name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
RestrictedProduct.homeoBot._proof_1 | Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace | [
"Function.LeftInverse",
"Filter.Eventually",
"Membership.mem",
"Bot.bot",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"Subtype.mk",
"Eq.refl",
"Set.instMembership",
"DFunLike.coe",
"Filter",
"Filter.instBot",
"Filter.eventually_bot",
"Set"
] | false |
IsScalarTower.invertibleAlgebraCoeNat._proof_1 | Mathlib.RingTheory.AlgebraTower | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"Algebra",
"AddZeroClass.toAddZero",
"Algebra.toModule",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.toAddMonoidWithO... | false |
_private.Mathlib.Analysis.SpecificLimits.FloorPow.0.sum_div_pow_sq_le_div_sq._simp_1_9 | Mathlib.Analysis.SpecificLimits.FloorPow | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
CategoryTheory.Limits.isColimitCoconeOfHasColimitCurryCompColim._proof_2 | Mathlib.CategoryTheory.Limits.Fubini | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.colim",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp"... | false |
IsMulFreimanHom.inv | Mathlib.Combinatorics.Additive.FreimanHom | [
"Eq.mpr",
"IsMulFreimanHom",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IsMulFreimanHom.mk",
"Multiset.map",
"IsMulFreimanHom.map_prod_eq_map_prod",
"congrArg",
"Multiset.prod",
"DivisionCommMonoid",
"Pi.instInv",
"Membership.mem",
"DivisionMonoid.toDivInvOneMon... | true |
_private.Mathlib.Algebra.Polynomial.Expand.0.Polynomial.contract_mul_expand._simp_1_2 | Mathlib.Algebra.Polynomial.Expand | [
"Finset",
"Membership.mem",
"HasSubset.Subset",
"Finset.instSetLike",
"Finset.subset_iff",
"propext",
"Finset.instHasSubset",
"Eq",
"SetLike.instMembership"
] | false |
_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.lt_omega0._simp_1_2 | Mathlib.SetTheory.Ordinal.Arithmetic | [
"Preorder.toLT",
"Ordinal.partialOrder",
"Cardinal",
"PartialOrder.toPreorder",
"Cardinal.ord",
"Ordinal.card",
"Cardinal.partialOrder",
"LT.lt",
"propext",
"Eq",
"Cardinal.lt_ord",
"Ordinal"
] | false |
_private.Init.Data.Format.Basic.0.Std.Format.SpaceResult.recOn | Init.Data.Format.Basic | [
"_private.Init.Data.Format.Basic.0.Std.Format.SpaceResult",
"_private.Init.Data.Format.Basic.0.Std.Format.SpaceResult.rec",
"_private.Init.Data.Format.Basic.0.Std.Format.SpaceResult.mk",
"Nat",
"Bool"
] | false |
CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans_map_f | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Coalgebra.mk",
"CategoryTheory.Endofunctor.Coalgebra.instCategory",
"CategoryTheory.Endofunctor.Coalgebra.str",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Endofunctor.Coalgebra.V",
"... | true |
CategoryTheory.Limits.PreservesColimit.rec | Mathlib.CategoryTheory.Limits.Preserves.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.mapCocone",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.IsColimit",
"Nonempty",
"CategoryTheory.Limits.PreservesColimit.mk",
"CategoryTheory.Limits.PreservesColimit",
"CategoryTheory.Category"
] | false |
CommRingCat.Colimits.Prequotient._sizeOf_inst | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CommRingCat",
"CommRingCat.Colimits.Prequotient._sizeOf_1",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.Prequotient",
"SizeOf.mk",
"SizeOf"
] | false |
Lean.Elab.Tactic.SimpKind.casesOn | Lean.Elab.Tactic.Simp | [
"Lean.Elab.Tactic.SimpKind.rec",
"Lean.Elab.Tactic.SimpKind.simp",
"Lean.Elab.Tactic.SimpKind.dsimp",
"Lean.Elab.Tactic.SimpKind.simpAll",
"Lean.Elab.Tactic.SimpKind"
] | false |
_private.Mathlib.Topology.MetricSpace.Thickening.0.Metric.eventually_notMem_thickening_of_infEDist_pos._simp_1_2 | Mathlib.Topology.MetricSpace.Thickening | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"not_lt",
"LT.lt",
"propext",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
PresheafOfModules.surjective_of_epi | Mathlib.Algebra.Category.ModuleCat.Presheaf.EpiMono | [
