForall",
"Bot.bot",
"false_iff",
"funext",
"Iff",
"Sym2.fromRel_bot",
"Iff.intro",
"Sym2.fromRel_prop",
"propext",
"Set.instEmptyCo... | true |
Lean.Grind.CommRing.Poly.NonnegCoeffs.num | Init.Grind.Ring.CommSemiringAdapter | [
"Lean.Grind.CommRing.Poly.NonnegCoeffs",
"Lean.Grind.CommRing.Poly.NonnegCoeffs.num",
"GE.ge",
"Int",
"instOfNat",
"OfNat.ofNat",
"Int.instLEInt",
"Lean.Grind.CommRing.Poly.num"
] | true |
_private.Init.Data.SInt.Lemmas.0.ISize.toInt64_lt._simp_1_1 | Init.Data.SInt.Lemmas | [
"instLTISize",
"Int",
"ISize.lt_iff_toInt_lt",
"Int.instLTInt",
"LT.lt",
"propext",
"ISize",
"Eq",
"ISize.toInt"
] | false |
SimpleGraph.Walk.IsCycle.mapLe | Mathlib.Combinatorics.SimpleGraph.Paths | [
"Iff.mpr",
"SimpleGraph.Walk.IsCycle",
"SimpleGraph.Walk",
"LE.le",
"SimpleGraph",
"SimpleGraph.Walk.mapLe",
"SimpleGraph.Walk.mapLe_isCycle",
"SimpleGraph.instLE"
] | true |
Lean.Grind.CommRing.lt_mul | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly.denote_mulConst",
"Iff.mpr",
"Int.cast",
"Eq.mpr",
"instHSMul",
"Lean.Grind.Ring.zsmul_eq_intCast_mul",
"Lean.Grind.CommRing.Poly",
"HMul.hMul",
"congrArg",
"Lean.Grind.CommRing.Poly.beq'",
"Decidable.decide.congr_simp",
"Lean.Grind.IntModule.toNatModule",
"Lean.Gri... | true |
CategoryTheory.Limits.preservesLimit_subsingleton | Mathlib.CategoryTheory.Limits.Preserves.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.PreservesLimit.casesOn",
"CategoryTheory.Limits.IsLimit",
"Subsingleton.intro",
"CategoryTheory.Limits.PreservesLimit.mk",
"Nonempty",
"Subsingleton... | true |
SSet.Truncated.Edge.CompStruct.d₀._autoParam | Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Metric.preimage_vadd_closedBall | Mathlib.Topology.MetricSpace.IsometricSMul | [
"Metric.vadd_closedBall",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real",
"IsIsometricVAdd",
"AddMonoid.toAddSemigroup",
"congrArg",
"Set.vaddSet",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"HVAdd.hVAdd",
"AddAction",
"AddAct... | true |
Lean.Meta.RefinedDiscrTree.ExprInfo.noConfusionType | Mathlib.Lean.Meta.RefinedDiscrTree.Basic | [
"Lean.Meta.RefinedDiscrTree.ExprInfo",
"Lean.Expr",
"Lean.FVarId",
"Lean.Meta.RefinedDiscrTree.ExprInfo.casesOn",
"List",
"Lean.LocalInstances",
"Eq",
"Lean.LocalContext",
"Lean.Meta.Config"
] | false |
_private.Mathlib.Topology.MetricSpace.Pseudo.Defs.0.Metric.uniformity_eq_comap_nhds_zero._simp_1_1 | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Filter.instMembership",
"Real",
"Real.instZero",
"uniformity",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"Membership.mem",
"Exists",
"Prod.mk",
"GT.gt",
"And",
"PseudoMetricSpace",
"Metric.mem_uniformity_dist",
"LT.lt",
"propext",
"Zero.toOfNat0",
"Dist.dist",
"PseudoMetr... | false |
CategoryTheory.instFinallySmallOfHasTerminal | Mathlib.CategoryTheory.Limits.FinallySmall | [
"CategoryTheory.Functor",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Preorder.toLE",
"instInhabitedPUnit",
"CoheytingAlgebra.toOrderTop",
"Preorder.smallCategory",
"CompleteDistribLattice.toCoframe",
"PUnit.instCompleteBooleanA... | true |
Std.DTreeMap.Internal.Impl.maxKeyD.match_1 | Std.Data.DTreeMap.Internal.Queries | [
