name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
UniformSpace.hausdorff.isClosed_setOf_totallyBounded | Mathlib.Topology.UniformSpace.Closeds | [
"Filter.instMembership",
"UniformSpace",
"Eq.mpr",
"TotallyBounded",
"Set.setOf_subset_setOf_of_imp",
"Set.iUnion_mono''",
"SetRel",
"Iff.of_eq",
"congrArg",
"uniformity",
"setOf",
"Set.mem_iUnion._simp_1",
"Set.mem_of_subset_of_mem",
"Set.Finite",
"Function.comp",
"Membership.mem",
... | true |
Bornology.IsVonNBounded.image_multilinear | Mathlib.Topology.Algebra.Module.Multilinear.Bounded | [
"NormedCommRing.toSeminormedCommRing",
"Bornology.vonNBornology",
"ContinuousSMul",
"Pi.topologicalSpace",
"Bornology.IsVonNBounded",
"Bornology.IsVonNBounded.image_multilinear'",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Subtype.finite",
"Pi.uniqueOfIsEmpty",
"AddMonoid... | true |
UInt64.toUInt16_lt._simp_1 | Init.Data.UInt.Lemmas | [
"UInt64.instOfNat",
"UInt64.toUInt16",
"UInt64",
"instLTUInt64",
"instHMod",
"HMod.hMod",
"UInt16",
"LT.lt",
"instModUInt64",
"propext",
"instLTUInt16",
"OfNat.ofNat",
"UInt64.toUInt16_lt",
"Eq"
] | false |
CategoryTheory.Functor.leftOpRightOpEquiv._proof_1 | Mathlib.CategoryTheory.Opposites | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"Quiver.Hom.unop",
"CategoryTheory.NatTrans.rightOp",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Category.opposite",
"Eq.refl",
"CategoryTheory.Catego... | false |
_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.Internal.List.insertEntry.eq_1 | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"cond",
"Std.Internal.List.replaceEntry",
"Std.Internal.List.insertEntry",
"List.cons",
"List",
"Std.Internal.List.containsKey",
"Eq.refl",
"Sigma.mk",
"BEq",
"Eq",
"Sigma"
] | true |
curveIntegral_symm | Mathlib.MeasureTheory.Integral.CurveIntegral.Basic | [
"NegZeroClass.toNeg",
"Real",
"MeasureTheory.Measure",
"Pi.instNeg",
"RCLike.toNormedAlgebra",
"intervalIntegral.integral_comp_sub_left",
"Path.symm",
"NormedSpace",
"sub_self",
"Real.instZero",
"congrArg",
"sub_zero",
"AddCommGroup.toAddCommMonoid",
"Real.instSub",
"NormedSpace.toModule... | true |
_private.Mathlib.MeasureTheory.Measure.AddContent.0.MeasureTheory.addContent_iUnion_eq_tsum_of_disjoint_of_addContent_iUnion_le._simp_1_5 | Mathlib.MeasureTheory.Measure.AddContent | [
"propext",
"Eq",
"forall_apply_eq_imp_iff₂"
] | false |
smul_mem_asymptoticCone_iff | Mathlib.Topology.Algebra.AsymptoticCone | [
"AffineSpace.asymptoticNhds_smul",
"Eq.mpr",
"OrderTopology",
"instHSMul",
"Preorder.toLT",
"ContinuousSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"AddCommG... | true |
Matrix.transposeInvertibleEquivInvertible._proof_1 | Mathlib.Data.Matrix.Invertible | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Invertible.subsingleton",
"CommSemiring.toSemiring",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Matrix.invertibleOfInvertibleTranspose",
"instDistribOfSemiring",
"CommSemiring",
"NonUnitalNonAssocSemir... | false |
Std.Tactic.BVDecide.BVUnOp.eval_not | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"Std.Tactic.BVDecide.BVUnOp.eval",
"BitVec",
"Std.Tactic.BVDecide.BVUnOp.not",
"Nat",
"Complement.complement",
"Eq.refl",
"Eq",
"BitVec.instComplement"
] | true |
CategoryTheory.PreGaloisCategory.autMapHom_apply | Mathlib.CategoryTheory.Galois.GaloisObjects | [
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"DivInvMonoid.toMonoid",
"CategoryTheory.PreGaloisCategory.IsConnected",
"Group.toDivInvMonoid",
"CategoryTheory.PreGaloisCategory.IsGalois",
"MulOneClass.toMulOne",
"CategoryThe... | true |
List.consecutivePairs | Mathlib.Data.List.Defs | [
"List.zip",
"List.tail",
"List",
"Prod"
] | true |
Std.DHashMap.Raw.Equiv.mem_iff | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Eq.mpr",
"_private.Std.Data.DHashMap.RawLemmas.0.Std.DHashMap.Raw.Equiv.mem_iff._simp_1_1",
"congrArg",
"Std.DHashMap.Raw",