"Eq.mpr",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"RingCat.ring",
"ModuleCat.epi_iff_surjective... | true |
iInf_lt_top._simp_1 | Mathlib.Order.CompleteLattice.Basic | [
"Preorder.toLT",
"iInf",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toBoundedOrder",
"CompleteLattice.toCompleteSemilatticeInf",
"OrderTop.toTop",
"BoundedOrder.toOrderTop",
"LT.lt",
"propext",
"Compl... | false |
CategoryTheory.Limits.pushout_inl_inv_inr_of_right_isIso_assoc | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso | [
"CategoryTheory.Category.assoc",
"CategoryTheory.IsIso",
"CategoryTheory.Limits.pushout_inr_iso_of_left_iso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"congr",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.... | true |
SSet.oneTruncation₂._proof_2 | Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | [
"SSet.OneTruncation₂",
"CategoryTheory.ReflQuiv",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SSet.Truncated",
"id",
"CategoryTheory.ReflQuiv.of",
"instOfNatNat",
"LE.le",
"instLENat",
"SSet.OneTruncation₂.map",
"Nat",
"Category... | false |
Lean.Widget.instRpcEncodableInteractiveGoal.enc._@.Lean.Widget.InteractiveGoal.3114798910._hygCtx._hyg.1 | Lean.Widget.InteractiveGoal | [
"Pure.pure",
"Lean.SubExpr.instToJsonMVarId",
"Lean.Json",
"Lean.Widget.RpcEncodablePacket._@.Lean.Widget.InteractiveGoal.3114798910._hygCtx._hyg.1",
"Option.mapM",
"Lean.instFromJsonString",
"Lean.Server.WithRpcRef",
"Monad.toApplicative",
"String",
"Lean.instToJsonBool",
"Lean.Widget.SubexprIn... | false |
_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.infer.getParamInfo.match_5 | Lean.Compiler.LCNF.InferBorrow | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Array",
"Option.none",
"Unit",
"Lean.Compiler.LCNF.Purity.impure",
"Lean.Compiler.LCNF.Param",
"Option"
] | false |
MulHomClass | Mathlib.Algebra.Group.Hom.Defs | [
"outParam",
"Mul",
"MulHomClass.mk",
"FunLike"
] | true |
Homeomorph.compStarAlgEquiv'._proof_10 | Mathlib.Topology.ContinuousMap.Star | [
"Algebra.to_smulCommClass",
"instHSMul",
"SemilinearMapClass.toMulActionSemiHomClass",
"NonUnitalAlgHomClass.instLinearMapClass",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Homeomorph.compStarAlgEquiv'._proof_1",
"IsTopologicalSemiring",
"ContinuousStar",
"ContinuousMap",
"Add... | false |
TopologicalSpace.OpenNhdsOf.mk.sizeOf_spec | Mathlib.Topology.Sets.Opens | [
"instSizeOfDefault",
"TopologicalSpace.OpenNhdsOf",
"TopologicalSpace.Opens",
"Membership.mem",
"TopologicalSpace.OpenNhdsOf.mk",
"TopologicalSpace.OpenNhdsOf._sizeOf_inst",
"instOfNatNat",
"TopologicalSpace.Opens.carrier",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"Nat",
"TopologicalSpac... | true |
Std.HashSet.Raw.contains_empty | Std.Data.HashSet.RawLemmas | [
"Std.HashMap.Raw.contains_empty",
"Std.HashSet.Raw.contains",
"Unit",
"Bool",
"Hashable",
"EmptyCollection.emptyCollection",
"Bool.false",
"BEq",
"Eq",
"Std.HashSet.Raw.instEmptyCollection",
"Std.HashSet.Raw"
] | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.add_bmod_eq_add_bmod_left._simp_1_1 | Init.Data.Int.DivMod.Lemmas | [
"Int",
"instHAdd",
"Int.bmod_add_cancel_left",
"HAdd.hAdd",
"Int.bmod",
"Nat",
"propext",
"Int.instAdd",
"Eq"
] | false |
Lean.Parser.Term.ensureTypeOf | Lean.Parser.Term | [
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"Lean.Parser.strLit",
"instHAndThenOfAndThen",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.ppSpace",
"Lean.Parser.withAntiquot",
"Bool.true",
"Unit",
"Nat",
"Lean.Parser.withCache",
"Lean.Parser.maxPrec",
"OfNat... | true |
_private.Mathlib.Geometry.Manifold.Algebra.Monoid.0.contMDiffWithinAt_finset_prod._simp_1_1 | Mathlib.Geometry.Manifold.Algebra.Monoid | [
"Finset.prod_apply",
"Finset",
"Pi.commMonoid",
"Finset.prod",
"Eq.symm",
"Eq",
"CommMonoid"
] | false |
Int.tdiv_nonpos_of_nonneg_of_nonpos | Init.Data.Int.DivMod.Lemmas | [
"Int.tdiv_neg",
"Int.nonpos_of_neg_nonneg",
