name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Sum.swap_rightInverse | Mathlib.Data.Sum.Basic | [
"Sum.swap",
"Sum.swap_swap",
"Sum",
"Function.RightInverse"
] | true |
_private.Init.Data.Iterators.Lemmas.Combinators.FilterMap.0.Std.Iter.forIn_filterMapWithPostcondition.match_1.eq_2 | Init.Data.Iterators.Lemmas.Combinators.FilterMap | [
"Unit.unit",
"Std.Iter.forIn_filterMapWithPostcondition.match_1",
"Option.some",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Option"
] | true |
ContinuousLinearEquiv.conjContinuousAlgEquiv_apply_apply | Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap | [
"ContinuousLinearEquiv.symm",
"instSMulOfMul",
"ContinuousLinearMap.semiring",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"C... | true |
semicontinuous_restrict_iff._simp_1 | Mathlib.Topology.Semicontinuity.Defs | [
"semicontinuous_restrict_iff",
"Membership.mem",
"Set.Elem",
"TopologicalSpace",
"propext",
"Semicontinuous",
"instTopologicalSpaceSubtype",
"Set.restrict",
"SemicontinuousOn",
"Eq",
"Set.instMembership",
"Set"
] | false |
FreeAddMonoid.toList.eq_1 | Mathlib.Algebra.FreeMonoid.Basic | [
"FreeAddMonoid.toList",
"Equiv",
"List",
"Eq.refl",
"Equiv.refl",
"Eq",
"FreeAddMonoid"
] | true |
Lean.Lsp.Command.recOn | Lean.Data.Lsp.Basic | [
"Lean.Json",
"String",
"Array",
"Lean.Lsp.Command.rec",
"Lean.Lsp.Command.mk",
"Lean.Lsp.Command",
"Option"
] | false |
AlgebraicGeometry.Scheme.Modules.Hom.isIso_iff_isIso_app | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"Eq.mpr",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme",
"CategoryTheory.IsIso",
"Opposite",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"Function.Surjective.forall",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
... | true |
_private.Mathlib.Tactic.Widget.Conv.0.Mathlib.Tactic.Conv.pathToStx.match_3 | Mathlib.Tactic.Widget.Conv | [
"Mathlib.Tactic.Conv.Path.type",
"Mathlib.Tactic.Conv.Path.casesOn",
"Mathlib.Tactic.Conv.Path.arg",
"Nat",
"Mathlib.Tactic.Conv.Path.fun",
"Mathlib.Tactic.Conv.Path.body",
"Bool",
"Lean.Name",
"Mathlib.Tactic.Conv.Path"
] | false |
Nat.binaryRec'._proof_1 | Mathlib.Data.Nat.BinaryRec | [
"Nat.bit",
"Eq.mpr",
"False",
"Nat.bit_eq_zero_iff",
"congrArg",
"and_self",
"False.elim",
"Nat.add_eq_zero_iff._simp_1",
"Bool.false_eq_true",
"Eq.mp",
"not_true_eq_false",
"id",
"instOfNatNat",
"imp_self._simp_1",
"Nat.casesAuxOn",
"Bool.true",
"instHAdd",
"And",
"Bool.casesOn"... | false |
PrincipalSeg.ordinal_type_lt | Mathlib.SetTheory.Ordinal.Basic | [
"Preorder.toLT",
"Ordinal.partialOrder",
"PrincipalSeg",
"PartialOrder.toPreorder",
"Ordinal.type",
"IsWellOrder",
"Nonempty.intro",
"LT.lt",
"Ordinal"
] | true |
Mathlib.Tactic.Abel.AbelNF.Config.mk._flat_ctor | Mathlib.Tactic.Abel | [
"Mathlib.Tactic.Abel.AbelNF.Config.mk",
"Mathlib.Tactic.Abel.AbelMode",
"Lean.Meta.TransparencyMode",
"Mathlib.Tactic.Abel.AbelNF.Config",
"Mathlib.Tactic.AtomM.Recurse.Config.mk",
"Bool"
] | false |
Mathlib.Tactic.ITauto.IProp.and'.noConfusion | Mathlib.Tactic.ITauto | [
"Mathlib.Tactic.ITauto.AndKind",
"Mathlib.Tactic.ITauto.IProp",
"Mathlib.Tactic.ITauto.IProp.and'",
"id",
"Mathlib.Tactic.ITauto.IProp.noConfusion",
"Eq"
] | false |
AlgebraicGeometry.Scheme.LocalRepresentability.glueData._proof_14 | Mathlib.AlgebraicGeometry.Sites.Representability | [
"AlgebraicGeometry.Scheme.LocalRepresentability.glueData._proof_6",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme.LocalRepresentability.glueData._proof_5",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Algebra... | false |
Mathlib.Meta.FunProp.LambdaTheorems._sizeOf_1 | Mathlib.Tactic.FunProp.Theorems | [
"Mathlib.Meta.FunProp.LambdaTheoremType._sizeOf_inst",
"Std.HashMap._sizeOf_inst",
"instHashableProd",
"Mathlib.Meta.FunProp.LambdaTheoremType",
"instOfNatNat",
"Std.HashMap",