"Membership.mem",
"Std.DHashMap.Raw.contains",
"Std.DHashMap.Raw.Equiv.contains_eq",
"id",
"_priva... | true |
Set.BijOn.union | Mathlib.Data.Set.Function | [
"Set.SurjOn.union_union",
"Set.SurjOn",
"Set.instUnion",
"Set.BijOn.surjOn",
"And",
"Set.MapsTo",
"And.intro",
"Set.MapsTo.union_union",
"Set.BijOn",
"Set.BijOn.mapsTo",
"Union.union",
"Set.InjOn",
"Set"
] | true |
LieSubmodule.lowerCentralSeries_eq_lcs_comap | Mathlib.Algebra.Lie.Nilpotent | [
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"Eq.mpr",
"CommRing",
"Nat.recAux",
"LieSubmodule.comap_bracket_eq",
"LieRing.toAddCommGroup",
"LieSubmodule.instLieRingModuleSubtypeMem",
"LieSubmodule.instTop",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieSub... | true |
HopfAlgCat.noConfusionType | Mathlib.Algebra.Category.HopfAlgCat.Basic | [
"CommRing",
"HopfAlgCat.casesOn",
"HopfAlgebra",
"HopfAlgCat",
"CommRing.toCommSemiring",
"HEq",
"Ring.toSemiring",
"Eq",
"Ring"
] | false |
CategoryTheory.ShortComplex.instPreservesLimitsOfShapeπ₂ | Mathlib.Algebra.Homology.ShortComplex.Limits | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instPreservesLimitsOfShapeπ₁",
... | true |
CategoryTheory.Idempotents.functorExtension₁._proof_1 | Mathlib.CategoryTheory.Idempotents.FunctorExtension | [
"CategoryTheory.Functor",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"CategoryTheory.Idempotents.Karoubi.comp_p",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Idempotents.Karo... | false |
ContinuousLinearMap.instSMul._proof_1 | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"instHSMul",
"Continuous",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"ContinuousLinearMap.toLinearMap",
"DistribSMul.toSMulZeroClass",
"LinearMap.toAddHom",
"ContinuousConstSMul",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"AddZero.toZero",
"Continuo... | false |
_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.doubling_lt_golden_ratio._simp_1_23 | Mathlib.Combinatorics.Additive.VerySmallDoubling | [
"Finset",
"Membership.mem",
"Set.Elem",
"Set.toFinset",
"Fintype",
"Finset.instSetLike",
"propext",
"Set.mem_toFinset",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
NormedField.instRankLeOneNNRealValuation._proof_3 | Mathlib.Topology.Algebra.Valued.NormedValued | [
"NormedCommRing.toNormedRing",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"NormedRing.toRing",
"StrictMono",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"LinearOrderedCommMonoidWithZero.toLinearO... | false |
Matrix.diagonal_mulVec_single | Mathlib.Data.Matrix.Mul | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Pi.apply_single",
"id",
"Pi.single",
"MulZeroClass.mul_zero",
"funext",
"Fintype",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"Matrix.mulVec_diagonal",
"NonUnitalNonAssocSemiring",
"Matrix.mulVec... | true |
_private.Mathlib.Analysis.Asymptotics.Theta.0.Asymptotics.isTheta_const_const_iff._simp_1_2 | Mathlib.Analysis.Asymptotics.Theta | [
"Asymptotics.isBigO_const_const_iff",
"Filter.NeBot",
"Asymptotics.IsBigO",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"NormedAddCommGroup.toNorm",
"propext",
"Zero.toOfNat0",
"NormedAddCommGroup.toAddCommGroup",
"AddCo... | false |
Lean.Doc.instBEqListItem.beq | Lean.DocString.Types | [
"Array.instBEq",
"Array",
"BEq.beq",
"_private.Lean.DocString.Types.0.Lean.Doc.instBEqListItem.beq.match_1",
"Bool",
"Lean.Doc.ListItem",
"Bool.false",
"BEq"
] | true |
Std.DTreeMap.isSome_maxKey?_iff_isEmpty_eq_false | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.isEmpty",
"Std.DTreeMap.maxKey?",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Bool.true",
"Iff",
"Std.DTreeMap.wf",
"Bool",
"Option.isSome",
"Bool.false",
"Eq",
"Std.DTreeMap.Internal.Impl.isSome_maxKey?_iff_isEmpty_eq_false"
] | true |
Mathlib.Tactic.Monoidal.instMonadNormalizeNaturalityMonoidalM.match_1 | Mathlib.Tactic.CategoryTheory.Monoidal.PureCoherence | [