"Eq.rec",
"Int.instNegInt",
"Int.neg_nonneg_of_nonpos",
"Int",
"LE.le",
"Int.tdiv",
"Int.tdiv_nonneg",
"instOfNat",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"Int.instLEInt"
] | true |
ContinuousNeg.rec | Mathlib.Topology.Algebra.Group.Defs | [
"ContinuousNeg.mk",
"Continuous",
"ContinuousNeg",
"TopologicalSpace",
"Neg",
"Neg.neg"
] | false |
AlgebraicGeometry.Scheme.instAddCommGroupEllAdicCohomology._proof_19 | Mathlib.AlgebraicGeometry.Sites.ElladicCohomology | [
"CategoryTheory.sheafCompose",
"AlgebraicGeometry.Scheme.instAddCommGroupEllAdicCohomology._aux_4",
"AddCommGrpCat.FilteredColimits.forget_preservesFilteredColimits",
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"AddCommGrpCat.hasLimit",
"Nat.Prime",
"AlgebraicGeometry.... | false |
_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeInductiveDecl.mk.noConfusion | Lean.Elab.MutualInductive | [
"Lean.Expr",
"id",
"Int",
"Array",
"Lean.Declaration",
"Lean.Elab.Command.PreElabHeaderResult",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeInductiveDecl",
"Eq",
"_private.Lean.Elab.MutualInductive.0.Lean.Elab.Command.FinalizeInductiveDecl.noConfusion",
"_private.Lean.Elab.Mutu... | false |
AlgebraicGeometry.Scheme.pretopology.congr_simp | Mathlib.AlgebraicGeometry.Sites.Pretopology | [
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.Pullback.instHasPullbacks",
"Eq.rec",
"CategoryTheory.MorphismProperty.IsStableUnderBaseChange",
"CategoryTheory.Pretopology",
"AlgebraicGeometry.Scheme.pretopology",
"Eq.ndrec",
"Eq.refl",
"CategoryTheory.Cat... | true |
CFC.rpow_mul_rpow_neg | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"Eq.mpr",
"add_neg_cancel",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"HMul.hMul",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.instZero",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialO... | true |
_private.Batteries.Data.RBMap.WF.0.Batteries.RBNode.Ordered.append.match_1_9 | Batteries.Data.RBMap.WF | [
"Batteries.RBNode",
"Ordering",
"Batteries.RBNode.cmpLT",
"And.casesOn",
"And",
"Batteries.RBColor.red",
"And.intro",
"Batteries.RBNode.All",
"Batteries.RBNode.node",
"Batteries.RBNode.Ordered"
] | false |
HasProd.congr_cofinite₀ | Mathlib.Topology.Algebra.InfiniteSum.Group | [
"CommMonoidWithZero.toCommMonoid",
"Iff.mpr",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"Trans.trans",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"DivisionCommMonoid.toDivisionMonoid",
"CommMonoid.toCommSe... | true |
_private.Mathlib.Data.Set.Subsingleton.0.Set.nontrivial_iff_pair_subset.match_1_1 | Mathlib.Data.Set.Subsingleton | [
"Exists",
"Set.instSingletonSet",
"Insert.insert",
"HasSubset.Subset",
"Ne",
"And.casesOn",
"And",
"Exists.casesOn",
"Set.instInsert",
"And.intro",
"Exists.intro",
"Singleton.singleton",
"Set.instHasSubset",
"Set"
] | false |
_private.Mathlib.Topology.Homotopy.LocallyContractible.0.instStronglyLocallyContractibleSpaceProd.match_9 | Mathlib.Topology.Homotopy.LocallyContractible | [
"Filter.instMembership",
"_private.Mathlib.Topology.Homotopy.LocallyContractible.0.instStronglyLocallyContractibleSpaceProd.match_1",
"Membership.mem",
"nhds",
"Set.Elem",
"ContractibleSpace",
"Prod.mk",
"And.casesOn",
"TopologicalSpace",
"And",
"_private.Mathlib.Topology.Homotopy.LocallyContrac... | false |
Finite.Set.finite_range | Mathlib.Data.Set.Finite.Range | [
"Fintype.ofFinite",
"instFinitePLift",
"Finite",
"Classical.propDecidable",
"inferInstance",
"Set.Elem",
"PLift",
"Finite.of_fintype",
"Set.fintypeRange",
"Set.range",
"Eq"
] | true |
Submodule.smithNormalFormOfLE._proof_8 | Mathlib.LinearAlgebra.FreeModule.PID | [
"Submodule",
"IsDomain",
"CommRing",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Fin.castLE",
"Submodule.addCommMonoid",
"Finite",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup... | false |
CategoryTheory.Limits.ProductsFromFiniteCofiltered.isLimitFiniteSubproductsCone | Mathlib.CategoryTheory.Limits.Constructions.Filtered | [
