name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Topology.«_aux_Mathlib_Topology_Defs_Filter___macroRules_Topology_term𝓝ˢ_1» | Mathlib.Topology.Defs.Filter | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad",
"Lean.TSyntax.... | false |
TopologicalSpace.secondCountableTopology_iInf | Mathlib.Topology.Bases | [
"Eq.mpr",
"TopologicalSpace.SecondCountableTopology.mk'",
"TopologicalSpace.countableBasis",
"iInf",
"TopologicalSpace.countable_countableBasis",
"congrArg",
"SecondCountableTopology",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"id",
"generateFrom_i... | true |
ENNReal.toReal_lt_toReal | Mathlib.Data.ENNReal.Real | [
"Eq.mpr",
"ENNReal.canLift",
"Real",
"ENNReal.ofNNReal",
"Preorder.toLT",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Real.instLT",
"Exists",
"id",
"NNReal",
"Ne",
"ENNReal.coe_lt_coe._simp_1",
"NNReal.instPartialOrder",
"Iff",
"ENNReal.toReal",
"Exists.casesOn",
"LT.lt",
... | true |
Finsupp.lcoeFun._proof_2 | Mathlib.LinearAlgebra.Finsupp.Pi | [
"Finsupp.instFunLike",
"Pi.Function.module",
"instHSMul",
"Pi.addCommMonoid",
"Finsupp.module",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"AddZero.toZero",
... | false |
Set.nontrivial_of_einfsep_ne_top | Mathlib.Topology.MetricSpace.Infsep | [
"Iff.mpr",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.nontrivial_of_einfsep_lt_top",
"Ne",
"lt_top_iff_ne_top",
"OrderTop.toTop",
"LT.lt",
"ENNReal",
"ENNReal.instPartialOrder",
"ENNReal.instTop",
"EDist",
"Top.top",
"Set.Nontrivial",
"Set.einfsep",
"ENNReal.in... | true |
Lean.SMap.rec | Lean.Data.SMap | [
"Lean.PHashMap",
"Std.HashMap",
"Lean.SMap.mk",
"Lean.SMap",
"Bool",
"Hashable",
"BEq"
] | false |
EuclideanGeometry.instNonemptySphere | Mathlib.Geometry.Euclidean.Sphere.Basic | [
"Real",
"Real.instZero",
"EuclideanGeometry.Sphere",
"Nonempty.intro",
"EuclideanGeometry.Sphere.mk",
"MetricSpace",
"Classical.arbitrary",
"Nonempty",
"Zero.toOfNat0",
"OfNat.ofNat"
] | true |
Lean.Meta.eqnThmSuffixBase | Lean.Meta.Eqns | [
"String"
] | true |
Matrix.vec_mul_eq_vecMul | Mathlib.LinearAlgebra.Matrix.Vec | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"HMul.hMul",
"eq_false",
"congrArg",
"Matrix",
"Matrix.instHMulOfFintypeOfMulOfAddCommMonoid",
"Matrix.one_apply_ne",
"Matrix.vecMul",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Commute",
"id",
"NonUnitalSemiring.toNonUnitalNo... | true |
LeanSearchClient.SearchResult.mk._flat_ctor | LeanSearchClient.Syntax | [
"String",
"LeanSearchClient.SearchResult.mk",
"LeanSearchClient.SearchResult",
"Option"
] | false |
LocallyConstant.ext | Mathlib.Topology.LocallyConstant.Basic | [
"DFunLike.ext",
"LocallyConstant",
"TopologicalSpace",
"LocallyConstant.instFunLike",
"Eq",
"DFunLike.coe"
] | true |
_private.Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors.0.MonoidAlgebra.instIsLeftCancelMulZeroOfIsCancelAddOfUniqueProds._simp_2 | Mathlib.Algebra.MonoidAlgebra.NoZeroDivisors | [
"Finset",
"Finsupp.support",
"Finset.instEmptyCollection",
"propext",
"Zero.toOfNat0",
"Finsupp.support_eq_empty",
"EmptyCollection.emptyCollection",
"Finsupp.instZero",
"OfNat.ofNat",
"Eq",
"Finsupp",
"Zero"
] | false |
_private.Mathlib.RingTheory.Valuation.Discrete.Basic.0.IsDiscreteValuationRing.mker_valuation_eq_isUnitSubmonoid._simp_1_6 | Mathlib.RingTheory.Valuation.Discrete.Basic | [
"Classical.not_not",
"propext",
"Eq",
"Not"
] | false |
CategoryTheory.GradedObject.mapTrifunctorMapFunctorObj._proof_1 | Mathlib.CategoryTheory.GradedObject.Trifunctor | [
"CategoryTheory.Functor",
"CategoryTheory.GradedObject.HasMap",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.GradedObject.mapTrifunctorMapMap",
"Prod.mk",
"CategoryTheory.Category.comp_id"... | false |