"Option.ctorIdx",
"Lean.Expr.const",
"Option.some",
"Nat.hasNotBit",
"Mathlib.Tactic.Monoidal.Context.instCat",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Mathlib.Tactic.Monoidal.Context.C",
"Mathlib.Tactic.Monoidal.Context.level₁",
"Lean.Name.mkStr2",
"Mathlib.Tactic.Monoidal.Context",
"Lean.... | false |
ProbabilityTheory.preCDF_le_one | Mathlib.Probability.Kernel.Disintegration.CondCDF | [
"MeasureTheory.Measure.IicSnd",
"ProbabilityTheory.preCDF",
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.Measure.fst.instIsFiniteMeasure",
"ProbabilityTheory.setLIntegral_preCDF_fst",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"MeasurableSet",
"congrArg",
"Set.univ",
"Filter.Eventuall... | true |
Metric.Snowflaking.preimage_toSnowflaking_emetricBall | Mathlib.Topology.MetricSpace.Snowflaking | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real.instLE",
"Real",
"Equiv.instEquivLike",
"Metric.Snowflaking.toSnowflaking",
"Real.instZero",
"Real.instInv",
"ENNReal.instPowReal",
"Real.instLT",
"Equiv",
"Metric.Snowflaking.instEDist",
"LE.le",
"Metric.eball",
"PseudoEMetricSpace",
... | true |
Finset.min_union | Mathlib.Data.Finset.Max | [
"LinearOrder.toDecidableEq",
"Finset.instUnion",
"Finset",
"LinearOrder",
"Finset.inf_union",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finset.min",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"SemilatticeInf.toMin",
"WithTop.some",
"WithTop.instOrderTop",
"WithTop.semi... | true |
Lean.Compiler.LCNF.Code.collectUsed | Lean.Compiler.LCNF.Basic | [
"Inhabited.default",
"Lean.instEmptyCollectionFVarIdHashSet",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Code",
"Inhabited",
"EmptyCollection.emptyCollection",
"optParam",
"Lean.FVarIdHashSet",
"Inhabited.mk"
] | true |
Std.Http.URI.EncodedString.decode | Std.Internal.Http.Data.URI.Encoding | [
"Pure.pure",
"UInt8.instOfNat",
"HMul.hMul",
"Std.Http.URI.hexDigitToUInt8?",
"_private.Std.Internal.Http.Data.URI.Encoding.0.Std.Http.URI.EncodedString.decode._proof_1",
"Monad.toApplicative",
"String",
"ByteArray.push",
"_private.Std.Internal.Http.Data.URI.Encoding.0.Std.Http.URI.EncodedString.dec... | true |
CategoryTheory.Subgroupoid.instSetLikeSigmaHom | Mathlib.CategoryTheory.Groupoid.Subgroupoid | [
"SetLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Groupoid",
"CategoryTheory.Subgroupoid.instSetLikeSigmaHom._proof_1",
"SetLike.mk",
"CategoryTheory.Subgroupoid",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Groupoid.toCategory",
"CategoryTheory.Sub... | true |
ENat.one_lt_card._simp_1 | Mathlib.SetTheory.Cardinal.Finite | [
"Nontrivial",
"instAddMonoidWithOneENat",
"AddMonoidWithOne.toOne",
"ENat",
"LT.lt",
"True",
"eq_true",
"One.toOfNat1",
"instLTENat",
"OfNat.ofNat",
"ENat.card",
"Eq",
"ENat.one_lt_card"
] | false |
Lean.Expr.isDIte | Lean.Util.Recognizers | [
"Lean.Expr.isAppOfArity",
"Lean.Expr",
"instOfNatNat",
"Nat",
"Bool",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
edist_lt_top | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Preorder.toLT",
"ENNReal.ofReal",
"PartialOrder.toPreorder",
"ENNReal.ofReal_lt_top",
"Eq.rec",
"PseudoMetricSpace",
"edist_dist",
"PseudoMetricSpace.toEDist",
"LT.lt",
"ENNReal",
"ENNReal.instPartialOrder",
"ENNReal.instTop",
"Dist.dist",
"PseudoMetricSpace.toDist",
"EDist.edist",
"T... | true |
CategoryTheory.Functor.PullbackObjObj.mk.inj | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.PullbackObjObj.mk",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.IsPullback",
"CategoryTheory.Functor.PullbackObjObj",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.map",
"And",... | true |
FirstOrder.Language.DefinableSet.coe_bot | Mathlib.ModelTheory.Definability | [
"Bot.bot",
"FirstOrder.Language.DefinableSet",
"FirstOrder.Language.Structure",
"SetLike.coe",
"FirstOrder.Language.DefinableSet.instBot",