"CategoryTheory.Limits.HasProduct",
"Opposite",
"CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj",
"CategoryTheory.Limits.HasLimitsOfShape",
"Finset",
"CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso",
"PartialOrder.toPreorder",
"CategoryTheory.Discrete.functor",
"CategoryThe... | true |
BoxIntegral.unitPartition.mem_prepartition_iff | Mathlib.Analysis.BoxIntegral.UnitPartition | [
"BoxIntegral.unitPartition.prepartition._proof_5",
"Eq.mpr",
"Nat.instMulZeroClass",
"Real",
"BoxIntegral.TaggedPrepartition.mk",
"BoxIntegral.Prepartition",
"Finset.mem_image",
"congrArg",
"Finset",
"Iff.rfl",
"BoxIntegral.unitPartition.tag",
"BoxIntegral.TaggedPrepartition.mem_mk",
"BoxInt... | true |
inner_conj_symm | Mathlib.Analysis.InnerProductSpace.Basic | [
"SeminormedAddCommGroup",
"Inner.inner",
"CommSemiring.toSemiring",
"RingHom",
"NormedField.toField",
"Field.toSemifield",
"RCLike.toDenselyNormedField",
"RCLike",
"RingHom.instFunLike",
"InnerProductSpace.toInner",
"Semifield.toCommSemiring",
"starRingEnd",
"DenselyNormedField.toNormedField... | true |
Submonoid.isLocalizationMap_of_group | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"exists_const._simp_1",
"Membership.mem",
"Exists",
"Group.isUnit",
"MulOne.toMul",
"Subtype",
"HDiv.hDiv",
"Prod.mk",
"CommGroup",
"One.instNonempty",
"Prod.fst",
"Subtype.mk",
"Group.toDivInvMonoid",
"Submonoid.IsLocali... | true |
Multiset.map_univ_coe | Mathlib.Data.Multiset.Fintype | [
"Finset.univ",
"Multiset.map",
"congrArg",
"Multiset.coeEmbedding",
"Finset",
"Multiset.fintypeCoe",
"Finset.map",
"Function.comp",
"Membership.mem",
"Multiset.count",
"Multiset",
"Eq.mp",
"Prod.mk",
"Sigma.fst",
"Multiset.toEnumFinset",
"Multiset.map_univ_coeEmbedding",
"Finset.val"... | true |
Quotient.hrecOn | Init.Core | [
"Setoid",
"Quotient.mk",
"Quotient",
"HasEquiv.Equiv",
"instHasEquivOfSetoid",
"HEq",
"Quot.hrecOn",
"Setoid.r"
] | true |
Mathlib.Tactic.BicategoryLike.Mor₁.tgt._unsafe_rec | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.Mor₁.tgt._unsafe_rec",
"_private.Mathlib.Tactic.CategoryTheory.Coherence.Datatypes.0.Mathlib.Tactic.BicategoryLike.Mor₁.e.match_1",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.Obj",
"Mathlib.Tactic.BicategoryLike.Atom₁",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"Mathlib.Tacti... | false |
SSet.Truncated.HomotopyCategory.BinaryProduct.functorCompInverseIso_hom_app | Mathlib.AlgebraicTopology.SimplicialSet.HoFunctorMonoidal | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"SSet.Truncated.HomotopyCategory.BinaryProduct.inverse",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SSet.Truncat... | true |
Lean.Compiler.LCNF.MonadCodeBind.rec | Lean.Compiler.LCNF.Bind | [
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Code",
"Lean.Compiler.LCNF.MonadCodeBind.mk",
"Lean.Compiler.LCNF.MonadCodeBind"
] | false |
Nat.nth_apply_eq_orderIsoOfNat | Mathlib.Data.Nat.Nth | [
"Eq.mpr",
"congrArg",
"setOf",
"Nat.nth._proof_1",
"Classical.propDecidable",
"Set.Finite",
"Nat.instAntisymmLe",
"Membership.mem",
"List.getD",
"Set.Elem",
"id",
"Nat.Subtype.orderIsoOfNat",
"OrderIso",
"instOfNatNat",
"LE.le",
"Nat.nth.eq_1",
"instLENat",
"dif_neg",
"instIsTran... | true |
_private.Mathlib.Data.Set.Function.0.Set.bijOn_singleton._simp_1_2 | Mathlib.Data.Set.Function | [
"eq_comm",
"propext",
"Eq"
] | false |
Array.mkSlice_roi_eq_mkSlice_roo | Init.Data.Slice.Array.Lemmas | [
"Std.Rci.mk",
"Std.Rco.Sliceable.mkSlice",
"Subarray",
"Array.mkSlice_rci_eq_mkSlice_rco",
"congrArg",
"instSliceableArrayNatSubarray_1",
"instSliceableArrayNatSubarray_4",
"instOfNatNat",
"Std.Roi.mk",
"instSliceableArrayNatSubarray_2",
"Array",
"instHAdd",
"Std.Rci.Sliceable.mkSlice",
"H... | true |
SimplicialObject.Split.Hom.mk.injEq | Mathlib.AlgebraicTopology.SimplicialObject.Split | [
"SimplicialObject.Split.Hom.mk",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"SimplicialObject.Splitting.ι",