Std.Internal.List.minKey!_modifyKey | Std.Data.Internal.List.Associative | [
"Std.Internal.List.replaceEntry",
"Std.Internal.List.DistinctKeys",
"Ord",
"congrArg",
"Std.Internal.List.getValueCast?",
"Std.TransOrd",
"Eq.rec",
"Eq.mp",
"id",
"Std.Internal.List.getValueCast?.congr_simp",
"Bool.true",
"Std.Internal.List.minKey!",
"List",
"Unit",
"Std.Internal.List.is... | true |
Mathlib.Tactic.ITauto.instLTIProp | Mathlib.Tactic.ITauto | [
"LT.mk",
"Mathlib.Tactic.ITauto.IProp",
"Ordering",
"Mathlib.Tactic.ITauto.IProp.cmp",
"Ordering.lt",
"Eq",
"LT"
] | true |
Lean.Meta.RefinedDiscrTree.PreDiscrTree.ctorIdx | Mathlib.Lean.Meta.RefinedDiscrTree.Initialize | [
"Lean.Meta.RefinedDiscrTree.PreDiscrTree",
"Nat"
] | false |
measurable_measure_prodMk_left | Mathlib.MeasureTheory.Measure.Prod | [
"Eq.mpr",
"MeasureTheory.Measure",
"MeasurableSet",
"ENNReal.instAddCommMonoid",
"MeasureTheory.Measure.sum_apply_of_countable",
"congrArg",
"AddMonoid.toAddZeroClass",
"Measurable",
"ENNReal.measurableSpace",
"ENNReal.instContinuousAdd",
"AddZeroClass.toAddZero",
"id",
"SummationFilter.inst... | true |
Std.DHashMap.getKeyD_diff_of_not_mem_left | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.instSDiff",
"congrArg",
"Std.DHashMap.Raw",
"Membership.mem",
"Eq.mp",
"Std.DHashMap.instMembership",
"Std.DHashMap.wf",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"Std.DHashMap.getKeyD",
"LawfulHashable",
"Std.DHashMap.Internal.Raw₀.getKeyD_diff_of_contains_eq_false... | true |
IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow | Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | [
"Subalgebra.instSetLike",
"IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow",
"IsIntegralClosure",
"Nat.Prime",
"IsIntegralClosure.equiv",
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"Rat",
"NumberField.RingOfIntegers.instAlgebra_... | true |
Pi.measurableNeg | Mathlib.MeasureTheory.Group.Arithmetic | [
"Iff.mpr",
"Pi.instNeg",
"measurable_pi_iff",
"MeasurableNeg.mk",
"Measurable",
"measurable_pi_apply",
"MeasurableSpace",
"Measurable.neg",
"Neg",
"MeasurableSpace.pi",
"MeasurableNeg",
"Neg.neg"
] | true |
Batteries.OrientedOrd.instLexOrd | Batteries.Classes.Deprecated | [
"Eq.mpr",
"Batteries.instOrientedCmpCompareOnOfOrientedOrd",
"Ord",
"Batteries.instOrientedCmpCompareLex",
"congrArg",
"compareLex",
"Ordering",
"inferInstance",
"lexOrd_def",
"id",
"Ord.compare",
"Prod.fst",
"Batteries.OrientedOrd.eq_1",
"compareOn",
"Batteries.OrientedOrd",
"Batterie... | true |
CategoryTheory.Limits.preservesSmallestCofilteredLimits_of_preservesCofilteredLimits | Mathlib.CategoryTheory.Limits.Preserves.Filtered | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesCofilteredLimitsOfSize",
"CategoryTheory.Limits.preservesCofilteredLimitsOfSize_shrink",
"CategoryTheory.Category"
] | true |
LSeries.notation._aux_Mathlib_NumberTheory_LSeries_Basic___unexpand_LSeries_delta_1 | Mathlib.NumberTheory.LSeries.Basic | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
ValuationSubring.linearOrderOverring._proof_3 | Mathlib.RingTheory.Valuation.ValuationSubring | [
"ValuationSubring.instPartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Subtype",
"LE.le",
"Std.Total.total",
"Or",
"ValuationSubring.le_total_ideal",
"Field",
"ValuationSubring",
"Subtype.instLE"
] | false |
continuousAt_prod_of_discrete_right | Mathlib.Topology.ContinuousOn | [
"Eq.mpr",
"ContinuousWithinAt",
"congrArg",
"ContinuousAt",
"DiscreteTopology",
"Set.univ",
"instTopologicalSpaceProd",
"continuousWithinAt_prod_of_discrete_right",
"id",
"Prod.mk",
"_private.Mathlib.Topology.ContinuousOn.0.continuousAt_prod_of_discrete_right._simp_1_1",
"Prod.fst",
"Topolog... | true |