"Set.instEmptyCollection",
"FirstOrder.Language",
"EmptyCollection.emptyCollection",
"FirstOrder.Language.DefinableSet.instSetLike",
"Eq",
"rfl",
"Set"
] | true |
ArchimedeanClass.orderHom | Mathlib.Algebra.Order.Archimedean.Class | [
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddCommGroup.toAddGroup",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"ArchimedeanOrder.instPreorder",
"AddGroup.toSubNegMon... | true |
_private.Mathlib.CategoryTheory.Shift.Localization.0.CategoryTheory.Functor.commShiftOfLocalization._simp_1 | Mathlib.CategoryTheory.Shift.Localization | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"CategoryTheory.NatTrans",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.NatTrans.app... | false |
ExteriorAlgebra.ιInv | Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | [
"AlgHom.toLinearMap",
"CommRing",
"TrivSqZeroExt",
"Semiring.toModule",
"ExteriorAlgebra.ιInv._proof_3",
"QuadraticMap.instZero",
"Ring.toNonAssocRing",
"ExteriorAlgebra",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"instAlgebraCliffordAlgebra",
"MulOpposite",
"QuadraticForm",... | true |
_private.Lean.Meta.InferType.0.Lean.Meta.inferMVarType | Lean.Meta.InferType | [
"Pure.pure",
"Lean.MetavarContext.findDecl?",
"Lean.Meta.State",
"Lean.MetavarContext",
"Lean.MVarId",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Applicative.toPure",
"Unit",
"Lean.Core.CoreM",
"_private.Lean.Meta.InferType.0.Lean.Meta.inferMVarType.match_1",
"Lean.Meta.instMonadMetaM"... | true |
AddOpposite.instCommMonoid._proof_2 | Mathlib.Algebra.Group.Opposite | [
"HMul.hMul",
"Monoid.toMulOneClass",
"AddOpposite",
"MulOne.toMul",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"AddOpposite.unop",
"Eq",
"CommMonoid",
"AddOpposite.instMul",
"rfl",
"instHMul"
] | false |
_private.Mathlib.LinearAlgebra.Matrix.Charpoly.Eigs.0.Matrix.mem_spectrum_iff_not_isUnit_eval_charpoly._simp_1_1 | Mathlib.LinearAlgebra.Matrix.Charpoly.Eigs | [
"Algebra.algebraMap",
"spectrum",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"HSub.hSub",
"IsUnit",
"Algebra",
"RingHom",
"Membership.mem",
"CommSemiring",
"SubNegMonoid.toSub",
"RingHom.instFunLike",
"instHSub",
"AddGroup.toSubNegMonoid",
"spectrum.mem_iff",
"Semiring.to... | false |
ENormedCommMonoid.toESeminormedCommMonoid | Mathlib.Analysis.Normed.Group.Defs | [
"ESeminormedCommMonoid",
"TopologicalSpace",
"ENormedCommMonoid"
] | true |
_private.Init.Data.Nat.Lcm.0.Nat.lcm_pos._simp_1_1 | Init.Data.Nat.Lcm | [
"Nat.pos_iff_ne_zero",
"Ne",
"instOfNatNat",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | false |
Equiv.algebra | Mathlib.Algebra.Algebra.TransferInstance | [
"MulOne.toOne",
"instHSMul",
"RingHom.mk",
"Equiv.instEquivLike",
"Equiv.algebra._proof_6",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Equiv.algebra._proof_4",
"OneHom.mk",
"Algebra",
"RingHom",
"Algebra.toSMul",
"Equiv",
"MonoidHom.mk",
"SMul.mk",
"NonAssocSemiring.toMulZeroOne... | true |
ZMod.intCast_cast_mul | Mathlib.Data.ZMod.Basic | [
"Int.cast",
"Eq.mpr",
"HMul.hMul",
"ZMod.cast",
"ZMod.commRing",
"congrArg",
"CommSemiring.toSemiring",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"instHMod",
"Int",
"AddGroupWithOne.toIntCast",
"CommRing.toNonAssocCommRing",
"Nat.cast",
"ZMod",
"NonAssocRing.toNonUnita... | true |
Lean.Elab.InlayHintLinkLocation._sizeOf_inst | Lean.Elab.InfoTree.InlayHints | [
"Lean.Elab.InlayHintLinkLocation._sizeOf_1",
"SizeOf.mk",
"Lean.Elab.InlayHintLinkLocation",
"SizeOf"
] | false |
Lean.Meta.Grind.EMatch.State.recOn | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.EMatchTheoremsArray",
"Lean.Meta.Grind.EMatch.State.rec",
"Lean.PHashMap",
"Lean.Meta.Grind.EMatch.State",
"Lean.Meta.Grind.PreInstanceSet",
"Lean.PArray",
"Lean.Meta.Grind.DelayedTheoremInstance",
"Lean.Meta.Grind.EMatchTheorem",
"Lean.PHashSet",
"List",
"Lean.Meta.Sym.instHash... | false |