"Std.DTreeMap.Internal.Impl.casesOn",
"namedPattern",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | false |
Path.Homotopic.pi_lift | Mathlib.Topology.Homotopy.Product | [
"Eq.mpr",
"Pi.topologicalSpace",
"congrArg",
"Path.pi",
"Path.Homotopic.pi._proof_1",
"Quotient.map",
"Path.Homotopic.pi",
"inferInstance",
"id",
"Setoid",
"Quotient.choice",
"Path.Homotopic.Quotient",
"Quotient.map.congr_simp",
"Quotient.mk",
"Path.Homotopic.setoid",
"piSetoid",
"To... | true |
Complex.cosh_two_mul | Mathlib.Analysis.Complex.Trigonometric | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Complex.sinh",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"two_mul",
"Complex.instMul",
"id",
"MulOne.toMul",
"Distrib.toAdd",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"AddCommMonoidWithOne.to... | true |
CategoryTheory.Functor.CoreMonoidal.mk'._auto_3 | Mathlib.CategoryTheory.Monoidal.Functor | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
instFiniteProp | Mathlib.Data.Fintype.EquivFin | [
"Finite",
"instSubsingleton",
"Finite.of_subsingleton"
] | true |
Primcodable.ulower | Mathlib.Computability.Primrec.Basic | [
"instEncodableULower",
"Primcodable.mk",
"Primcodable.ulower._proof_1",
"Primcodable.toEncodable",
"Primcodable",
"ULower"
] | true |
Std.IterM.toList_filter | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Pure.pure",
"Eq.mpr",
"Option.guard",
"congrArg",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"instMonadLiftT",
"Option.some",
"Std.Iterators.Finite",
"id",
"instDecidableEqBool",
"LawfulMonad",
"Applicative.toPure",
"Std.IterM.filter",
"Std.Iterator",
"Bool.true",
"Option.none",... | true |
_private.Mathlib.Analysis.AbsoluteValue.Equivalence.0.AbsoluteValue.exists_one_lt_lt_one_pi_of_not_isEquiv.match_1_11 | Mathlib.Analysis.AbsoluteValue.Equivalence | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Exists",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Subtype",
"Ne",
"DivisionRing.toRing",
"Field.toSemifield",
"Subtype.mk",
"Subtype.restrict",
"... | false |
Aesop.CasesTarget.ctorIdx | Aesop.RuleTac.Basic | [
"Array",
"Aesop.CasesPattern",
"Nat",
"Lean.Name",
"Aesop.CasesTarget.casesOn",
"Aesop.CasesTarget"
] | false |
Ideal.Filtration.mem_submodule._simp_1 | Mathlib.RingTheory.Filtration | [
"Subalgebra.instSetLike",
"Finsupp.instFunLike",
"Submodule",
"CommRing",
"Ideal.Filtration.mem_submodule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Polynomial.algebraOfAlgebra",
"Membership.mem",
"AddCommGroup",
"Algebra.id",
"Subtype",
"Ideal.Filtration.submodule",
"Su... | false |
PiLp.basisFun.eq_1 | Mathlib.Analysis.Normed.Lp.PiLp | [
"Pi.Function.module",
"Module.Basis.ofEquivFun",
"Semiring.toModule",
"AddCommGroup.toAddCommMonoid",
"Finite",
"WithLp.instAddCommGroup",
"PiLp",
"PiLp.basisFun",
"Module.Basis",
"Ring.toAddCommGroup",
"Pi.addCommGroup",
"ENNReal",
"Eq.refl",
"WithLp.instModule",
"Ring.toSemiring",
"E... | true |
Std.Iterators.Types.ArrayIterator._sizeOf_1 | Std.Data.Iterators.Producers.Monadic.Array | [
"Std.Iterators.Types.ArrayIterator",
"instOfNatNat",