"SimplicialObject.Split.X",
"Quiver.Hom",
"Eq.propIntro",
"CategoryTheory.Functor.category",
"Lean.injEq_helper",
"SimplicialObject.Splitting.N",
"SimplicialObject.Split",
"au... | true |
ProjectiveSpectrum | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology | [
"SetLike",
"CommRing",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Nat.instAddMonoid",
"AddSubmonoidClass",
"CommRing.toCommSemiring",
"GradedRing",
"Nat",
"instDecidableEqNat",
"AddMonoidWithOne.toAddMonoid",
"CommRing.toRing",
"Ring.toAdd... | true |
mdifferentiableAt_add_left | Mathlib.Geometry.Manifold.Algebra.Monoid | [
"WithTop.charZero",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ContMDiffAt.mdifferentiableAt",
"NormedSpace",
"CommSemiring.toSemiring",
"contMDiffAt_add_left",
"NeZero.charZero_one",
"MDifferentiableAt",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"WithTop.addMonoidWithOne",
"AddMonoidW... | true |
Ordnode.merge_nil_right | Mathlib.Data.Ordmap.Invariants | [
"Ordnode",
"Ordnode.nil",
"Ordnode.merge",
"Eq",
"rfl"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKeyD_insert_self._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
Fin.instMax_mathlib._proof_1 | Mathlib.Order.Fin.Basic | [
"Fin.isLt",
"Fin.val",
"LinearOrder.toMax",
"Max.max",
"Nat",
"LT.lt",
"instLTNat",
"max_rec'",
"Fin",
"Nat.instLinearOrder"
] | false |
AlgHom.FinitePresentation.of_finiteType | Mathlib.RingTheory.FinitePresentation | [
"AlgHom.FinitePresentation",
"AlgHom.FiniteType",
"CommRing",
"CommSemiring.toSemiring",
"AlgHom",
"Algebra",
"RingHom.FinitePresentation.of_finiteType",
"IsNoetherianRing",
"CommRing.toCommSemiring",
"Iff",
"AlgHom.toRingHom"
] | true |
MeasureTheory.measure_preimage_add_right | Mathlib.MeasureTheory.Group.Measure | [
"MeasurableEquiv.instEquivLike",
"Eq.mpr",
"Trans.trans",
"MeasureTheory.Measure",
"MeasurableEquiv.map_apply",
"congrArg",
"AddMonoid.toAddZeroClass",
"MeasureTheory.map_add_right_eq_self",
"AddZeroClass.toAddZero",
"id",
"MeasurableEquiv.addRight",
"MeasurableAdd",
"instTransEq",
"Measur... | true |
LinearMap.IsPerfPair.restrictScalars_of_field | Mathlib.LinearAlgebra.PerfectPairing.Restrict | [
"LinearMap.IsPerfPair.restrict",
"LinearMap.restrictScalarsRange₂",
"Eq.mpr",
"LinearMap.range_comp_of_range_eq_top",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"SetLike.mem_coe._simp_1",
"IsScalarTower.to_smulCommClass'",
"RingHomSurjective.ids",
"Submodule.module._proof_1",
"Linea... | true |
Std.ExtTreeMap.maxKey.congr_simp | Std.Data.ExtTreeMap.Lemmas | [
"Ordering",
"Eq.rec",
"Ne",
"Std.TransCmp",
"Std.ExtTreeMap",
"Std.ExtTreeMap.maxKey",
"Eq.ndrec",
"Eq.refl",
"EmptyCollection.emptyCollection",
"Std.ExtTreeMap.instEmptyCollection",
"Eq"
] | true |
_private.Lean.Meta.Basic.0.Lean.Meta.withNewLocalInstancesImpAux | Lean.Meta.Basic | [
"_private.Lean.Meta.Basic.0.Lean.Meta.withNewLocalInstancesImp",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"Lean.Meta.mapMetaM",
"MonadControlT",
"Nat",
"Monad"
] | true |
Lean.Meta.Sym.ExprPtr.mk.inj | Lean.Meta.Sym.ExprPtr | [
"Lean.Meta.Sym.ExprPtr.mk",
"Lean.Expr",
"Lean.Meta.Sym.ExprPtr",
"Eq",
"Lean.Meta.Sym.ExprPtr.mk.noConfusion"
] | true |
RestrictedProduct.instZSMul._proof_1 | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"SetLike",
"instHSMul",
"zsmul_mem",
"Filter.Eventually",
"SubNegMonoid",
"Membership.mem",
"Int",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"Filter.Eventually.mono",
"SetLike.coe",
"HSMul.hSMul",
"AddSubgroupClass",
"Subtype.val",
"Set.instMembership",
"DFunLike.coe",
"... | false |
ComplexShape.down' | Mathlib.Algebra.Homology.ComplexShape | [
"IsRightCancelAdd",
"ComplexShape.down'._proof_1",
"ComplexShape",
"instHAdd",
"HAdd.hAdd",
"ComplexShape.down'._proof_2",
"Eq",
"ComplexShape.mk",
"Add"
] | true |