CategoryTheory.IsCofiltered.minToRight._proof_1 | Mathlib.CategoryTheory.Filtered.Basic | [
"Exists.choose_spec",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Exists",
"CategoryTheory.IsCofilteredOrEmpty",
"CategoryTheory.IsCofilteredOrEmpty.cone_objs",
"True",
"CategoryTheory.Category.toCategoryStruct",
"Exists.choose",
"CategoryTheory.Category"
] | false |
ValuationSubring.instSemilatticeSup | Mathlib.RingTheory.Valuation.ValuationSubring | [
"SemilatticeSup.mk",
"ValuationSubring.instPartialOrder",
"Lattice.toSemilatticeSup",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"inferInstance",
"PartialOrder",
"CommRing.toNonAssocCommRing",
"Field.toCommRing",
"ValuationSubring.ofLE",
"Subring",
"Max.max",
"... | true |
_private.Mathlib.Data.Set.Prod.0.Set.EqOn.right_of_eqOn_prodMap._proof_1_1 | Mathlib.Data.Set.Prod | [
"Prod.map_snd",
"False",
"eq_false",
"congrArg",
"Classical.byContradiction",
"Eq.mp",
"id",
"Prod.mk",
"Prod.map",
"True",
"eq_true",
"Eq.refl",
"Prod",
"Eq.symm",
"Eq",
"Prod.snd",
"Not",
"Eq.trans",
"True.intro"
] | false |
instReprOrdering | Init.Data.Ord.Basic | [
"instReprOrdering.repr",
"Ordering",
"Repr.mk",
"Repr"
] | true |
Valuation.IsRankOneDiscrete.valueGroup₀_equiv_withZeroMulInt._proof_3 | Mathlib.RingTheory.Valuation.Discrete.RankOne | [
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"DivInvOneMonoid.toInvOneClass",
"ValuationClass.toMonoidWithZeroHomClass",
"Subgroup.zpowers_inv",
"Valuation.IsRankOneDiscrete.generator'",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMon... | false |
Multiset.mapEquiv_aux._proof_3 | Mathlib.Data.Multiset.Fintype | [
"inferInstance",
"Multiset",
"id",
"IsEmpty",
"Quotient.mk",
"List",
"Zero.toOfNat0",
"Multiset.ToType",
"Multiset.instIsEmptyToTypeOfNat",
"List.isSetoid",
"OfNat.ofNat",
"List.nil",
"Multiset.instZero",
"DecidableEq"
] | false |
Zsqrtd.isCoprime_of_dvd_isCoprime | Mathlib.NumberTheory.Zsqrtd.Basic | [
"Int.cast",
"Eq.mpr",
"False",
"Dvd.dvd",
"Zsqrtd.re",
"Zsqrtd.ext",
"CommRing.toNonUnitalCommRing",
"Zsqrtd.instZero",
"congrArg",
"CommSemiring.toSemiring",
"Int.euclideanDomain",
"False.elim",
"_private.Mathlib.NumberTheory.Zsqrtd.Basic.0.Zsqrtd.isCoprime_of_dvd_isCoprime._simp_1_1",
"s... | true |
Aesop.mkLocalRuleSet | Aesop.RuleSet | [
"Pure.pure",
"_private.Aesop.RuleSet.0.Aesop.mkLocalRuleSet._proof_2",
"Array.mkEmpty",
"Lean.Meta.Simp.SimprocEntry",
"Aesop.RuleName",
"Aesop.BaseRuleSet.merge",
"Array.push",
"Aesop.LocalRuleSet.mk",
"instForInOfForIn'",
"ReaderT",
"Aesop.unindexPredicate?",
"Lean.Meta.instHashableOrigin",
... | true |
_private.Lean.Elab.PreDefinition.TerminationMeasure.0.Lean.Elab.TerminationMeasure.structuralArg._sparseCasesOn_1 | Lean.Elab.PreDefinition.TerminationMeasure | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Set.definable_finset_sup | Mathlib.ModelTheory.Definability | [
"Eq.mpr",
"Set.Definable.union",
"Lattice.toSemilatticeSup",
"Finset.sup_insert",
"Set.Definable",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Set.definable_empty",
"congrArg",
"Finset",
"Classical.propDecidable",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"S... | true |
_private.Mathlib.RingTheory.Flat.Rank.0.PrimeSpectrum.rankAtStalk_pos_iff_comap_surjective._simp_1_3 | Mathlib.RingTheory.Flat.Rank | [
"Set.univ",
"Set.eq_univ_iff_forall",
"Membership.mem",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.CategoryTheory.Monoidal.Mon.0.CategoryTheory.Functor.FullyFaithful.isMonHom_preimage._simp_3 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.monObjObj",
"CategoryTheory.Functor.map",
"CategoryTheory.Functor.LaxMonoidal.μ",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.Functor.ob... | false |
Lean.Grind.Ring.OfSemiring.Q.ind | Init.Grind.Ring.Envelope | [
