name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
self_le_mul_right | Mathlib.Algebra.Order.Monoid.Canonical.Defs | [
"HMul.hMul",
"Mul",
"CanonicallyOrderedMul",
"LE.le",
"LE",
"le_self_mul",
"instHMul"
] | true |
MulAction.fixedBy_one_eq_univ | Mathlib.GroupTheory.GroupAction.FixedPoints | [
"Iff.mpr",
"Monoid",
"MulOne.toOne",
"Monoid.toMulOneClass",
"Set.univ",
"Set.eq_univ_iff_forall",
"MulAction.fixedBy",
"Membership.mem",
"one_smul",
"MulOneClass.toMulOne",
"MulAction",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"Set.instMembership",
"Set"
] | true |
_private.Init.Data.Nat.Div.Lemmas.0.Nat.add_div_of_dvd_add_add_one._proof_1_1 | Init.Data.Nat.Div.Lemmas | [
"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",
"Lean.Omega.combo_s... | false |
LipschitzWith.uniformEquicontinuous | Mathlib.Topology.MetricSpace.UniformConvergence | [
"UniformContinuous",
"Eq.mpr",
"LipschitzWith",
"Equiv.instEquivLike",
"congrArg",
"UniformFun.instPseudoEMetricSpace",
"Function.swap",
"Function.comp",
"Eq.mp",
"id",
"Equiv",
"UniformFun.uniformSpace",
"NNReal",
"UniformFun.lipschitzWith_ofFun_iff",
"PseudoEMetricSpace",
"LipschitzW... | true |
AlgebraicGeometry.Scheme.IdealSheafData.radical_mul | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"AlgebraicGeometry.Scheme",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Opposite",
"HMul.hMul",
"CommRingCat.carrier",
"CommRing.toNonUnitalCommRing",
"AlgebraicGeometry.PresheafedSpace.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"congrArg",
"CommSemiring.toSe... | true |
FunLike.subNegZeroMonoid._proof_5 | Mathlib.Data.FunLike.Group | [
"instHSMul",
"IsSMulApply",
"SMul",
"FunLike.coe_smul'",
"AddMonoid.toNSMul",
"SubNegZeroMonoid.toSubNegMonoid",
"SubNegZeroMonoid",
"Nat",
"Pi.instSMul",
"HSMul.hSMul",
"SubNegMonoid.toAddMonoid",
"Eq",
"DFunLike.coe",
"FunLike"
] | false |
CStarMatrix.instNormedAddCommGroup._proof_12 | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"CStarMatrix.toCLM._proof_5",
"Pi.uniformSpace",
"Pi.Function.module",
"CStarMatrix.instModule",
"NegZeroClass.toNeg",
"Real",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"instSMulOfMul",
"Dist.mk",
"AddCommGroup.toAddCommMonoid",
"WithCStarModule.instCStarModule",
"CStarMatrix.toCLM",
"N... | false |
MaximalFor.not_gt | Mathlib.Order.Minimal | [
"Preorder.toLT",
"MaximalFor",
"MaximalFor.not_prop_of_gt",
"Preorder.toLE",
"LT.lt",
"Not",
"Preorder"
] | true |
CategoryTheory.MonoidalCategory.DayConvolution.hexagon_reverse | Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided | [
"CategoryTheory.MonoidalCategory.DayConvolution.convolution",
"CategoryTheory.BraidedCategory.braiding_tensor_right_hom",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory.DayConvolution",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Categor... | true |
Matrix.transposeRingEquiv._proof_2 | Mathlib.Data.Matrix.Basic | [
"Matrix.add",
"Matrix",
"MulOpposite",
"MulOpposite.opAddEquiv",
"Equiv.toFun",
"AddCommMonoid",
"instHAdd",
"MulOpposite.instAdd",
"HAdd.hAdd",
"AddEquiv.trans",
"AddEquiv.map_add'",
"AddCommSemigroup.toAddCommMagma",
"AddEquiv.toEquiv",
"AddCommMonoid.toAddCommSemigroup",
"Eq",
"Matr... | false |
RingCat.Colimits.instRingColimitType._proof_8 | Mathlib.Algebra.Category.Ring.Colimits | [
"RingCat.Colimits.Prequotient.one",