CategoryTheory.Limits.pushoutCoconeOfLeftIso_ι_app_none | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Iso | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.pushoutCoconeOfLeftIso",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.PushoutCocone.condition_zero",
"Categ... | true |
LinearMap.lTensor_ker_subtype_tensorKerEquiv_symm | Mathlib.RingTheory.Flat.Equalizer | [
"Submodule",
"IsScalarTower.to_smulCommClass'",
"LinearEquiv.symm",
"CommRing",
"_private.Mathlib.RingTheory.Flat.Equalizer.0.LinearMap.lTensor_ker_subtype_tensorKerInv",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"Submodule.addCom... | true |
MulSemiringActionHomClass.toMulSemiringActionHom._proof_6 | Mathlib.GroupTheory.GroupAction.Hom | [
"Monoid",
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"NonAssocSemiring.toMulZeroOneClass",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",
"OneHom.toFun",
"MulSemiringActionHomClass.toMulSemiringActionHom._proof_1",
"RingHomClass.toRingHom",
"OneHom.... | false |
String.Pos.Raw.byteIdx_unoffsetBy | Init.Data.String.PosRaw | [
"String.Pos.Raw.unoffsetBy",
"HSub.hSub",
"instSubNat",
"String.Pos.Raw",
"instHSub",
"Nat",
"String.Pos.Raw.byteIdx",
"Eq",
"rfl"
] | true |
Std.Sat.AIG.RefVec.fold.go_decl_eq._unary | Std.Sat.AIG.RefVecOperator.Fold | [
"Std.Sat.AIG.RefVec.get",
"Eq.mpr",
"Lean.Omega.LinearCombo.coordinate_eval_6",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"False",
"Decidable.casesOn",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"Std.Sat.AIG.BinaryInput",
"of_decide_eq_true",
"le_of_le_of_eq",... | false |
Lean.Parser.Command.eoi._regBuiltin.Lean.Parser.Command.eoi.formatter_3 | Lean.Parser.Command | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.Parser.Command.eoi.formatter",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
Ordinal.iSup_eq_lsub_or_succ_iSup_eq_lsub | Mathlib.SetTheory.Ordinal.Family | [
"Preorder.toLT",
"Ordinal.iSup_le_lsub",
"Order.succ",
"Ordinal.partialOrder",
"iSup",
"PartialOrder.toPreorder",
"LE.le.antisymm",
"Order.succ_le_of_lt",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Ordinal.instSuccOrder",
"eq_or_lt_of_le",
"Ordinal.instConditionallyCom... | true |
one_div_lt_of_neg | Mathlib.Algebra.Order.Field.Basic | [
"Eq.mpr",
"DivInvMonoid.toInv",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"IsStrictOrderedRing",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Field.t... | true |
Finset.ite_prod_one | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Decidable",
"Finset.prod",
"Finset.prod_const_one",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"True",
"eq_self",
"of_eq_true",
"One.toOfNat1",
"Eq.refl",
"ite_congr",
"OfNat.ofNat",
"Eq",
"CommMonoid",
"Not",
"... | true |
DifferentiableWithinAt.insert' | Mathlib.Analysis.Calculus.FDeriv.Basic | [
"Iff.mpr",
"AddCommGroup.toAddCommMonoid",
"NormedField.toField",
"AddCommGroup",
"Insert.insert",
"Field.toSemifield",
"TopologicalSpace",
"Semifield.toDivisionSemiring",
"Set.instInsert",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"differentiableWithinAt_insert",
"Differenti... | true |
SemidirectProduct.lift | Mathlib.GroupTheory.SemidirectProduct | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"SemidirectProduct.lift._proof_2",
"SemidirectProduct",
"OneHom.mk",
"MulAut.instGroup",
"SemidirectProduct.right",
"Group",
"MulAut",
"MulOne.toMul",
"MonoidHom.comp",
"DivInvMonoid.toMonoid",
"... | true |
List.getLast_replicate_succ | Mathlib.Data.List.Basic | [
"List.getLast",
"Eq.mpr",
"List.replicate",
"List.replicate_succ'",
"congrArg",
"List.getLast_append_singleton",
"List.ne_nil_of_length_eq_add_one",
"id",
"List.length_replicate",
"Ne",
"instOfNatNat",
"List.cons",
"instHAppendOfAppend",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Eq.... | true |
FiberBundleCore.localTriv_symm_apply | Mathlib.Topology.FiberBundle.Basic | [
"FiberBundleCore.indexAt",
"FiberBundleCore.Fiber",
"instTopologicalSpaceProd",
"Bundle.TotalSpace.mk",
"FiberBundleCore.toTopologicalSpace",
"FiberBundleCore.TotalSpace",