"Mathlib.Meta.FunProp.LambdaTheorems.rec",
"Mathlib.Meta.FunProp.LambdaTheorem._sizeOf_inst",
"Array._sizeOf_inst",
"Array... | false |
_private.Mathlib.NumberTheory.PellMatiyasevic.0.Pell.matiyasevic.match_1_5 | Mathlib.NumberTheory.PellMatiyasevic | [
"Dvd.dvd",
"HMul.hMul",
"HSub.hSub",
"Exists",
"instSubNat",
"instMulNat",
"instOfNatNat",
"Or.casesOn",
"And.casesOn",
"And",
"Nat.ModEq",
"instHSub",
"Exists.casesOn",
"Nat.instDvd",
"Nat",
"And.intro",
"LT.lt",
"Exists.intro",
"Or.inl",
"Or",
"instLTNat",
"OfNat.ofNat",
... | false |
Affine.Simplex.instFintypePointsWithCircumcenterIndex.match_3 | Mathlib.Geometry.Euclidean.Circumcenter | [
"Unit.unit",
"Sum.casesOn",
"Sum",
"instOfNatNat",
"Sum.inl",
"PUnit.casesOn",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Sum.inr",
"Nat",
"instAddNat",
"PUnit.unit",
"OfNat.ofNat",
"Fin"
] | false |
String.Slice.skipSuffix?_prop_eq_some_iff | Init.Data.String.Lemmas.Pattern.TakeDrop.Pred | [
"Iff.mpr",
"String.Slice.Pattern.CharPred.Decidable.instBackwardPatternForallCharPropOfDecidablePred",
"_private.Init.Data.String.Lemmas.Pattern.TakeDrop.Pred.0.String.Slice.skipSuffix?_prop_eq_some_iff._simp_1_1",
"Iff.of_eq",
"String.Slice.Pos.prev",
"congrArg",
"Option.some",
"String.Slice",
"Exi... | true |
Submodule.annihilator | Mathlib.RingTheory.Ideal.Maps | [
"Submodule",
"Module.annihilator",
"Submodule.addCommMonoid",
"Membership.mem",
"Subtype",
"Submodule.module",
"Ideal",
"AddCommMonoid",
"Submodule.setLike",
"Semiring",
"Module",
"SetLike.instMembership"
] | true |
_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum.stableUnderSpecialization_singleton._simp_1_5 | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"forall_eq",
"propext",
"Eq"
] | false |
WellFoundedLT.finite_of_iSupIndep | Mathlib.Order.CompactlyGenerated.Basic | [
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"iSupIndep",
"Finite",
"OrderBot.toBot",
"WellFoundedLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"iSupIndep.injective",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"Finite.o... | true |
summable_star_iff' | Mathlib.Topology.Algebra.InfiniteSum.Constructions | [
"Pi.instStarForall",
"summable_star_iff",
"ContinuousStar",
"SummationFilter",
"StarAddMonoid.toInvolutiveStar",
"AddCommMonoid",
"TopologicalSpace",
"Iff",
"StarAddMonoid",
"InvolutiveStar.toStar",
"AddCommMonoid.toAddMonoid",
"Summable",
"Star.star"
] | true |
_private.Mathlib.Algebra.Homology.HomotopyCofiber.0.HomologicalComplex.homotopyCofiber.descSigma_ext_iff._simp_1_1 | Mathlib.Algebra.Homology.HomotopyCofiber | [
"And",
"propext",
"Sigma.mk.inj_iff",
"HEq",
"Sigma.mk",
"Eq",
"Sigma"
] | false |
Lean.Meta.Grind.EMatchTheoremConstraint.notDefEq | Lean.Meta.Tactic.Grind.Extension | [
"Lean.Meta.Grind.EMatchTheoremConstraint",
"Lean.Meta.Grind.CnstrRHS",
"Lean.Meta.Grind.EMatchTheoremConstraint.notDefEq",
"Nat"
] | true |
LowerSet.coe_div._simp_2 | Mathlib.Algebra.Order.UpperLower | [
"instHDiv",
"IsOrderedMonoid",
"Preorder.toLE",
"HDiv.hDiv",
"CommGroup",
"Group.toDivInvMonoid",
"SetLike.coe",
"DivInvMonoid.toDiv",
"LowerSet.coe_div",
"Set.div",
"CommGroup.toGroup",
"LowerSet",
"LowerSet.instDiv",
"Eq.symm",
"Eq",
"Preorder",
"CommGroup.toCommMonoid",
"Set",
... | false |
pinGroup.star_mul_self | Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup | [
"pinGroup.coe_star_mul_self",
"CommRing",
"Submonoid.mul",
"HMul.hMul",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"QuadraticForm",
"Membership.mem",
"pinGroup",
"AddCommGroup",
"Subtype",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
... | true |
Lean.Grind.CommRing.instReprMon.repr._sunfold | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Power",
"Std.Format.instAppend",
"_private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.instReprMon.repr.match_1",