"CategoryTheory.Functor",
"Mul.mk",
"HMul.hMul",
"Quot.sound",
"Quot.map₂",
"AddGroupWithOne.toAddMonoidWithOne",
"RingCat.Colimits.Relation.mul_1",
"Quot.inductionOn",
"RingCat.Colimits.colimitSetoid",
"CategoryTheory.SmallCategory",
"RingCat.Colimits.Prequ... | false |
Batteries.Tactic.GeneralizeProofs.AContext.depth | Batteries.Tactic.GeneralizeProofs | [
"Nat",
"Batteries.Tactic.GeneralizeProofs.AContext"
] | true |
_private.Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2.0.MeasureTheory.inner_condExpL2_eq_inner_fun._simp_1_2 | Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2 | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"Submodule.starProjection",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"Submodule.addCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Submodule.HasOrthogonalProje... | false |
CategoryTheory.MonoidalCategory.tensorIso_def | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.MonoidalCategory.tensorIso",
"CategoryTheory.MonoidalCategory.whiskerLeftIso",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.whiskerRightIso",
"CategoryTheory.Iso",
"CategoryTheory.MonoidalCategory.tensorHom_def",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
... | true |
Mathlib.Tactic.ITauto.Proof.intro | Mathlib.Tactic.ITauto | [
"Mathlib.Tactic.ITauto.Proof.intro",
"Mathlib.Tactic.ITauto.Proof",
"Lean.Name"
] | true |
ENNReal.logOrderIso_symm | Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp | [
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"OrderIso",
"OrderIso.symm",
"ENNReal.logOrderIso",
"ENNReal.instLE",
"ENNReal",
"instPartialOrderEReal",
"Eq",
"rfl",
"EReal.expOrderIso"
] | true |
_private.Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic.0.vectorSpan_range_eq_span_range_vsub_left_ne._simp_1_4 | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | [
"Membership.mem",
"Set.instSingletonSet",
"Set.mem_singleton_iff",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimTargetInfo.expr | Lean.Elab.Tactic.Induction | [
"Lean.Expr",
"_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimTargetInfo"
] | true |
_private.Mathlib.NumberTheory.Harmonic.Bounds.0.harmonic_le_one_add_log._simp_1_3 | Mathlib.NumberTheory.Harmonic.Bounds | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"IsOrderedRing",
"Nat.cast_nonneg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LE.le",
"Nat.cast",
"Nat",
"True",
"eq_true",
"Semiring",
"Zero.toOfNat0",
... | false |
Mathlib.Tactic.FieldSimp.DenomCondition.none.sizeOf_spec | Mathlib.Tactic.FieldSimp | [
"Mathlib.Tactic.FieldSimp.DenomCondition.none",
"Lean.Expr.const",
"Mathlib.Tactic.FieldSimp.DenomCondition",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Mathlib.Tactic.FieldSimp.DenomCondition._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"Lean.Expr.app",
"Eq.refl",
... | true |
CategoryTheory.Functor.Monoidal.ε_η._autoParam | Mathlib.CategoryTheory.Monoidal.Functor | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Array.count_pos_iff | Init.Data.Array.Count | [
"congrArg",
"Array.instMembership",
"LawfulBEq",
"Membership.mem",
"Exists",
"Array.countP_pos_iff._simp_1",
"instOfNatNat",
"_private.Init.Data.Array.Count.0.Array.count_pos_iff._simp_1_3",
"Array",
"iff_self",
"Bool.true",
"funext",
"And",
"BEq.beq",
"Iff",
"Array.countP",
"Nat",
... | true |