Vector.append_assoc_symm | Init.Data.Vector.Lemmas | [
"Vector.cast_mk._proof_1",
"Array.instAppend",
"Array.append_assoc",
"Vector.instHAppendHAddNat",
"Vector",
"congrArg",
"Vector.casesOn",
"Eq.rec",
"Vector.cast.congr_simp",
"Vector.mk_append_mk._proof_1",
"Vector.append_assoc_symm._proof_2",
"Array",
"instHAppendOfAppend",
"instHAdd",
"... | true |
_private.Mathlib.Data.Seq.Parallel.0.Computation.BisimO.match_1.splitter._sparseCasesOn_3 | Mathlib.Data.Seq.Parallel | [
"Nat.ne_of_beq_eq_false",
"Sum.ctorIdx",
"Nat.shiftRight",
"Sum",
"Nat.hasNotBit",
"instOfNatNat",
"Sum.inl",
"Nat.land",
"Sum.inr",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Sum.rec"
] | false |
List.anyM_pure | Init.Data.List.Monadic | [
"Pure.pure",
"Eq.mpr",
"congrArg",
"Monad.toApplicative",
"id",
"LawfulMonad",
"List.rec",
"Bool.false_or",
"Applicative.toPure",
"_private.Init.Data.List.Monadic.0.List.anyM.match_1.splitter",
"List.cons",
"_private.Init.Data.List.Control.0.List.anyM.match_1",
"Bool.true",
"funext",
"Li... | true |
Option.forIn_toList | Init.Data.Option.List | [
"instForInOfForIn'",
"Option.toList",
"Option.instMembership",
"Option.casesOn",
"Option.some",
"inferInstance",
"ForIn.forIn",
"Membership",
"ForInStep",
"Option.none",
"List",
"List.instMembership",
"Eq.ndrec",
"Eq.refl",
"Eq.symm",
"Monad",
"Eq",
"Option",
"Option.instForIn'In... | true |
Filter.le_limsup_of_frequently_le' | Mathlib.Order.LiminfLimsup | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Filter.liminf_le_of_frequently_le'",
"CompleteLattice.toConditionallyCompleteLattice",
"LE.le",
"Filter.limsup",
"Filter.Frequently",
"OrderDual.instCompleteLattice",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyCompleteLattice.t... | true |
MeasureTheory.posConvolution._proof_1 | Mathlib.Analysis.Convolution | [
"Real",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Real.semiring",
"smulCommClass_self",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",
"NormedAddCommGroup.toAddCommGroup",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.toAddMonoid",
"Real.no... | false |
Shrink.instNonUnitalCommRing | Mathlib.Algebra.Ring.Shrink | [
"Equiv.nonUnitalCommRing",
"NonUnitalCommRing",
"Shrink",
"Equiv.symm",
"equivShrink",
"Small"
] | true |
injective_frobenius._simp_1 | Mathlib.FieldTheory.Perfect | [
"PerfectRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommSemiring.toSemiring",
"injective_frobenius",
"RingHom",
"ExpChar",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Monoid.toPow",
"CommSemiring",
"frobenius",
"RingHom.instFunLike",
"Nat",
"True",
"Semiring.toMonoid",
"eq_true",
... | false |
ULift.distribMulAction'._proof_2 | Mathlib.Algebra.Module.ULift | [
"Monoid",
"ULift.addZeroClass",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"ULift",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"ULift.distribSMul'",
"AddZero.toZero",
"instHAdd",
"DistribSMul.smul_add",
"HAdd.hAdd",
"AddMonoid",
"AddZero.toAd... | false |
CategoryTheory.Limits.colimitLimitToLimitColimitCone._proof_4 | Mathlib.CategoryTheory.Limits.ColimitLimit | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.colim",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.HasLimit",
"CategoryTheory.Functor.uncurry",
"CategoryTheory.Functor... | false |
RelHom.instFintype | Mathlib.Data.Fintype.Pi | [
"RelHom",
"DecidableRel",
"Pi.instFintype",
"RelHom.instFintype._proof_5",
"Subtype.fintype",
"Equiv.mk",
"RelHom.instFintype._proof_3",
"Subtype",
"forall_prop_decidable",
"Fintype.ofEquiv",
"RelHom.instFintype._proof_1",
"RelHom.toFun",
"Subtype.mk",
"RelHom.map_rel'",
"Fintype",
"Fi... | true |
CategoryTheory.Limits.widePushoutShapeOp._proof_3 | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.widePushoutShapeOpMap",
"CategoryTheory.subsingleton_of_unop",
"CategoryTheory.Limits.WidePushoutShape.category",
... | false |