"Std.Format.line",
"Lean.Grind.CommRing.instReprPower",
"Std.Format.group",
"GE.ge",
"instOfNatNat",
"Int",
"instLENat",
"instHAppendOfAppend",
"Unit",
... | false |
IsCyclotomicExtension.Rat.p_mem_span_zeta_sub_one | Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal | [
"Eq.mpr",
"Nat.instMulZeroOneClass",
"Nat.Prime",
"Semiring.toModule",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"Ideal.absNorm",
"Nat.instOne",
"outParam",
"NumberField.instCommRingRingOfIntegers",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"Ideal.absNorm_mem",
"HEq.... | true |
AddSubgroup.coe_pathComponentZero | Mathlib.Topology.Connected.PathConnected | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"pathComponent",
"AddSubgroup",
"TopologicalSpace",
"AddZero.toZero",
"AddGroup",
"AddGroup.toSubNegMonoid",
"SetLike.coe",
"AddSubgroup.pathComponentZero",
"AddSubgroup.instSetLike",
"Zero.toOfNat0",
"Eq.refl",
"SubNegMonoid.toAddMonoi... | true |
spectrum.spectralRadius_le_liminf_pow_nnnorm_pow_one_div | Mathlib.Analysis.Normed.Algebra.Spectrum | [
"ENNReal.instCanonicallyOrderedAdd",
"ENNReal.coe_ne_top._simp_1",
"AddGroup.toSubtractionMonoid",
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"ENNReal.rpow_eq_zero_iff._simp_1",
"le_refl",
"False",
"Real.partialOrder",
"Real",
"ENNReal.ofNNReal",
"DivInvMonoid.toIn... | true |
NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply._proof_1 | Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind | [
"Submodule.span_eq_bot._simp_1",
"Submodule",
"False",
"Nat.instMulZeroClass",
"Nat.Prime",
"Semiring.toModule",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"eq_false",
"Nat.instOne",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Fact",
"Ad... | false |
CategoryTheory.BraidedCategory.ofCartesianMonoidalCategory._proof_10 | Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CartesianMonoidalCategory.comp_lift",
"CategoryTheory.BraidedCategory.ofCartesianMonoidalCategory._proof_2",
"CategoryTheory.Cartesi... | false |
LatticeHom.snd | Mathlib.Order.Hom.Lattice | [
"Lattice",
"Lattice.toSemilatticeSup",
"SemilatticeSup.toMax",
"Prod.instLattice",
"LatticeHom",
"LatticeHom.mk",
"Prod",
"Prod.snd",
"SupHom.mk",
"LatticeHom.snd._proof_2",
"LatticeHom.snd._proof_1"
] | true |
CategoryTheory.ComposableArrows.isoMk₅._proof_14 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.ComposableArrows.homMk₅",
"instNeZeroNatHAdd_1",
"CategoryTheory.Iso.inv_hom_id",
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._proof_246",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ComposableArrows.isoMk₅._proof_8",
"CategoryThe... | false |
Lean.Linter.MissingDocs.mkHandler | Lean.Linter.MissingDocs | [
"Inhabited.default",
"Lean.ImportM.Context",
"instInhabitedError",
"IO",
"instInhabitedEIO",
"Lean.Linter.MissingDocs.Handler",
"Lean.Name",
"IO.Error",
"instInhabitedReaderT",
"Lean.ImportM"
] | true |
SimpleGraph.Coloring.sumEquiv | Mathlib.Combinatorics.SimpleGraph.Sum | [
"SimpleGraph.Coloring.sumEquiv._proof_1",
"Equiv.mk",
"Sum",
"SimpleGraph.Coloring.sumEquiv._proof_2",
"Equiv",
"Prod.mk",
"Prod.fst",
"SimpleGraph.Coloring",
"SimpleGraph",
"SimpleGraph.Coloring.sumRight",
"SimpleGraph.sum",
"SimpleGraph.Coloring.sumLeft",
"Prod",
"Prod.snd",
"SimpleGra... | true |
Std.Net.AddressFamily.ipv4.sizeOf_spec | Std.Net.Addr | [
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Std.Net.AddressFamily",
"Eq.refl",
"Std.Net.AddressFamily._sizeOf_inst",
"OfNat.ofNat",
"Eq",
"Std.Net.AddressFamily.ipv4"
] | true |
Std.IterM.toArray_filterMap | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Pure.pure",
"_private.Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap.0.Std.IterM.toArray_filterMap._simp_1_1",
"Std.IterM.toArray",
"congrArg",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"instMonadLiftT",