"OpenPartialHomeomorph.toFun'",
"FiberBundleCore.proj",
"Prod.fst",
"FiberBundleCore.localTriv",
"TopologicalSpace",
"Fibe... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.getD_insert_self._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 |
Finset.sum_range_tsub | Mathlib.Algebra.BigOperators.Group.Finset.Basic | [
"Eq.mpr",
"Nat.zero_le",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Monotone",
"HSub.hSub",
"AddLeftMono",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"id",
"OrderedSub",
"Nat.le_succ",
"instOfNatNat",
"tsub_eq_of_eq_add",
"LE.le",
"zero_add"... | true |
Set.Finite.exists_finset | Mathlib.Data.Set.Finite.Basic | [
"Finset",
"Set.Finite",
"Membership.mem",
"Exists",
"Set.Elem",
"Set.toFinset",
"Nonempty.intro",
"Iff",
"Fintype",
"Finset.instSetLike",
"Nonempty.casesOn",
"Exists.intro",
"Set.Finite.nonempty_fintype",
"Nonempty",
"Eq.refl",
"Set.mem_toFinset",
"Eq",
"Set.instMembership",
"Set... | true |
CategoryTheory.isPreconnected_op | Mathlib.CategoryTheory.IsConnected | [
"CategoryTheory.IsPreconnected",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.IsPreconnected.mk",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Functor.category",
"CategoryTheory.Discrete.instSubsingletonDiscreteH... | true |
CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.functorObj._proof_1 | Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Monoidal.tensorUnit_map",
"CategoryTheory.ComonObj",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.C... | false |
Module.Presentation.cokernel_relation | Mathlib.Algebra.Module.Presentation.Cokernel | [
"Submodule",
"RingHomSurjective.ids",
"Module.Presentation.toRelations",
"Module.Presentation",
"Ring.toNonAssocRing",
"Submodule.Quotient.addCommGroup",
"AddCommGroup.toAddCommMonoid",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Submodule.hasQuotient",
"Module.Presentation.cokernelRelations.matc... | true |
SubAddAction.SMulMemClass.subtype._proof_1 | Mathlib.GroupTheory.GroupAction.SubMulAction | [
"SetLike",
"AddMonoid.toAddSemigroup",
"SubAddAction.SMulMemClass.toAddAction",
"Membership.mem",
"Subtype",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddSemigroupAction.toVAdd",
"AddMonoid",
"instHVAdd",
"VAddMemClass",
"Subtype.val",
"Eq",
"SetLike.instMembership",... | false |
Real.smoothTransition.one_of_one_le | Mathlib.Analysis.SpecialFunctions.SmoothTransition | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Real.instLE",
"Real",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"GroupWithZero.toDivInvMonoid",
"DivInvOneMonoid.toInvOneClass",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"div_eq_one_iff_eq",
"Real.in... | true |
_private.Mathlib.ModelTheory.Complexity.0.FirstOrder.Language.BoundedFormula.toPrenex.match_1.eq_2 | Mathlib.ModelTheory.Complexity | [
"FirstOrder.Language.BoundedFormula.imp",
"FirstOrder.Language.Term",
"Sum",
"instOfNatNat",
"FirstOrder.Language.BoundedFormula.equal",
"FirstOrder.Language.BoundedFormula.falsum",
"instHAdd",
"HAdd.hAdd",
"FirstOrder.Language.BoundedFormula.toPrenex.match_1",
"Nat",
"FirstOrder.Language.Relati... | true |
isStablyFiniteRing_iff | Mathlib.Data.Matrix.Mul | [
"Matrix.instMulOneOfFintypeOfDecidableEqOfAddCommMonoid",
"IsStablyFiniteRing",
"IsStablyFiniteRing.casesOn",
"Matrix",
"instDecidableEqFin",
"AddCommMonoid",
"Fin.fintype",
"IsDedekindFiniteMonoid",
"Iff",
"Nat",
"Iff.intro",
"IsStablyFiniteRing.mk",
"MulOne",
"Fin"
] | true |
CompareReals.instCommRingQ._proof_7 | Mathlib.Topology.UniformSpace.CompareReals | [
"CompareReals.Q",
"Add.mk",
"CompareReals.instCommRingQ._proof_3",
"AddSemigroup.mk",
"Rat.add_zero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"CompareReals.instCommRingQ._aux_4",
"Zero.mk",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"CompareReals.instCommRingQ._aux_1"
] | false |
TopCommRingCat.forgetToTopCatCommRing | Mathlib.Topology.Category.TopCommRingCat | [