"Lean.Grind.Ring.OfSemiring.r",
"Quot.ind",
"Lean.Grind.Ring.OfSemiring.Q.mk",
"Lean.Grind.Semiring",
"Lean.Grind.Ring.OfSemiring.Q",
"Prod"
] | true |
CochainComplex.IsKProjective.homotopyZero_def | Mathlib.Algebra.Homology.HomotopyCategory.KProjective | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"CategoryTheory.Abelian... | true |
CategoryTheory.Limits.spanIsoMk._auto_3 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Parser.Command.GrindCnstr.notStrictValue.parenthesizer | Lean.Meta.Tactic.Grind.Parser | [
"Lean.Parser.optional.parenthesizer",
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Name.mkStr5",
"Lean.Parser.ident.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPr... | true |
Mathlib.Tactic.ITauto.applyProof | Mathlib.Tactic.ITauto | [
"Inhabited.default",
"Lean.NameMap",
"Lean.MVarId",
"Lean.Expr",
"Lean.Meta.MetaM",
"Unit",
"Mathlib.Tactic.ITauto.Proof",
"Lean.Meta.instInhabitedMetaM"
] | true |
String.contains_bool_eq | Init.Data.String.Lemmas.Pattern.Find.Pred | [
"String.toSlice",
"String.Slice.Pattern.CharPred.instToForwardSearcherForallCharBoolDefaultForwardSearcher",
"String.Slice.contains_bool_eq",
"congrArg",
"String",
"String.contains",
"String.Slice.Pattern.ToForwardSearcher.DefaultForwardSearcher.instIteratorLoopIdSearchStep",
"String.Slice",
"String... | true |
OrderDual.btw | Mathlib.Order.Circular | [
"Btw",
"Btw.btw",
"OrderDual",
"Btw.mk"
] | true |
Aesop.RuleApplication.mk | Aesop.RuleTac.Basic | [
"Lean.Meta.SavedState",
"Aesop.RuleApplication.mk",
"Aesop.Subgoal",
"Array",
"Aesop.RuleApplication",
"Aesop.Percent",
"Aesop.Script.LazyStep",
"Option"
] | true |
_private.Std.Sat.CNF.Basic.0.Std.Sat.CNF.VarMem_append._simp_1_2 | Std.Sat.CNF.Basic | [
"Array.instAppend",
"Array.instMembership",
"Membership.mem",
"Array.mem_append",
"Array",
"instHAppendOfAppend",
"propext",
"Or",
"Eq",
"HAppend.hAppend"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.get!_union_of_contains_eq_false_right._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
_private.Lean.Meta.Constructions.SparseCasesOn.0.Lean.Meta.mkSparseCasesOn._sparseCasesOn_1 | Lean.Meta.Constructions.SparseCasesOn | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
instCountableFreeGroup | Mathlib.SetTheory.Cardinal.Free | [
"_private.Mathlib.SetTheory.Cardinal.Free.0.instCountableFreeGroup._proof_1",
"Countable",
"FreeGroup"
] | true |
Lean.Parser.Tactic.tacticHave' | Init.Tactics | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.const",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | true |
OpenAddSubgroup.coe_toOpens | Mathlib.Topology.Algebra.OpenSubgroup | [
"TopologicalSpace.Opens",
"OpenAddSubgroup.toOpens",
"TopologicalSpace.Opens.instSetLike",
"TopologicalSpace",
"OpenAddSubgroup",
"AddGroup",
"SetLike.coe",
"OpenAddSubgroup.instSetLike",
"Eq",
"rfl",
"Set"
] | true |
Lean.JsonRpc.MessageKind.notification.elim | Lean.Data.JsonRpc | [
"PULift.up",
"Lean.JsonRpc.MessageKind.ctorIdx",
"Lean.JsonRpc.MessageKind",
"Nat",
"Lean.JsonRpc.MessageKind.notification",
"Lean.JsonRpc.MessageKind.ctorElim",
"Eq.symm",
"Eq"
] | false |
NonUnitalSubsemiringClass.toNonUnitalCommSemiring._proof_2 | Mathlib.RingTheory.NonUnitalSubsemiring.Defs | [
"SetLike",
"HMul.hMul",
"NonUnitalCommSemiring.toCommSemigroup",
"CommSemigroup.mul_comm",
"Membership.mem",
"NonUnitalNonAssocSemiring.toMul",
"Subtype",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"Subtype.coe_injective",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"Distrib.toMul",
"Fu... | false |
_private.Mathlib.CategoryTheory.Sites.Sieves.0.CategoryTheory.Presieve.functorPushforward_monotone.match_1_1 | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"Exists",