"Std.Iterators.Finite",
"LawfulApplicative.toLawfulFunctor",
"Std.Iterators.Ty... | true |
_private.Lean.Data.Iterators.Producers.PersistentHashMap.0.Lean.PersistentHashMap.Node.measure.match_1.eq_2 | Lean.Data.Iterators.Producers.PersistentHashMap | [
"Lean.PersistentHashMap.Entry.entry",
"Lean.PersistentHashMap.Entry",
"Lean.PersistentHashMap.Entry.ref",
"Lean.PersistentHashMap.Node",
"Lean.PersistentHashMap.Entry.null",
"_private.Lean.Data.Iterators.Producers.PersistentHashMap.0.Lean.PersistentHashMap.Node.measure.match_1",
"Eq.refl",
"Eq"
] | true |
Rep.indResHomEquiv._proof_8 | Mathlib.RepresentationTheory.Induced | [
"Representation.IndV.mk",
"Rep.V",
"CommRing",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"Rep.ind",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Module.End.ins... | false |
Nat.nonempty_of_pos_sInf | Mathlib.Data.Nat.Lattice | [
"Eq.mpr",
"congrArg",
"Nat.sInf_eq_zero",
"Set.not_nonempty_iff_eq_empty",
"Classical.byContradiction",
"Membership.mem",
"Eq.mp",
"id",
"Ne",
"instOfNatNat",
"Nat.instInfSet",
"Set.Nonempty",
"Nat",
"LT.lt",
"propext",
"Set.instEmptyCollection",
"Or",
"instLTNat",
"EmptyCollecti... | true |
Subtype.mk_eq_bot_iff | Mathlib.Order.BoundedOrder.Basic | [
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"PartialOrder",
"Subtype",
"Bot.bot",
"Subtype.mk",
"Iff",
"Subtype.val",
"Eq",
"Iff.symm",
"Subtype.coe_eq_bot_iff",
"Subtype.instLE"
] | true |
AlgebraicGeometry.PresheafedSpace.restrict_presheaf | Mathlib.Geometry.RingedSpace.PresheafedSpace | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap",
"Parti... | true |
IsLocalRing.finrank_cotangentSpace_eq_zero_iff | Mathlib.RingTheory.Ideal.Cotangent | [
"Eq.mpr",
"IsNoetherianRing.strongRankCondition",
"CommRing",
"Semiring.toModule",
"instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Iff.rfl",
"IsLocalRing.subsingleton_cotangentSpace_iff",
"IsLocalRing.instModuleResidueFie... | true |
String.Slice.Pos.offset_str_le_offset_endExclusive | Init.Data.String.Basic | [
"Eq.mpr",
"String.Slice.Pos.str",
"_private.Init.Data.String.Basic.0.String.Slice.Pos.offset_str_le_offset_endExclusive._simp_1_1",
"congrArg",
"String.Slice.Pos.offset",
"String.Slice.byteIdx_rawEndPos",
"String.Slice.Pos.isValidForSlice",
"HSub.hSub",
"String.Slice.rawEndPos",
"String.Slice.Pos.... | true |
Std.TreeMap.minKey?_eq_some_minKey! | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.minKey?",
"Std.TreeMap.inner",
"Option.some",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.isEmpty",
"Std.DTreeMap.minKey?_eq_some_minKey!",
"Std.TreeMap.minKey!",
"Bool",
"Inhabited",
"Bool.false",
"Eq",
"Std.TreeMap",
"Option"
] | true |
_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.Model.ForwardSliceSearcher.Invariants.base | Init.Data.String.Lemmas.Pattern.String.ForwardSearcher | [
"String.Slice.pos",
"String.Pos.Raw.unoffsetBy",
"String.Slice",
"String.Pos.Raw",
"_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice.Pattern.Model.ForwardSliceSearcher.Invariants.isValidForSlice",
"_private.Init.Data.String.Lemmas.Pattern.String.ForwardSearcher.0.String.Slice... | true |
ENNReal.tsum_biUnion_le | Mathlib.Topology.Algebra.InfiniteSum.ENNReal | [
"LE.le.trans_eq",
"ENNReal.instAddCommMonoid",
"Finset",
"Membership.mem",
"Set.Elem",
"LE.le",
"SetLike.coe",
"Finset.instSetLike",
"tsum",
"ENNReal.instLE",
"ENNReal",
"ENNReal.instTopologicalSpace",
"Subtype.val",
"Set.instMembership",
"Finset.tsum_subtype",
"Set.iUnion",
"SetLike... | true |
_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Three.0.IsCyclotomicExtension.Rat.Three.lambda_dvd_or_dvd_sub_one_or_dvd_add_one._simp_1_2 | Mathlib.NumberTheory.NumberField.Cyclotomic.Three | [
"Finset.mem_singleton",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"propext",
"Finset.instSingleton",