Lean.Elab.Command.InductiveElabStep2.prefinalize | Lean.Elab.MutualInductive | [
"Lean.Elab.Command.InductiveElabStep2",
"Lean.Elab.Command.InductiveElabStep3",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"List",
"Lean.Elab.Term.TermElabM",
"Lean.Name"
] | true |
Std.DTreeMap.containsThenInsert_snd | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap.Internal.Impl.containsThenInsert_snd",
"Std.DTreeMap",
"Std.DTreeMap.insert",
"_private.Std.Data.DTreeMap.Lemmas.0.Std.DTreeMap.ext",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.containsThenInsert",
"Std.DTreeMap.wf",
"Bool",
"Eq",
"Prod.snd"
] | true |
UInt32.toNat_ofNat_of_lt | Init.Data.UInt.Lemmas | [
"UInt32.size",
"UInt32.toNat",
"UInt32.toNat_ofNat_of_lt'",
"Nat",
"LT.lt",
"UInt32",
"instLTNat",
"OfNat.ofNat",
"Eq",
"UInt32.instOfNat"
] | true |
Std.Iterators.Types.Flatten.IsPlausibleStep.rec | Init.Data.Iterators.Combinators.Monadic.FlatMap | [
"Std.Iterators.Types.Flatten.IsPlausibleStep.innerYield",
"Std.IterStep",
"Std.Iterators.Types.Flatten.IsPlausibleStep.outerDone",
"Option.some",
"Std.IterM.IsPlausibleStep",
"Std.IterStep.skip",
"Std.IterM.mk",
"Std.Iterators.Types.Flatten.IsPlausibleStep.outerYield",
"Std.Iterator",
"Option.none... | false |
Subgroup.map_symm_eq_iff_map_eq | Mathlib.Algebra.Group.Subgroup.Map | [
"Eq.mpr",
"MulEquiv.refl",
"MulEquiv.instEquivLike",
"MonoidHom",
"Subgroup.map",
"Monoid.toMulOneClass",
"congrArg",
"MulEquiv.trans",
"MulEquiv.symm_trans_self",
"MulEquiv.instMulEquivClass",
"Group",
"Subgroup.map_id",
"id",
"MulOne.toMul",
"MonoidHomClass.toMonoidHom",
"MonoidHom.c... | true |
Lean.Meta.Simp.instInhabitedContext | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.Simp.instInhabitedContext.default",
"Inhabited",
"Lean.Meta.Simp.Context",
"Inhabited.mk"
] | true |
_private.Mathlib.MeasureTheory.Integral.IntegrableOn.0.MeasureTheory.integrableAtFilter_atBot_iff.match_1_1 | Mathlib.MeasureTheory.Integral.IntegrableOn | [
"Filter.instMembership",
"MeasureTheory.Measure",
"Membership.mem",
"MeasureTheory.IntegrableOn",
"ContinuousENorm",
"And.casesOn",
"MeasureTheory.IntegrableAtFilter",
"MeasurableSpace",
"TopologicalSpace",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Filter.atBot",
"Filter",
... | false |
Fintype.one_lt_card_iff_nontrivial | Mathlib.Data.Fintype.EquivFin | [
"Nontrivial",
"Eq.mpr",
"Mathlib.Tactic.Contrapose.contrapose_iff₁",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Fintype.card",
"id",
"instOfNatNat",
"LE.le",
"not_lt._simp_1",
"Iff",
"Fintype",
"Nat",
"congr",
"LT.lt",
"Subsingleton",
"not_nontrivial_iff_subsingleton.... | true |
Order.isSuccPrelimit_iff_of_noMax | Mathlib.Order.SuccPred.Limit | [
"IsMin.isSuccPrelimit",
"Preorder.toLT",
"Order.IsSuccPrelimit.isMin_of_noMax",
"Order.IsSuccPrelimit",
"NoMaxOrder",
"Preorder.toLE",
"Iff",
"Iff.intro",
"IsSuccArchimedean",
"SuccOrder",
"IsMin",
"Preorder"
] | true |
Std.Roo.noConfusionType | Init.Data.Range.Polymorphic.PRange | [
"Std.Roo.casesOn",
"HEq",
"Std.Roo"
] | false |
Set.instCompleteAtomicBooleanAlgebra._proof_5 | Mathlib.Data.Set.BooleanAlgebra | [
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"DistribLattice.toLattice",
"Bot.bot",
"LE.le",
"Set.instBooleanAlgebra",
"SemilatticeSup.toPartialOrder",
"BooleanAlgebra.bot_le",
"BooleanAlgebra.toBot",
"BooleanAlgebra.toDistribLattice",
"Set"
] | false |
CategoryTheory.Limits.WalkingMulticospan.Hom.casesOn | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.MulticospanShape.snd",
"CategoryTheory.Limits.WalkingMulticospan.Hom.rec",
"CategoryTheory.Limits.WalkingMulticospan.Hom",
"CategoryTheory.Limits.WalkingMulticospan.right",
"CategoryTheory.Limits.WalkingMulticospan.Hom.id",
"CategoryTheory.Limits.MulticospanShape.fst",
"CategoryTh... | false |
Lean.Grind.CommRing.Mon.mult.injEq | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Power",
"Lean.Grind.CommRing.Mon.mult.inj",