"CategoryTheory.Functor.map",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryS... | false |
JoinedIn.mono | Mathlib.Topology.Connected.PathConnected | [
"Real",
"JoinedIn",
"Membership.mem",
"Set.Elem",
"JoinedIn.somePath",
"HasSubset.Subset",
"TopologicalSpace",
"Path.instFunLike",
"Path",
"JoinedIn.somePath_mem",
"Exists.intro",
"Set.instMembership",
"DFunLike.coe",
"unitInterval",
"Set.instHasSubset",
"Set"
] | true |
Lean.Lsp.LeanFileProgressProcessingInfo.mk.inj | Lean.Data.Lsp.Extra | [
"Lean.Lsp.LeanFileProgressProcessingInfo.mk.noConfusion",
"Lean.Lsp.LeanFileProgressKind",
"Lean.Lsp.LeanFileProgressProcessingInfo",
"And",
"And.intro",
"Lean.Lsp.Range",
"Lean.Lsp.LeanFileProgressProcessingInfo.mk",
"Eq"
] | true |
Std.Tactic.BVDecide.BVExpr.bitblast.mkFullAdderCarry._proof_1 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Add | [
"Std.Sat.AIG.Ref.cast",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.BinaryInput",
"Std.Sat.AIG.BinaryInput.mk",
"Std.Sat.AIG.Entrypoint.ref",
"LE.le",
"instLENat",
"Std.Sat.AIG.Ref",
"Std.Sat.AIG.mkAndCached",
"Std.Sat.AIG",
"Nat",
"Std.Sat.AIG.mkXorCached",
"Hashable",
... | false |
_private.Mathlib.Analysis.InnerProductSpace.Projection.FiniteDimensional.0._aux_Mathlib_Analysis_InnerProductSpace_Projection_FiniteDimensional___unexpand_Inner_inner_1 | Mathlib.Analysis.InnerProductSpace.Projection.FiniteDimensional | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.matchesIdent",
"Lean.Name.mkNum",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
"EStateM... | false |
SimpleGraph.Subgraph.instInfSet._proof_2 | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"SimpleGraph.Subgraph.edge_vert",
"SimpleGraph.Subgraph",
"Set.iInter",
"SimpleGraph.Adj",
"Membership.mem",
"SimpleGraph",
"And",
"And.left",
"Set.mem_iInter₂_of_mem",
"SimpleGraph.Subgraph.Adj",
"Set.instMembership",
"SimpleGraph.Subgraph.verts",
"Set"
] | false |
Condensed.lanPresheafNatIso | Mathlib.Condensed.Discrete.Colimit | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Functor.mapCocone",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Condensed.lanPresheafIso",
"Profinite.diagram",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.co... | true |
_private.Mathlib.Algebra.Homology.CochainComplexOpposite.0.CochainComplex.homotopyUnop._proof_4 | Mathlib.Algebra.Homology.CochainComplexOpposite | [
"Eq.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"neg_inj._simp_1",
"AddGroupWithOne.toAddMonoidWithOne",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Int",
"NonUnitalNonAssocRing.toHasDistribNeg",
"AddMonoidWithOne.toOne",
"Int.instCommRi... | false |
LieModule.genWeightSpace_zero_normalizer_eq_self | Mathlib.Algebra.Lie.Weights.Basic | [
"LieHom",
"Module.End.instRing",
"LieSubmodule.instSetLike",
"Eq.mpr",
"CommRing",
"instHSMul",
"Module.End.instMonoid",
"instSMulOfMul",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"sub_zero",
"AddCommGroup.toAddCommMonoid",
"pow_succ",
"LinearMap.addCommGro... | true |
CategoryTheory.Localization.liftNatIso_hom | Mathlib.CategoryTheory.Localization.Predicate | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Localization.liftNatIso",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Localization.liftNatTrans",
"CategoryTheory.Iso",
"CategoryTheory.Functor.IsLocalization",... | true |
isZGroup_iff_exists_mulEquiv | Mathlib.GroupTheory.SpecificGroups.ZGroup | [
"SemidirectProduct.mulEquivSubgroup",
"Subgroup.instFiniteSubtypeMem",
"isCyclic_of_surjective",
"IsZGroup.instOfIsCyclic",
"Nat.Coprime",
"instNormalCommutator",
"MonoidHom.range",
"Eq.ge",
"MulEquiv.instEquivLike",
"IsZGroup.coprime_commutator_index",
"MonoidHom",