"Singleton.singleton",
"Eq",
"SetLike.instMembership"
] | false |
TensorPower.gmonoid._proof_3 | Mathlib.LinearAlgebra.TensorPower.Basic | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"GradedMonoid.GOne.toOne",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"TensorPower.gMul",
"Sigma.fst",
"TensorPower.gOne",
"zero_add",
"AddCommMonoid",
"TensorPower",
"CommSemiring",
"AddZ... | false |
Std.Internal.IO.Async.BaseAsync.toRawBaseIO | Std.Internal.Async.Basic | [
"Std.Internal.IO.Async.MaybeTask",
"Std.Internal.IO.Async.BaseAsync",
"BaseIO"
] | true |
AddMonoid.End.mulRight | Mathlib.Algebra.Ring.Basic | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidHom.mul",
"AddMonoid.End.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddMonoidHom.flip",
"AddCommMonoid.toAddMonoid",
"AddMonoid.End",
"AddMonoidHom",
"NonUnitalNonAssocSemiring"
] | true |
_private.Mathlib.Data.NNReal.Defs.0.Real.toNNReal_le_toNNReal_iff._simp_1_1 | Mathlib.Data.NNReal.Defs | [
"Real.instLE",
"Real",
"PartialOrder.toPreorder",
"Preorder.toLE",
"NNReal",
"LE.le",
"NNReal.instPartialOrder",
"propext",
"Eq.symm",
"Eq",
"NNReal.toReal",
"NNReal.coe_le_coe"
] | false |
TensorProduct.assoc_tensor' | Mathlib.LinearAlgebra.TensorProduct.Associator | [
"LinearEquiv.symm",
"LinearEquiv.toLinearMap_inj",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"LinearEquiv.rTensor",
"LinearMap.instFunLike",
"TensorProduct.ext_fourfold''",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"LinearEquiv.toLinearMap",
"congrFun",
"RingHomInvPair.id... | true |
Std.TreeMap.Raw.insertMany_cons | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.insert",
"instForInOfForIn'",
"_private.Std.Data.TreeMap.Raw.Lemmas.0.Std.TreeMap.Raw.ext",
"Ordering",
"inferInstance",
"Std.DTreeMap.Raw.Const.insertMany_cons",
"Prod.mk",
"Id",
"Std.TreeMap.Raw.inner",
"Membership",
"List.cons",
"Std.TreeMap.Raw",
"List",
"List.instMemb... | true |
_private.Mathlib.Tactic.CancelDenoms.Core.0.Mathlib.Tactic.cancelDenominatorsTarget | Mathlib.Tactic.CancelDenoms.Core | [
"ReaderT",
"Lean.MVarId.replaceTargetEq",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.Elab.Tactic.Context",
"Mathlib.Tactic.CancelDenoms.cancelDenominatorsInType",
"Lean.MVarId",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"liftM",
"ReaderT.instMonadLift",
"Lean.Elab.Tactic.instMonadTacti... | true |
MvQPF.Fix.ind | Mathlib.Data.QPF.Multivariate.Constructions.Fix | [
"Eq.mpr",
"congrArg",
"TypeVec.PredLast",
"HEq.refl",
"MvQPF.wSetoid",
"PFunctor.B",
"MvQPF.Fix.mk",
"Fin2.fz",
"Quot.ind",
"MvQPF.Fix.ind_aux",
"Fin2.casesOn",
"Exists",
"id",
"TypeVec.append1",
"instOfNatNat",
"MvFunctor.LiftP",
"MvPFunctor.A",
"Quotient.mk",
"MvQPF.toMvFunctor... | true |
Fin.val_addNat | Init.Data.Fin.Lemmas | [
"Fin.val",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Fin",
"Eq",
"Fin.addNat",
"rfl"
] | true |
HasProd.nat_mul_neg_add_one | Mathlib.Topology.Algebra.InfiniteSum.NatInt | [
"Eq.mpr",
"False",
"Finset.prod_mul_distrib",
"_private.Mathlib.Topology.Algebra.InfiniteSum.NatInt.0.HasProd.nat_mul_neg_add_one._simp_1_4",
"Int.ctorIdx",
"HMul.hMul",
"Finset.instUnion",
"Monoid.toMulOneClass",
"congrArg",
"Function.Injective.injOn",
"_private.Mathlib.Topology.Algebra.Infinit... | true |
dvd_of_mul_right_eq | Mathlib.Algebra.Divisibility.Basic | [
"Semigroup",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"Dvd.intro",
"semigroupDvd",
"Eq",
"instHMul"
] | true |
one_le_pow_mul_abs_eval_div | Mathlib.Algebra.Polynomial.DenomsClearable | [
"Int.instAddCommGroup",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"not_le",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"Polynomial.eval",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MulOne.toOne",
... | true |