"Array._sizeOf_inst",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"instSizeOfNat",
"SizeOf",
"OfNat.ofNat",
"Std.Iterators.Types.ArrayIterator.rec"
] | false |
Finset.univ_finset_eq_singleton_empty_iff._simp_1 | Mathlib.Data.Finset.Basic | [
"Finset",
"Set.univ",
"Set.instSingletonSet",
"IsEmpty",
"Finset.instEmptyCollection",
"propext",
"EmptyCollection.emptyCollection",
"Singleton.singleton",
"Finset.univ_finset_eq_singleton_empty_iff",
"Eq",
"Set"
] | false |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.readyForRatAdd_ofArray._proof_1_2 | Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"Bool",
"instAddNat",
"instLTNat",
"Array.mk",
"Prod",
"OfNat.ofNat",
"Std.Tactic.BVDecide.LRAT.Internal.PosFin",
"Array.size",
"List.nil"
] | false |
Cardinal.blsub_lt_ord_of_isRegular | Mathlib.SetTheory.Cardinal.Regular | [
"Eq.mpr",
"Preorder.toLT",
"Cardinal.IsRegular",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Cardinal.IsRegular.cof_ord",
"id",
"Ordinal.blsub_lt_ord",
"Cardinal.ord",
"Ordinal.card",
"Cardinal.partialOrder",
"Ordinal.blsub",
"LT.lt",
"Ordinal.cof",
"E... | true |
IsScalarTower.restrictScalars | Mathlib.Algebra.Algebra.RestrictScalars | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"Module.restrictScalars",
"IsScalarTower.of_compH... | true |
CategoryTheory.DifferentialObject.Hom.recOn | Mathlib.CategoryTheory.DifferentialObject | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.DifferentialObject.Hom.mk",
"CategoryTheory.shiftFunctor",
"CategoryTheory.DifferentialObject.obj",
"CategoryTheory.Functor.map",
"CategoryTheory.DifferentialObject.Hom",
"AddMonoidWithO... | false |
CategoryTheory.ShortComplex.cyclesMapIso_inv | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.Iso",
"CategoryTheory.ShortComplex.cyclesMapIso",
"CategoryTheory.ShortComplex.cyclesMap",
"CategoryTheory.Shor... | true |
Finset.factorization_lcm | Mathlib.Algebra.GCDMonoid.FinsetLemmas | [
"Nat.lcm",
"Finsupp.instFunLike",
"not_exists._simp_1",
"instNormalizedGCDMonoidNat",
"False",
"Nat.instMulZeroClass",
"Lattice.toSemilatticeSup",
"instDistribLatticeNat",
"Finset.sup_insert",
"eq_false",
"Nat.instNontrivial",
"congrArg",
"Finset",
"forall_eq_or_imp._simp_1",
"instInhabi... | true |
CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT | Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | [
"WithBot.instPreorder",
"CategoryTheory.Functor",
"CategoryTheory.Triangulated.TStructure.eTruncLTGELTSelfToGELT",
"WithTop.instPreorder",
"CategoryTheory.Functor.Additive",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Triangulated.TStr... | true |
Std.DTreeMap.Internal.Impl.Const.alterₘ | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"HSub.hSub",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.OrientedOrd",
"Std.DTreeMap.Internal.Cell.Const.alter",
"Std.DTreeMap.Internal.Impl.size",
"instSubNat",
"instOfNatNat",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"Std.DTr... | true |
groupHomology.toCycles | Mathlib.RepresentationTheory.Homological.GroupHomology.Basic | [
"CommRing",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CommSemiring.toSemiring",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Group",