"Lean.Grind.CommRing.Mon.mult",
"Eq.propIntro",
"Lean.injEq_helper",
"And",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Lean.Grind.CommRing.Mon"
] | true |
Equiv.Perm.two_le_card_support_cycleOf_iff._simp_1 | Mathlib.GroupTheory.Perm.Cycle.Factors | [
"Equiv.Perm.instDecidableRelSameCycle",
"Equiv.Perm.support",
"Equiv.instEquivLike",
"Ne",
"instOfNatNat",
"LE.le",
"instLENat",
"Fintype",
"Equiv.Perm",
"Nat",
"propext",
"Finset.card",
"Equiv.Perm.two_le_card_support_cycleOf_iff",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"EquivLike.toF... | false |
LinearIndependent.repr | Mathlib.LinearAlgebra.LinearIndependent.Defs | [
"Submodule",
"LinearEquiv.symm",
"Semiring.toModule",
"Finsupp.module",
"Submodule.addCommMonoid",
"Membership.mem",
"Subtype",
"Submodule.module",
"LinearMap",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"LinearEquiv.toLinearMap",
"NonAssocSe... | true |
Lean.Meta.LiftLetsConfig.noConfusion | Init.MetaTypes | [
"Lean.Meta.ExtractLetsConfig",
"Eq.ndrec",
"Eq.refl",
"Lean.Meta.LiftLetsConfig.casesOn",
"Eq",
"Lean.Meta.LiftLetsConfig.noConfusionType",
"Lean.Meta.LiftLetsConfig"
] | false |
_private.Batteries.Data.DList.Lemmas.0.Batteries.DList.push.match_1.eq_1 | Batteries.Data.DList.Lemmas | [
"Batteries.DList",
"instHAppendOfAppend",
"List",
"Batteries.DList.push.match_1",
"Eq.refl",
"Batteries.DList.mk",
"List.instAppend",
"Eq",
"HAppend.hAppend",
"List.nil"
] | true |
Functor._aux_Mathlib_Control_Functor___unexpand_Functor_mapConstRev_1 | Mathlib.Control.Functor | [
"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 |
AlgebraicGeometry.StructureSheaf.sectionsSubalgebra | Mathlib.AlgebraicGeometry.StructureSheaf | [
"AlgebraicGeometry.StructureSheaf.Localizations",
"Submodule",
"CommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"Submodule.toAddSubmonoid",
"Subsemigroup.mk",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Pi.module",
"AddMonoid.toAddZeroClass",
"AlgebraicGeometry.StructureShe... | true |
Ideal.cotangentToQuotientSquare | Mathlib.RingTheory.Ideal.Cotangent | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"Semiring.toModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Ideal.Cotangent",
"Membership.mem",
"Algebra.id",
"Subtype",
"Ideal.instAddCommGroupCotangent",
"instOfNatNa... | true |
Std.TreeMap.Raw.Equiv.getEntryLE!_eq | Std.Data.TreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.Equiv.constGetEntryLE!_eq",
"Std.TreeMap.Raw.WF.out",
"Std.TreeMap.Raw.Equiv.inner",
"Ordering",
"Std.TreeMap.Raw.getEntryLE!",
"Std.TreeMap.Raw.Equiv",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Inhabited",
"Prod",
"Eq"
] | true |
iSup_psigma' | Mathlib.Order.CompleteLattice.Basic | [
"PSigma.snd",
"iSup_psigma",
"iSup",
"PSigma.mk",
"CompleteSemilatticeSup.toSupSet",
"CompleteLattice.toCompleteSemilatticeSup",
"PSigma.fst",
"Eq.symm",
"CompleteLattice",
"PSigma",
"Eq"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getD_erase._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
String.rawEndPos.eq_1 | Init.Data.String.Iterator | [
"String",
"String.utf8ByteSize",
"String.Pos.Raw",
"String.rawEndPos",
"String.Pos.Raw.mk",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.Limits.colimitIsoFlipCompColim_hom_app | Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.colim",
"CategoryTheory.Functor.category",
"CategoryTheory.Funct... | true |
CategoryTheory.Cat.Hom.ext | Mathlib.CategoryTheory.Category.Cat | [
"CategoryTheory.Functor",
"HEq.refl",
"CategoryTheory.Cat.str",
"Eq.casesOn",
"CategoryTheory.Cat",
"CategoryTheory.Bundled.α",
"Eq.ndrec",
"CategoryTheory.Cat.Hom.ofFunctor",
"Eq.refl",
"HEq",
"CategoryTheory.Cat.Hom",
"_private.Mathlib.CategoryTheory.Category.Cat.0.CategoryTheory.Cat.Hom.ext... | true |
Frm.carrier | Mathlib.Order.Category.Frm | [
"Frm"
] | true |