_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_add_top_coe._simp_1_2 | Mathlib.Topology.Instances.EReal.Lemmas | [
"Real",
"EReal",
"instAddCommMonoidEReal",
"Real.instAdd",
"instHAdd",
"HAdd.hAdd",
"EReal.coe_add",
"AddCommSemigroup.toAddCommMagma",
"Eq.symm",
"AddCommMonoid.toAddCommSemigroup",
"Eq",
"Real.toEReal",
"AddCommMagma.toAdd"
] | false |
Std.DHashMap.Internal.AssocList.map | Std.Data.DHashMap.Internal.AssocList.Basic | [
"Std.DHashMap.Internal.AssocList.nil",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.map.go",
"Std.DHashMap.Internal.AssocList"
] | true |
Matroid.IsCircuit | Mathlib.Combinatorics.Matroid.Circuit | [
"Matroid.Dep",
"Set.instLE",
"Minimal",
"Matroid",
"Set"
] | true |
Submodule.IsMinimalPrimaryDecomposition.mem_associatedPrimes | Mathlib.RingTheory.Lasker | [
"Eq.mpr",
"Submodule",
"Submodule.colon",
"congrArg",
"CommSemiring.toSemiring",
"Submodule.IsMinimalPrimaryDecomposition",
"Finset",
"Set.univ",
"Membership.mem",
"Submodule.IsMinimalPrimaryDecomposition.image_radical_eq_associated_primes",
"id",
"Ideal",
"AddCommMonoid",
"CommSemiring",
... | true |
CategoryTheory.SingleObj.toEnd | Mathlib.CategoryTheory.SingleObj | [
"Monoid",
"MulOne.toOne",
"Monoid.toMulOneClass",
"Equiv",
"MulOne.toMul",
"CategoryTheory.SingleObj.star",
"CategoryTheory.End.mul",
"CategoryTheory.End",
"MulOneClass.toMulOne",
"CategoryTheory.SingleObj",
"MulEquiv",
"CategoryTheory.SingleObj.categoryStruct",
"Equiv.refl",
"MulEquiv.mk"... | true |
_private.Mathlib.LinearAlgebra.Dimension.Free.0.Module.Free.rank_eq_mk_of_infinite_lt._simp_1_1 | Mathlib.LinearAlgebra.Dimension.Free | [
"Cardinal",
"Cardinal.mk",
"AddCommMonoid",
"Module.Free.ChooseBasisIndex",
"Module.Free",
"StrongRankCondition",
"Semiring",
"Module.rank",
"Module",
"Eq.symm",
"Eq",
"Module.Free.rank_eq_card_chooseBasisIndex"
] | false |
UInt32.ofBitVec_ofFin | Init.Data.UInt.Lemmas | [
"instPowNat",
"BitVec.ofFin",
"instOfNatNat",
"instNatPowNat",
"UInt32.ofBitVec",
"HPow.hPow",
"UInt32.ofFin",
"Nat",
"UInt32",
"instHPow",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars._proof_4 | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | [
"Eq.mpr",
"CommRing",
"instHSMul",
"Semiring.toModule",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Ten... | false |
Turing.TM0.Stmt.noConfusion | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"HEq.refl",
"Turing.TM0.Stmt.casesOn",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq",
"Turing.TM0.Stmt",
"Turing.TM0.Stmt.noConfusionType",
"Turing.Dir"
] | false |
_private.Mathlib.Computability.TuringMachine.Tape.0.Turing.Tape.write_nth.match_1_1 | Mathlib.Computability.TuringMachine.Tape | [
"Turing.Tape",
"Int.casesOn",
"Int.ofNat",
"Int",
"instOfNat",
"Nat",
"Inhabited",
"Int.negSucc",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
HomologicalComplex₂.ofGradedObject | Mathlib.Algebra.Homology.HomologicalBicomplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.Hom.mk",
"HomologicalComplex₂.ofGradedObject._proof_3",
"HomologicalComplex",
"Prod.mk",
"HomologicalComplex.mk",
"ComplexShape",
"HomologicalC... | true |
accPt_iff_frequently | Mathlib.Topology.ClusterPt | [
"_private.Mathlib.Topology.ClusterPt.0.accPt_iff_frequently._simp_1_2",
"congrArg",
"Membership.mem",
"nhds",
"Set.instSingletonSet",
"Ne",
"Filter.Frequently",
"iff_self",
"TopologicalSpace",
"SDiff.sdiff",
"funext",
"ClusterPt",
"And",
"Iff",
"_private.Mathlib.Topology.ClusterPt.0.accP... | true |
_private.Init.Data.SInt.Lemmas.0.Int16.toNatClampNeg_ofNat_of_lt._proof_1_2 | Init.Data.SInt.Lemmas | [
"instPowNat",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id... | false |
FirstOrder._aux_Mathlib_ModelTheory_LanguageMap___unexpand_FirstOrder_Language_withConstants_1 | Mathlib.ModelTheory.LanguageMap | [
"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 |