"Nat.instAddCancelCommMonoid",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid"... | true |
LSeries.eq_of_LSeries_eventually_eq | Mathlib.NumberTheory.LSeries.Injectivity | [
"Real",
"LSeries_eventually_eq_zero_iff'",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"LSeries_sub_eventuallyEq_zero_of_LSeries_eventually_eq",
"AddGroupWithOne.toAddGroup",
"PartialOrder.toPreorder",
"HSub.hSub",
"EReal",
"Complex.instZero",
"Preorder.toLE",
"CoheytingAlgebra.toOrderTop",
... | true |
Lean.Meta.Grind.Arith.Cutsat.Search.Kind.recOn | Lean.Meta.Tactic.Grind.Arith.Cutsat.SearchM | [
"Lean.Meta.Grind.Arith.Cutsat.Search.Kind",
"Lean.Meta.Grind.Arith.Cutsat.Search.Kind.int",
"Lean.Meta.Grind.Arith.Cutsat.Search.Kind.rec",
"Lean.Meta.Grind.Arith.Cutsat.Search.Kind.rat"
] | false |
Std.DHashMap.Raw.all | Std.Data.DHashMap.RawDef | [
"Pure.pure",
"Unit.unit",
"instDecidableNot",
"Monad.toApplicative",
"Std.DHashMap.Raw",
"Option.some",
"ForInStep.done",
"instDecidableEqBool",
"Prod.mk",
"ForIn.forIn",
"Sigma.fst",
"Id.run",
"Id",
"Applicative.toPure",
"ForInStep",
"Prod.fst",
"Bool.true",
"Option.none",
"Std.... | true |
_private.Std.Time.Time.Unit.Basic.0.Std.Time.Millisecond.Offset.ofHours._proof_1 | Std.Time.Time.Unit.Basic | [
"Rat.instOfNat",
"Int.cast",
"instHDiv",
"of_decide_eq_true",
"Rat",
"Rat.instIntCast",
"id",
"HDiv.hDiv",
"Int",
"Bool.true",
"instOfNat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"instDecidableEqRat",
"Decidable.decide",
"Eq",
"Rat.instDiv"
] | false |
Fin.castPred_lt_castPred | Mathlib.Data.Fin.SuccPred | [
"Fin.castPred",
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Fin.last",
"LT.lt",
"instLTFin",
"instAddNat",
"OfNat.ofNat",
"Fin",
"Fin.ne_last_of_lt"
] | true |
_private.Mathlib.Algebra.Order.BigOperators.Group.Finset.0.Multiset.finsetSum_eq_sup_iff_disjoint._simp_1_6 | Mathlib.Algebra.Order.BigOperators.Group.Finset | [
"imp_and",
"And",
"propext",
"Eq"
] | false |
add_comm | Mathlib.Algebra.Group.Defs | [
"AddCommMagma",
"AddCommMagma.add_comm",
"instHAdd",
"HAdd.hAdd",
"Eq",
"AddCommMagma.toAdd"
] | true |
Ordnode.eraseMax._sunfold | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode",
"Ordnode.eraseMax.match_1",
"Ordnode.node",
"Ordnode.eraseMax",
"Unit",
"Ordnode.balanceL",
"Nat",
"Ordnode.nil"
] | false |
_private.Mathlib.RingTheory.Polynomial.UniversalFactorizationRing.0.MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix._proof_1_3 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"dite_congr",
"Fin.instIsLinearOrder",
"HMul.hMul",
"eq_false",
"Fin.castAdd",
"Int.Linear.Expr.eq_of_norm_eq",
"Lean.Grind.ToInt.toInt",
"AddMonoidAlgebra.commRing",
"c... | false |
cantorToTernary._proof_1 | Mathlib.Topology.Instances.CantorSet | [
"Zero.ofOfNat0",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"NeZero",
"OfNat.ofNat"
] | false |
Lean.Meta.Grind.Arith.CollectDecVars.State.ctorIdx | Lean.Meta.Tactic.Grind.Arith.Util | [
"Lean.Meta.Grind.Arith.CollectDecVars.State",
"Nat"
] | false |
AddSubgroup.le_prod_iff | Mathlib.Algebra.Group.Subgroup.Basic | [
"Eq.mpr",