"Monoid.toMulOneClass",
"... | true |
Finset.noncommProd_mulSingle | Mathlib.Data.Finset.NoncommProd | [
"one_pow",
"Finset.mem_univ",
"Monoid",
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"MonoidHom.instFunLike",
"HMul.hMul",
"Finset.univ",
"and_true",
"Function.onFun",
"MonoidHom",
"Pi.mulSingle_eq_same",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Commute",
"Monoid... | true |
Topology.IsQuotientMap.trivializationOfSMulDisjoint.match_7 | Mathlib.Topology.Covering.Quotient | [
"Membership.mem",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.pi.coconeOfCoconeCompEval | Mathlib.CategoryTheory.Limits.Pi | [
"CategoryTheory.pi.coconeOfCoconeCompEval._proof_1",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Pi.eval",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.Cocone.mk",
"Cat... | true |
CategoryTheory.ShortComplex.ShortExact.fIsKernel._proof_1 | Mathlib.Algebra.Homology.ShortComplex.ShortExact | [
"CategoryTheory.Mono",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.ShortExact.mono_f",
"CategoryTheory.Preadditive",
"CategoryTheory.Preadditive.preadditiveHasZeroMorphisms",
"CategoryTheory.ShortComplex.ShortExact",
"CategoryTheory.ShortComplex.f",
... | false |
Nat.getElem?_toArray_rio | Init.Data.Range.Polymorphic.NatLemmas | [
"Std.Rco.toArray",
"congrArg",
"Nat.getElem?_toArray_rco",
"HSub.hSub",
"Std.Rio.mk",
"Option.some",
"Nat.toArray_rio_eq_toArray_rco",
"Std.PRange.instIsAlwaysFiniteNat_1",
"instSubNat",
"instOfNatNat",
"Array",
"Option.none",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Std.PRange.instUpward... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_210 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_209",
"instBEqOfDecidableEq",
"List.idxOfNth",
"GetElem.getElem",
"List.getElem_filter_eq_getElem_getElem_findIdxs._proof_5",
"List.f... | false |
Batteries.PairingHeapImp.Heap.foldTreeM._f | Batteries.Data.PairingHeap | [
"Pure.pure",
"Batteries.PairingHeapImp.Heap.below",
"Monad.toApplicative",
"Batteries.PairingHeapImp.Heap.size.match_1",
"Applicative.toPure",
"Unit",
"Batteries.PairingHeapImp.Heap",
"Monad.toBind",
"Batteries.PairingHeapImp.Heap.nil",
"Bind.bind",
"Monad",
"Batteries.PairingHeapImp.Heap.node... | false |
ENat.card_prod | Mathlib.SetTheory.Cardinal.Finite | [
"HMul.hMul",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
"Cardinal.toENat_lift",
"Cardinal.lift",
"OrderRingHom.instFunLike",
"Cardinal.mk",
"Cardinal.instMul",
"instPreorderENat",
"OrderRingHom",
"instDistribOfSemiring",
"OrderR... | true |
_private.Mathlib.Data.Set.Image.0.Set.disjoint_image_left._simp_1_1 | Mathlib.Data.Set.Image | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Set.instInter",
"Set.instDistribLattice",
"Set.disjoint_iff_inter_eq_empty",
"Inter.inter",
"Set.instBoundedOrder",
"BoundedOrder.toOrderBot",
"propext",
"Set.instEmptyCollec... | false |
_private.Mathlib.Tactic.GCongr.Core.0.Lean.MVarId.gcongr.match_1 | Mathlib.Tactic.GCongr.Core | [
"DoResultPR",
"DoResultPR.return",
"PUnit",
"Bool",
"DoResultPR.casesOn",
"DoResultPR.pure"
] | false |
ModuleCat.forget₂AddCommGroup_reflectsLimitOfSize | Mathlib.Algebra.Category.ModuleCat.Limits | [
"CategoryTheory.Limits.ReflectsLimitsOfSize",
"CategoryTheory.Limits.ReflectsLimitsOfSize.mk",
"AddCommGrpCat.instCategory",
"ModuleCat",
"ModuleCat.forget₂AddCommGroup_reflectsLimitOfShape",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddCommGroup.toAddGrou... | true |
ENNReal.instCommSemiring._proof_16 | Mathlib.Data.ENNReal.Basic | [
"NNReal.instCommSemiring",
"Mul.mk",
"Semigroup.toMul",
"HMul.hMul",
"LinearOrder.toDecidableEq",
"AddCommMonoidWithOne.toAddCommMonoid",
"ENNReal.instCommSemiring._proof_8",
"WithTop.instCommSemiring._proof_1",