CategoryTheory.Limits.colimit.ι_desc_apply | Mathlib.CategoryTheory.Limits.Types.Colimits | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"Eq.mp",
"id",
"CategoryTheory.Limits.colimit",
"CategoryTheory.ConcreteCategory",
"Mathlib.Tactic.Elementwise.hom_elementwise",
"CategoryTheory.Limits.... | true |
Lean.Elab.Term.elabOmission | Lean.Elab.BuiltinTerm | [
"Lean.Elab.Term.TermElab",
"Lean.Elab.Term.instMonadTermElabM",
"String",
"Lean.Meta.State",
"Lean.Core.instMonadOptionsCoreM",
"Lean.Syntax",
"Lean.instMonadOptionsOfMonadLift",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"ReaderT.instMonadLift",
"Lean.instToMessageDataString",
"Lean.Co... | true |
_private.Lean.Compiler.IR.ToIR.0.Lean.IR.ToIR.lowerDecl.match_1 | Lean.Compiler.IR.ToIR | [
"Lean.Compiler.LCNF.DeclValue.casesOn",
"Lean.Compiler.LCNF.DeclValue.extern",
"Lean.Compiler.LCNF.Code",
"Lean.Compiler.LCNF.Purity.impure",
"Lean.ExternAttrData",
"Lean.Compiler.LCNF.DeclValue.code",
"Lean.Compiler.LCNF.DeclValue"
] | false |
CategoryTheory.Limits.CoconeMorphism.inv_hom_id | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.CoconeMorphism.hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.Limits.Cocone.categor... | true |
Pi.Function.module | Mathlib.Algebra.Module.Pi | [
"Pi.addCommMonoid",
"Pi.module",
"AddCommMonoid",
"Semiring",
"Module"
] | true |
Ideal.sup_height_eq_ringKrullDim | Mathlib.RingTheory.Ideal.Height | [
"WithBot.instSupSet",
"Nontrivial",
"Iff.mpr",
"Eq.mpr",
"PrimeSpectrum.mk",
"instCompleteLatticeWithBot",
"False",
"CommRing",
"WithBot.some",
"Ideal.height_top",
"WithBot",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"instCompleteLinearOrderENat",
"Semiring.toModule",
"le_rfl",
"i... | true |
Std.DTreeMap.foldlM_eq_foldlM_keys | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"List.foldlM",
"Ordering",
"LawfulMonad",
"Std.DTreeMap.inner",
"Std.DTreeMap.Internal.Impl.foldlM_eq_foldlM_keys",
"Std.DTreeMap.foldlM",
"Std.DTreeMap.keys",
"Monad",
"Eq"
] | true |
ExistsAndEq.withExistsElimAlongPathImp._unsafe_rec | Mathlib.Tactic.Simproc.ExistsAndEq | [
"Qq.QuotedDefEq",
"Pure.pure",
"Lean.Meta.ppExpr",
"Lean.instantiateMVars",
"Lean.MonadError.mk",
"Qq.withLocalDeclQ",
"Lean.instMonadExceptOfExceptionCoreM",
"_private.Mathlib.Tactic.Simproc.ExistsAndEq.0.ExistsAndEq.findEq.go.match_5",
"Lean.Meta.mkFreshLevelMVar",
"Lean.MetavarKind.natural",
... | false |
Commute.self_pow | Mathlib.Algebra.Group.Commute.Defs | [
"Monoid",
"Commute.pow_right",
"Monoid.toMulOneClass",
"Commute",
"MulOne.toMul",
"Monoid.toPow",
"MulOneClass.toMulOne",
"Commute.refl",
"HPow.hPow",
"Nat",
"instHPow"
] | true |
bilinearIteratedFDerivTwo.eq_1 | Mathlib.Analysis.InnerProductSpace.Laplacian | [
"NormedCommRing.toNormedRing",
"NormedRing.toRing",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"bilinearIteratedFDerivWithinTwo._proof_1",
"ContinuousLinearMap.module",
... | true |
Std.TreeMap.get!_union | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.inner",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.get!",
"Std.DTreeMap.Const.get!_union",
"Inhabited",
"Union.union",
"Std.TreeMap.getD",
"Std.TreeMap.instUnion",
"Eq",
"Std.TreeMap"
] | true |
_private.Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar.0.MeasureTheory.Measure.tendsto_addHaar_inter_smul_zero_of_density_zero_aux2._simp_1_1 | Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | [
"AddGroup.toSubtractionMonoid",
"abs",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"AddRightMono",
"AddZeroClass.toAddZero",
"DistribLattice.toLattice",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",... | false |
_private.Lean.Elab.DocString.0.Lean.Doc.instMonadLiftTermElabMDocM.match_1 | Lean.Elab.DocString | [
"Lean.Doc.State.casesOn",
"List",
"Lean.Elab.Command.Scope",
"Lean.Doc.State",
"Lean.LocalInstances",