"AddMonoidHom.fst",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddSubmonoid.le_prod_iff",
"id",
"AddSubmonoid",
"LE.le",
"AddSubgroup",
"And",
"AddGroup",
"Iff",
"AddGroup.toSubNegMonoid",
"AddSubgrou... | true |
Int8.toInt64_xor | Init.Data.SInt.Bitwise | [
"BitVec.instXorOp",
"congrArg",
"Int8.toBitVec_xor",
"Int8.toInt64",
"Int8",
"Int64.toBitVec_xor",
"BitVec",
"Int64",
"instOfNatNat",
"instXorOpInt8",
"instXorOpInt64",
"Nat",
"congr",
"BitVec.signExtend_xor",
"True",
"HXor.hXor",
"eq_self",
"Iff.mp",
"BitVec.signExtend",
"of_e... | true |
Lean.Meta.Grind.Arith.Linear.Case.recOn | Lean.Meta.Tactic.Grind.Arith.Linear.SearchM | [
"Lean.FVarId",
"Lean.Meta.Grind.Arith.Linear.Struct",
"Lean.Meta.Grind.Arith.Linear.Case.mk",
"Lean.Meta.Grind.Arith.Linear.Case.rec",
"Lean.Meta.Grind.Arith.Linear.Case",
"Lean.Meta.Grind.Arith.Linear.DiseqCnstr"
] | false |
Localization.awayEquivAdjoin._proof_1 | Mathlib.RingTheory.Localization.Away.AdjoinRoot | [
"Polynomial.C",
"Polynomial.instOne",
"CommRing",
"HMul.hMul",
"AdjoinRoot",
"CommSemiring.toSemiring",
"IsUnit.of_mul_eq_one",
"HSub.hSub",
"IsUnit",
"RingHom",
"AdjoinRoot.root_isInv",
"Polynomial",
"instIsDedekindFiniteMonoid",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"inst... | false |
AddSubgroup.ofAddUnitsEquivType.eq_1 | Mathlib.Algebra.Group.Submonoid.Units | [
"AddUnits.val",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Equiv.mk",
"Subtype",
"AddSubmonoid.add",
"AddSubmonoid",
"AddSubgroup.ofAddUnitsEquivType._proof_4",
"AddSubgroup.ofAddUnitsEquivType._proof_1",
"AddSubgroup.ofAddUnitsEquivType._proof_2",
"Subtype.mk",
"AddSubgroup",
"AddSubgro... | true |
IsMax.of_succ_le | Mathlib.Order.SuccPred.Basic | [
"Order.succ",
"Preorder.toLE",
"Order.succ_le_iff_isMax",
"LE.le",
"Iff.mp",
"SuccOrder",
"Preorder",
"IsMax"
] | true |
Finset.sum_Icc_of_even_eq_range | Mathlib.Algebra.BigOperators.Group.Finset.Interval | [
"neg_add_rev",
"Int.instAddCommGroup",
"CharP.cast_eq_zero",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Nat.cast_succ",
"False",
"Nat.recAux",
"instHSMul",
"Preorder.toLT",
"Finset.Icc_succ_succ",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Finset.sum_pair",
"AddMo... | true |
Valuation.isOpen_closedBall | Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | [
"Filter.instMembership",
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"CommRing",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"ValuationClass.toMonoidWithZeroHomClass",
"AddGroupWithOne.toAddGroup",
"WithZero.instMo... | true |
Nat.multichoose._unary._proof_1 | Mathlib.Data.Nat.Choose.Basic | [
"invImage",
"PSigma.casesOn",
"Prod.mk",
"sizeOfWFRel",
"Lean.opaqueId",
"Nat",
"instSizeOfNat",
"Prod.instWellFoundedRelation",
"Prod",
"WellFounded",
"PSigma"
] | false |
Lean.TagAttributeExtra.getDecls | Batteries.Lean.AttributeExtra | [
"Lean.PersistentEnvExtensionState",
"Array.push",
"Lean.NameSet",
"Std.HashSet.fold",
"Id.run",
"Id",
"Lean.TagAttributeExtra",
"Lean.instInhabitedPersistentEnvExtensionState",
"Lean.Name.anonymous",
"Array",
"Lean.TagAttribute.getDecls.core",
"Lean.TagAttributeExtra.ext",
"Lean.TagAttribute... | true |