"ENNReal.instCommSemiring._proof_13",
"ENNReal.instCommSemiring._aux_6",
"ENNReal.in... | false |
smul_left_cancel_iff._simp_2 | Mathlib.Algebra.Group.Action.Basic | [
"instHSMul",
"Group",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulAction",
"propext",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
"smul_left_cancel_iff"
] | false |
Matrix.vecCons_inj._simp_1 | Mathlib.Data.Fin.VecNotation | [
"Matrix.vecCons_inj",
"And",
"Nat",
"propext",
"Fin",
"Nat.succ",
"Eq",
"Matrix.vecCons"
] | false |
LinearMap.ofAEval._proof_6 | Mathlib.Algebra.Polynomial.Module.AEval | [
"_private.Mathlib.Algebra.Polynomial.Module.AEval.0.LinearMap.ofAEval._simp_4",
"Semigroup",
"Eq.mpr",
"Polynomial.C",
"LinearEquiv.symm",
"Semigroup.toMul",
"instHSMul",
"HMul.hMul",
"Module.AEval.of",
"Monoid.toMulOneClass",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring... | false |
Rat.sub | Init.Data.Rat.Basic | [
"Nat.gcd",
"Rat.num",
"instHDiv",
"HMul.hMul",
"Rat.add._proof_1",
"Rat.sub._proof_2",
"Rat",
"Nat.instDecidableCoprime",
"HSub.hSub",
"Rat.normalize.den_nz",
"Rat.den",
"Rat.normalize.dvd_num",
"HDiv.hDiv",
"Ne",
"instMulNat",
"instOfNatNat",
"Int",
"Rat.maybeNormalize",
"Nat.ca... | true |
HopfAlgCat.MonoidalCategory.inducingFunctorData._proof_6 | Mathlib.Algebra.Category.HopfAlgCat.Monoidal | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"BialgCat.instBialgebra",
"BialgCat.category",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"Semiring.toModule",
"HopfAlgebraStruct.toBialgebra",
"CategoryTheory.MonoidalCategory.tensorIso",
"BialgCat",
"Ring.toNonAssocRing",
"LinearMap.ext",
"Bialgebra... | false |
CategoryTheory.Limits.natTransIntoForgetCompFiberwiseColimit._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.Grothendieck | [
"CategoryTheory.Cat.category",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.fiber",
"CategoryTheory.Grothendieck.base",
"CategoryTheory.Grothendieck.ι",
"CategoryTheory.eqToHom_naturality._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Category... | false |
CategoryTheory.BraidedCategory.Hexagon.functor₁₃₂ | Mathlib.CategoryTheory.Monoidal.Braided.Multifunctor | [
"CategoryTheory.Functor.flip₂₃",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.bifunctorComp₁₂",
"CategoryTheory.Category",
"CategoryTheory.MonoidalCategory.curriedTensor"
] | true |
jacobiTheta₂.eq_1 | Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"jacobiTheta₂_term",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"jacobiTheta₂",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Int",
"NormedCommRing.toNonUnitalNormedCommRing",
"NonUn... | true |
PeriodPair.mem_lattice | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | [
"Int.cast",
"Submodule",
"zsmul_eq_mul",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"Complex.commRing",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Complex.instNormedField",
"Membership.mem",
"Exists",
"Complex.instMul",
"Add... | true |
Std.Do._aux_Std_Do_PostCond___unexpand_Std_Do_PostCond_entails_1 | Std.Do.PostCond | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
DFinsupp.Lex.acc_zero | Mathlib.Data.DFinsupp.WellFounded | [
"False.elim",
"_private.Mathlib.Data.DFinsupp.WellFounded.0.DFinsupp.Lex.acc_zero.match_1_1",
"DFinsupp.instDFunLike",
"Acc",
"DFinsupp.instZero",
"Zero.toOfNat0",
"DFinsupp",
"OfNat.ofNat",
"DFinsupp.Lex",
"Eq",
"DFunLike.coe",
"Not",
"Acc.intro",
"Zero"
] | true |
Algebra.FormallySmooth.liftOfSurjective.eq_1 | Mathlib.RingTheory.Smooth.Basic | [
"CommRing",
"Algebra.FormallySmooth.lift._proof_1",
"Semiring.toModule",
"AlgEquiv.toAlgHom",
"Algebra.FormallySmooth.liftOfSurjective._proof_3",
"AlgEquiv.symm",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"RingHom",