_private.Mathlib.Analysis.Convex.StrictCombination.0.StrictConvex.centerMass_mem_interior._simp_1_4 | Mathlib.Analysis.Convex.StrictCombination | [
"lt_add_iff_pos_right",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"AddLeftStrictMono",
"HAdd.hAdd",
"LT.lt",
"propext",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"LT",
"AddLeftReflectLT"
] | false |
instAddCommGroupFreeAbelianGroup._aux_17 | Mathlib.GroupTheory.FreeAbelianGroup | [
"Int",
"DivInvMonoid.zpow",
"Group.toDivInvMonoid",
"FreeAbelianGroup",
"CommGroup.toGroup",
"Abelianization",
"FreeGroup",
"Abelianization.commGroup",
"FreeGroup.instGroup"
] | false |
Std.DHashMap.Internal.Raw₀.Const.get?ₘ | Std.Data.DHashMap.Internal.Model | [
"Std.DHashMap.Raw",
"instOfNatNat",
"Std.DHashMap.Internal.AssocList.get?",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.Internal.bucket",
"Std.DHashMap.Internal.Raw₀.Const.alterₘ._proof_1",
"Std.DHashMap.Internal.AssocList",
"Hashable",
"instLTNat",
"OfNat.ofNat",
"Subtype.val"... | true |
IsDedekindDomain.HeightOneSpectrum.algebraMap_adicCompletionIntegers_apply | Mathlib.RingTheory.DedekindDomain.AdicValuation | [
"Int.instAddCommGroup",
"UniformSpace.Completion.coe'",
"Multiplicative.linearOrder",
"CommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Int.instLinearOrder",
"IsFractionRing",
"RingEquiv.instEquivLike",
"WithVal.instAdd",
"IsDedekindDomain.HeightOneSpectrum",
"IsTopologicalDivision... | true |
Subfield.relrank.eq_1 | Mathlib.FieldTheory.Relrank | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Subfield.relrank",
"Subfield.toAlgebra",
"Semiring.toModule",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"Subfield.relrank._proof_1",
"Cardinal",
"IntermediateField",
"IntermediateField.toField",
"Subfield.relrank._proof_2",
"Membership.m... | true |
Lean.Server.Completion.ContextualizedCompletionInfo.mk._flat_ctor | Lean.Server.Completion.CompletionUtils | [
"Lean.Server.Completion.HoverInfo",
"Lean.Elab.CompletionInfo",
"Lean.Elab.ContextInfo",
"Lean.Server.Completion.ContextualizedCompletionInfo",
"Lean.Server.Completion.ContextualizedCompletionInfo.mk"
] | false |
List.toAssocList'._sunfold | Lean.Data.AssocList | [
"Lean.AssocList.nil",
"Lean.AssocList.cons",
"List.toAssocList'",
"_private.Lean.Data.AssocList.0.List.toAssocList'.match_1",
"List",
"Unit",
"Lean.AssocList",
"Prod"
] | false |
SymmetricAlgebra.algHom._proof_1 | Mathlib.LinearAlgebra.SymmetricAlgebra.Basic | [
"instSMulOfMul",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"IsScalarTower",
"MulOne.toMul",
"IsScalarTower.left",
"AddCommMonoid",
"CommSemiring",
"MulOneClass.toMulOne",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMono... | false |
Lean.Compiler.LCNF.JoinPointCommonArgs.AnalysisCtx._sizeOf_inst | Lean.Compiler.LCNF.JoinPoints | [
"Lean.Compiler.LCNF.JoinPointCommonArgs.AnalysisCtx._sizeOf_1",
"Lean.Compiler.LCNF.JoinPointCommonArgs.AnalysisCtx",
"SizeOf.mk",
"SizeOf"
] | false |
IsLocalization.Away.exists_isIntegral_mul_of_isIntegral_algebraMap | Mathlib.RingTheory.Localization.Integral | [
"Subalgebra.instSetLike",
"Nontrivial",
"Eq.mpr",
"Polynomial.C",
"RingHom.instRingHomClass",
"Polynomial.Monic.leadingCoeff_C_mul",
"CommRing",
"Polynomial.aeval_map_algebraMap",
"integralClosure.AlgebraIsIntegral",
"instHSMul",
"AlgHom.algHomClass",
"HMul.hMul",
"IsScalarTower.right",
"I... | true |
CompositionSeries.Equivalent.trans | Mathlib.Order.JordanHolder | [
"Lattice",
"Exists.choose_spec",
"Equiv.instEquivLike",
"Fin.succ",
"Equiv.trans",
"CompositionSeries",
"setOf",
"Equiv",
"RelSeries.length",
"Prod.mk",
"JordanHolderLattice.iso_trans",
"JordanHolderLattice.Iso",
"JordanHolderLattice",
"Exists.intro",
"RelSeries.toFun",
"Exists.choose"... | true |
Filter.EventuallyLE.rfl | Mathlib.Order.Filter.Basic | [
"Preorder.toLE",
"Filter.EventuallyLE.refl",
"Filter.EventuallyLE",
"Filter",
"Preorder"
] | true |
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