"CommRing",
"Continuous",
"CommSemiring.toSemiring",
"TopCommRingCat.instConcreteCategorySubtypeRingHomαContinuousCoe",
"TopCat.instCategory",
"ContinuousMap",
"TopCommRingCat.instCategory",
"RingHom",
"Subtype",
"TopCommRingCat.isTopologicalSpace",
"TopCat.str",
"CategoryTheory.forget₂",
"C... | true |
_private.Mathlib.Topology.Compactness.CompactSystem.0.IsCompactSystem.insert_univ._proof_1_2 | Mathlib.Topology.Compactness.CompactSystem | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Lean.Grind.not_not",
"Lean.Grind.nestedProof",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Set.univ",
"Classical.byContradiction",
"Classical.propDecidable",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"Insert... | false |
_private.Std.Time.Time.PlainTime.0.Std.Time.instDecidableEqPlainTime.decEq.match_1 | Std.Time.Time.PlainTime | [
"Std.Time.PlainTime",
"Std.Time.PlainTime.mk",
"Std.Time.Second.Ordinal",
"Std.Time.Nanosecond.Ordinal",
"Bool.true",
"Std.Time.PlainTime.casesOn",
"Std.Time.Hour.Ordinal",
"Std.Time.Minute.Ordinal"
] | false |
instBialgebraCarrierUnopCommAlgCatOfMonObjOpposite._proof_10 | Mathlib.Algebra.Category.CommBialgCat | [
"instBialgebraCarrierUnopCommAlgCatOfMonObjOpposite._proof_8",
"AlgEquiv.instEquivLike",
"CommRing",
"Semiring.toModule",
"Opposite",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"Algebra.toModule",
"Algebra.id",
"CommAlgCat.commRing",
"AlgEquivClass.toAlgHomClass",
"Algebra.TensorProduct... | false |
_private.Lean.Meta.Tactic.Grind.CollectParams.0.Lean.Meta.Grind.collectParams.match_1 | Lean.Meta.Tactic.Grind.CollectParams | [
"Prod.mk",
"Array",
"Bool",
"Lean.Meta.Grind.TParam",
"Prod",
"Prod.casesOn"
] | false |
AddAction.zmultiplesQuotientStabilizerEquiv._proof_4 | Mathlib.Data.ZMod.QuotientGroup | [
"AddSubgroup.comap",
"Eq.mpr",
"instHSMul",
"Function.isPeriodicPt_minimalPeriod",
"AddSubgroup.zmultiples_le",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"AddSubgroup.mem_zmultiples",
"congrArg",
"AddAction.mem_stabilizer_iff",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
... | false |
UInt32.toNat_toBitVec | Init.Data.UInt.Lemmas | [
"UInt32.toBitVec",
"UInt32.toNat",
"instOfNatNat",
"BitVec.toNat",
"Nat",
"UInt32",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
Int32.toInt_toInt64 | Init.Data.SInt.Lemmas | [
"Int32.toBitVec",
"of_decide_eq_true",
"Int64.toInt",
"BitVec.toInt_signExtend_of_le",
"id",
"instOfNatNat",
"Int",
"LE.le",
"Int32.toInt",
"instLENat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"Int32.toInt64",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"Nat.decLe",
"Int32"
] | true |
CategoryTheory.ObjectProperty.full_ιOfLE | Mathlib.CategoryTheory.ObjectProperty.FullSubcategory | [
"CategoryTheory.ObjectProperty.ιOfLE",
"Prop.le",
"LE.le",
"CategoryTheory.Functor.FullyFaithful.full",
"Pi.hasLe",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty.FullSubcategory",
"CategoryTheory.ObjectProperty.FullSubcategory.category",
"CategoryTheory.ObjectProperty",
... | true |
String.Slice.Pattern.Model.SlicesFrom | Init.Data.String.Lemmas.Pattern.Split | [
"String.Slice",
"String.Slice.Pattern.Model.SlicesFrom.mk",
"String.Slice.Pos"
] | true |
NonemptyFinLinOrd.dualEquiv._proof_3 | Mathlib.Order.Category.NonemptyFinLinOrd | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"NonemptyFinLinOrd.dualEquiv._proof_1",
"Quiver.Hom",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"LinOrd.carrier",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CategoryTheo... | false |
Std.HashMap.getElem!_filter' | Std.Data.HashMap.Lemmas | [
"Std.HashMap.getElem!_filter",
"Iff.mpr",
"Std.HashMap.getKey",
"Std.HashMap.filter",
"Option.pfilter",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Option.some",
"LawfulBEq",
"Membership.mem",
"Option.get!",
"Option.pfilter_congr",
"Std.HashMap",
"Bool.true",
"Option.filter",
"Std.Ha... | true |
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