"Algebra.FormallySmooth.liftOfSurjective._proof_2",
... | true |
Lean.Omega.IntList.dvd_gcd | Init.Omega.IntList | [
"Lean.Omega.IntList.gcd",
"Dvd.dvd",
"Nat.dvd_zero",
"Nat.dvd_zero._simp_1",
"Membership.mem",
"Eq.mp",
"id",
"instOfNatNat",
"List.rec",
"Int",
"Nat.cast",
"List.cons",
"Int.instDvd",
"_private.Init.Omega.IntList.0.Lean.Omega.IntList.dvd_gcd._simp_1_1",
"Nat.dvd_gcd",
"List",
"Nat.i... | true |
_private.Mathlib.MeasureTheory.Group.FundamentalDomain.0.MeasureTheory.termπ_3 | Mathlib.MeasureTheory.Group.FundamentalDomain | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
_private.Std.Data.DTreeMap.Internal.Balancing.0.Std.DTreeMap.Internal.Impl.balance!_eq_balanceₘ._proof_1_22 | Std.Data.DTreeMap.Internal.Balancing | [
"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'",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Std.DTreeMap.Internal.Impl.Balanced",
"Lean.Omega.Linear... | false |
NNReal.instLinearOrderedCommGroupWithZero._proof_1 | Mathlib.Data.NNReal.Defs | [
"CommMonoidWithZero.toCommMonoid",
"Semigroup.toMul",
"Real",
"PartialOrder.toPreorder",
"NNReal",
"Field.toSemifield",
"CommMonoid.toMonoid",
"CommMonoidWithZero.toZero",
"Monoid.toSemigroup",
"PosMulStrictMono",
"Nonneg.linearOrderedCommMonoidWithZero._proof_4",
"Semifield.toCommSemiring",
... | false |
RingHom.Etale.toAlgebra | Mathlib.RingTheory.RingHom.Etale | [
"CommRing",
"RingHom.Etale",
"CommSemiring.toSemiring",
"RingHom",
"Algebra.Etale",
"CommRing.toCommSemiring",
"Semiring.toNonAssocSemiring",
"RingHom.toAlgebra"
] | true |
Finset.prod_insert_of_eq_one_if_notMem | Mathlib.Algebra.BigOperators.Group.Finset.Basic | [
"MulOne.toOne",
"Monoid.toMulOneClass",
"Finset",
"Membership.mem",
"Insert.insert",
"Finset.instInsert",
"dite",
"Finset.prod",
"_private.Mathlib.Algebra.BigOperators.Group.Finset.Basic.0.Finset.prod_insert_of_eq_one_if_notMem._proof_1_2",
"MulOneClass.toMulOne",
"Finset.instSetLike",
"CommMo... | true |
BooleanSubalgebra.copy._proof_3 | Mathlib.Order.BooleanSubalgebra | [
"Sublattice",
"BooleanAlgebra",
"BooleanSubalgebra",
"BooleanSubalgebra.bot_mem'",
"Sublattice.carrier",
"Membership.mem",
"Eq.rec",
"Bot.bot",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanSubalgebra.copy._proof_1",
"BooleanSubalgebra.toSublattice",
"BooleanAlgebra.toBiheytingAlgebra",
"Se... | false |
codisjoint_bot._simp_1 | Mathlib.Order.Disjoint | [
"Codisjoint",
"codisjoint_bot",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Bot.bot",
"OrderTop.toTop",
"BoundedOrder.toOrderTop",
"BoundedOrder.toOrderBot",
"propext",
"Top.top",
"BoundedOrder",
"Eq"
] | false |
RCLike.inv_re | Mathlib.Analysis.RCLike.Basic | [
"RCLike.conj_re",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Norm.norm",
"Eq.mpr",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"AddMonoid.toAddSemigroup",
"Real.inst... | true |
MeasureTheory.Measure.AbsolutelyContinuous.add_left_iff | Mathlib.MeasureTheory.Measure.AbsolutelyContinuous | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MeasureTheory.Measure.AbsolutelyContinuous.smul_left",
"ENNReal.instModuleNNReal",
"NNReal.instCommSemiring",
"instHSMul",
"MeasureTheory.Measure",
"Semiring.toModule",
"IsScalarTower.right",
"ENNReal.instAddCommMonoid",
"congrArg",
"CommSe... | true |
Matrix.comp_diagonal_diagonal | Mathlib.Data.Matrix.Composition | [
"Matrix.comp",
"Eq.mpr",
"ne_or_eq",
"Equiv.instEquivLike",
"Matrix.zero_apply",
"instDecidableEqProd",
"congrArg",
"Matrix",
"Matrix.diagonal_apply_eq",
"id",
"Equiv",
"Prod.mk",
"Ne",
"ne_of_apply_ne",
"Prod.fst",
"Or.casesOn",
"Eq.ndrec",
"Zero.toOfNat0",
"Eq.refl",
"Or",
... | true |
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