AbsoluteValue.trivial.eq_1 | Mathlib.Analysis.AbsoluteValue.Equivalence | [
"Nontrivial",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AbsoluteValue.trivial._proof_2",
"IsOrderedRing",
"AbsoluteValue.trivial._proof_1",
"PartialOrder",
"AbsoluteValue.trivial._proof_3",
"AbsoluteValue.trivial._proof_5",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSemiring",
"A... | true |
Lean.Lsp.ResolveSupport.ctorIdx | Lean.Data.Lsp.Basic | [
"Lean.Lsp.ResolveSupport",
"Nat"
] | false |
Batteries.RBSet.Slow.instDecidableEMem | Batteries.Data.RBMap.Basic | [
"Batteries.RBSet",
"Batteries.RBSet.Slow.instDecidableEMem._aux_1",
"Decidable",
"Ordering",
"Batteries.RBSet.EMem",
"DecidableEq"
] | true |
Int.sub_neg_of_lt | Init.Data.Int.Order | [
"congrArg",
"HSub.hSub",
"Eq.mp",
"Int.instNegInt",
"Int",
"Int.add_lt_add_right",
"Int.instLTInt",
"Int.add_right_neg",
"instHAdd",
"instHSub",
"instOfNat",
"HAdd.hAdd",
"LT.lt",
"Int.instAdd",
"Int.instSub",
"OfNat.ofNat",
"Neg.neg"
] | true |
Mathlib.Tactic.Ring.Common.ExBaseNat.evalPos._unsafe_rec | Mathlib.Tactic.Ring.Common | [
"Mathlib.Tactic.Ring.Common.ExSumNat",
"Lean.Expr.const",
"Lean.Level",
"Mathlib.Tactic.Ring.Common.ExBaseNat",
"Mathlib.Tactic.Ring.Common.ExSumNat.evalPos._unsafe_rec",
"List.cons",
"Lean.Literal.natVal",
"Option.none",
"Qq.Quoted",
"Lean.Level.zero",
"Nat",
"Lean.Name.mkStr2",
"Lean.Expr.... | false |
TopologicalSpace.Opens.IsBasis | Mathlib.Topology.Sets.Opens | [
"TopologicalSpace.Opens",
"TopologicalSpace.Opens.instSetLike",
"TopologicalSpace",
"SetLike.coe",
"TopologicalSpace.IsTopologicalBasis",
"Set.image",
"Set"
] | true |
AddSubgroup.comap_sup_comap_le | Mathlib.Algebra.Group.Subgroup.Map | [
"AddSubgroup.comap",
"AddSubgroup.instCompleteLattice",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"Monotone.le_map_sup",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"SemilatticeSup.toMax",
"LE.... | true |
Lean.Lsp.instFromJsonCommand.fromJson | Lean.Data.Lsp.Basic | [
"Pure.pure",
"Lean.Json",
"Lean.instFromJsonString",
"Monad.toApplicative",
"String",
"Lean.instFromJsonOption",
"Lean.Name.mkStr3",
"Lean.Json.getObjValAs?",
"Lean.instFromJsonArray",
"Applicative.toPure",
"ToString.toString",
"Except.instMonad",
"Array",
"Lean.instFromJsonJson",
"instA... | true |
_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeContext.mk.noConfusion | Lean.Elab.MutualInductive | [
"Lean.Elab.Command.InductiveElabStep2",
"Lean.MetavarContext",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeContext.noConfusion",
"Lean.Expr",
"Lean.Meta.MetaM",
"id",
"Array",
"List",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeContext.mk",
"Lean.Name",
"L... | false |
isCountablyCompact_iUnion | Mathlib.Topology.Compactness.CountablyCompact | [
"Iff.mpr",
"Set.forall_mem_range",
"Finite",
"Membership.mem",
"Set.finite_range",
"IsCountablyCompact",
"TopologicalSpace",
"Set.Finite.isCountablyCompact_sUnion",
"Set.range",
"Set.instMembership",
"Set.iUnion",
"Set"
] | true |
WithBot.subtypeOrderIso._proof_10 | Mathlib.Order.Hom.WithTopBot | [
"WithBot.instPreorder",
"Function.LeftInverse",
"WithBot.some",
"WithBot",
"dite_congr",