"Lean.Doc.State.mk",
"Lean.Options",
"Lean.LocalContext",
"Lean.OpenDecl"
] | false |
LinearMap.mem_finiteRange_iff_hasFiniteRange | Mathlib.Algebra.Module.LinearMap.FiniteRange | [
"Eq.mpr",
"Submodule",
"CommRing",
"LinearMap.mem_finiteRange_iff_hasNoetherianRange",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Iff.rfl",
"LinearMap.HasNoetherianRange",
"Membership.mem",
"AddCommGroup",
"id",
"IsNoetherianRing",
"LinearMap.module",
"Linear... | true |
Lean.InternalExceptionId.toString | Lean.InternalExceptionId | [
"Lean.InternalExceptionId.idx",
"String",
"ToString.toString",
"instAppendString",
"instHAppendOfAppend",
"instToStringNat",
"Nat",
"Lean.InternalExceptionId",
"HAppend.hAppend",
"instToStringString"
] | true |
Polynomial.isMonicOfDegree_sub_add_two | Mathlib.Algebra.Polynomial.Degree.IsMonicOfDegree | [
"Nontrivial",
"sub_add",
"Eq.mpr",
"Polynomial.C",
"Nat.instMulZeroClass",
"Nat.instLattice",
"Trans.trans",
"Lattice.toSemilatticeSup",
"Nat.instIsOrderedAddMonoid",
"Polynomial.instNeg",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrAr... | true |
Booleanisation.instTop | Mathlib.Order.Booleanisation | [
"Booleanisation.comp",
"Booleanisation",
"Bot.bot",
"Top.mk",
"GeneralizedBooleanAlgebra.toBot",
"GeneralizedBooleanAlgebra",
"Top"
] | true |
Asymptotics.isLittleO_abs_right | Mathlib.Analysis.Asymptotics.Defs | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"Real.lattice",
"abs",
"Asymptotics.isLittleO_norm_right",
"Norm",
"Real.instAddGroup",
"Iff",
"Real.normedCommRing",
"NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing",
"NonUnitalSeminormedRing.toSeminormedAddCommGroup",
"Asymptotics.IsLittl... | true |
Lean.Firefox.ThreadWithCollideMaps.toThreadWithMaps | Lean.Util.Profiler | [
"Lean.Firefox.ThreadWithCollideMaps",
"Lean.Firefox.ThreadWithMaps"
] | true |
ContinuousLinearMap.toContinuousAffineMap._proof_2 | Mathlib.Topology.Algebra.ContinuousAffineMap | [
"Continuous",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"ContinuousLinearMap.toLinearMap",
"LinearMap.toAddHom",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousLinearMap.cont",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCommMonoid.toAddCommSemigroup",
"RingHom.id",
"Semiri... | false |
CategoryTheory.PreZeroHypercover.interFst._proof_2 | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.bind",
"CategoryTheory.PreZeroHypercover.inter",
"CategoryTheory.PreZeroHypercover.f",
"Equiv.instEquivLike",
"CategoryTheory.Limits.HasPullback",
"Equiv",
"CategoryTheory.PreZeroHypercover.X",
"Sigma.fst",
"CategoryTheory.PreZeroHypercover.pullback₁",
"CategoryTh... | false |
Dynamics.netEntropyEntourage_le_coverEntropyEntourage | Mathlib.Dynamics.TopologicalEntropy.NetEntropy | [
"Dynamics.netEntropyEntourage",
"Dynamics.netMaxcard_le_coverMincard",
"SetRel",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"ENat.toENNReal",
"LE.le",
"ENat.toENNReal_mono",
"Dynamics.coverMincard",
"Nat",
"instPartialOrderEReal",
"Dynamics.coverEntropyEntourage",
"ExpGrowth.expG... | true |
CategoryTheory.PreZeroHypercover.sumInl._proof_2 | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.PreZeroHypercover.X",
"Sum.inl",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover.sum",
"CategoryTheory.PreZeroHyper... | false |
_private.Lean.Meta.Sym.InstantiateS.0.Lean.Meta.Sym.instantiateRevBetaS'.visit.match_1 | Lean.Meta.Sym.InstantiateS | [
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.Expr.forallE",
"Lean.Expr.casesOn",
"List",
"Lean.MData",
"Lean.Expr.lam",
... | false |
Lean.Meta.Sym.Simp.Context | Lean.Meta.Sym.Simp.SimpM | [
"Lean.Meta.Sym.Simp.Context.mk"
] | true |
BitVec.getLsb | Init.Data.BitVec.Basic | [
"BitVec",
"BitVec.toNat",
"Fin.val",
"Nat",
"Nat.testBit",
"Bool",
"Fin"
] | true |
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