"WithBot.subtypeOrderIso._proof_6",
"Equiv.instEquivLike",
"congrArg",
"WithBot.instOrderBot",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Equiv.mk",
"PartialOrder",
... | false |
AddSubmonoid.mk_eq_top | Mathlib.Algebra.Group.Submonoid.Defs | [
"AddSubmonoid.instTop",
"AddSubsemigroup.instSetLike",
"congrArg",
"Set.univ",
"AddSubsemigroup.carrier",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid",
"AddSubmonoid.mk",
"iff_self",
"AddZero.toZero",
"AddZeroClass",
"Iff",
"SetLike.coe",
"AddSubsemigroup.instTop",
"AddSu... | true |
RingNorm.toAddGroupNorm | Mathlib.Analysis.Normed.Unbundled.RingSeminorm | [
"NonUnitalNonAssocRing",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"RingNorm.toRingSeminorm",
"RingNorm",
"RingSeminorm.toAddGroupSeminorm",
"RingNorm.eq_zero_of_map_eq_zero'",
"AddGroupNorm",
"AddGroupNorm.mk"
] | true |
Std.Time.ZonedDateTime.subMonthsClip | Std.Time.Zoned.ZonedDateTime | [
"Std.Time.ZonedDateTime.timestamp",
"Std.Time.PlainDateTime.toTimestampAssumingUTC",
"Std.Time.PlainDateTime.subMonthsClip",
"Std.Time.ZonedDateTime.ofTimestamp",
"Std.Time.PlainDateTime",
"Std.Time.Month.Offset",
"Std.Time.ZonedDateTime",
"Std.Time.ZonedDateTime.rules",
"Std.Time.Timestamp.toPlainD... | true |
Lean.Lsp.WorkspaceEdit.mk.inj | Lean.Data.Lsp.Basic | [
"Lean.Lsp.WorkspaceEdit",
"String",
"Lean.Lsp.TextEditBatch",
"Lean.Lsp.DocumentChange",
"Ord.compare",
"Lean.Lsp.WorkspaceEdit.mk",
"Array",
"Lean.Lsp.DocumentUri",
"Lean.Lsp.ChangeAnnotation",
"Lean.Lsp.WorkspaceEdit.mk.noConfusion",
"And",
"And.intro",
"String.instOrd",
"Eq",
"Std.Tre... | true |
CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.noConfusion | Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂._autoParam",
"HEq.refl",
"LinearOrder",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.categ... | false |
_private.Mathlib.Data.List.Sublists.0.List.Pairwise.sublists'._simp_1_5 | Mathlib.Data.List.Sublists | [
"List.map",
"Membership.mem",
"Exists",
"List",
"And",
"List.instMembership",
"propext",
"List.mem_map",
"Eq"
] | false |
Topology.IsOpenEmbedding.matrix_map | Mathlib.Topology.Instances.Matrix | [
"Pi.topologicalSpace",
"Matrix",
"Finite",
"Topology.IsOpenEmbedding.piMap",
"Pi.map",
"TopologicalSpace",
"Topology.IsOpenEmbedding",
"Matrix.map",
"instTopologicalSpaceMatrix"
] | true |
Lean.Parser.Command.macroRhs.parenthesizer | Lean.Parser.Syntax | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Bool.true",
"Lean.PrettyPrinter.Parenthesizer.withPosition.parenthesizer",
"Nat",
"Lean.PrettyPrinter.Pare... | true |
Representation.prod_apply_apply | Mathlib.RepresentationTheory.Basic | [
"Monoid",
"Representation",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Module.End.instSemiring",
"LinearMap.instFunLike",
"Prod.mk",
"LinearMap",
"Prod.fst",
"AddCommMonoid",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"MulOneClass.toMulOne",
"Se... | true |
Lean.Elab.Term.Do.Alt.mk._flat_ctor | Lean.Elab.Do.Legacy | [
"Lean.Syntax",
"Lean.Elab.Term.Do.Var",
"Array",
"Lean.Elab.Term.Do.Alt.mk",
"Lean.Elab.Term.Do.Alt"
] | false |
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