CategoryTheory.Limits.Pi.ι_π_eq_id | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"Function.update",
"CategoryTheory.Limits.HasProduct",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.Pi.ι",
"Quiver.Hom",
"CategoryTheory.Limits.F... | true |
Lean.Parser.ParserExtension.Entry.parser.sizeOf_spec | Lean.Parser.Extension | [
"Lean.Parser.ParserExtension.Entry",
"Lean.Parser.Parser",
"Lean.Parser.ParserExtension.Entry.parser",
"instOfNatNat",
"Lean.Parser.Parser._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"Lean.Name",
"Eq.refl",
"instSizeOfNat",... | true |
continuous_sup | Mathlib.Topology.Order.Lattice | [
"Continuous",
"instTopologicalSpaceProd",
"ContinuousSup.continuous_sup",
"Max",
"Prod.fst",
"TopologicalSpace",
"Max.max",
"ContinuousSup",
"Prod",
"Prod.snd"
] | true |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.induct_roo_left._proof_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"Lean.Omega.Int.ofNat_sub_sub",
"HSub.hSub",
"Lean.Omega.Int.ofNat_... | false |
Lean.Meta.Grind.Clean.State.rec | Lean.Meta.Tactic.Grind.Types | [
"Lean.PHashMap",
"Lean.Meta.Grind.Clean.State.mk",
"Lean.PHashSet",
"Nat",
"Lean.Meta.Grind.Clean.State",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | false |
IsLocalization.Away.algebraMap_pow_isUnit | Mathlib.RingTheory.Localization.Away.Basic | [
"Algebra.algebraMap",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"IsLocalization.Away",
"IsUnit",
"Algebra",
"RingHom",
"Membership.mem",
"instOfNatNat",
"IsUnit.pow",
"Subtype.mk",
"Monoid.toPow",
"CommSemiring",
"RingHom.instFunLike",
"HPow.hPow",
"pow_one",
"... | true |
Filter.mem_prod_top | Mathlib.Order.Filter.Prod | [
"Filter.instMembership",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Set.univ",
"Filter.mem_prod_principal",
"setOf",
"Membership.mem",
"Filter.principal_univ",
"id",
"_private.Mathlib.Order.Filter.Prod.0.Filter.mem_prod_top._simp_1_1",
"Prod.mk",
"iff_self",
"_private.Mathlib.Order.Filter.Prod.... | true |
CategoryTheory.Mon.instSymmetricCategory._proof_7 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.BraidedCategory.braiding_tensor_right_hom",
"CategoryTheory.Category.assoc",
"CategoryTheory.MonObj.instIsMonHomHomBraiding",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Cat... | false |
MonoidWithZeroHom.ValueGroup₀.mk | Mathlib.Algebra.GroupWithZero.Range | [
"GroupWithZero.toMonoidWithZero",
"Membership.mem",
"Units",
"Subtype",
"Subgroup",
"Units.instGroup",
"MonoidWithZeroHom.ValueGroup₀.mk._proof_2",
"dite",
"MonoidWithZeroHomClass",
"WithZero.instZero",
"MonoidWithZeroHom.ValueGroup₀",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
... | true |
uniformity_hasBasis_closed | Mathlib.Topology.UniformSpace.Basic | [
"Filter.instMembership",
"Iff.mpr",
"UniformSpace",
"Eq.mpr",
"SetRel",
"congrArg",
"Set.Subset.trans",
"subset_closure",
"Set.iInter",
"uniformity",
"setOf",
"instTopologicalSpaceProd",
"closure_eq_uniformity",
"Membership.mem",
"Exists",
"id",
"HasSubset.Subset",
"SetRel.comp",
... | true |
_private.Mathlib.SetTheory.Cardinal.Finite.0.ENat.card_pos._simp_1_2 | Mathlib.SetTheory.Cardinal.Finite | [
"CommSemiring.toSemiring",
"Ne",
"ENat",
"propext",
"instCommSemiringENat",
"Nonempty",
"Zero.toOfNat0",
"ENat.card_ne_zero_iff_nonempty",
"OfNat.ofNat",
"ENat.card",
"Eq",
"MulZeroClass.toZero",
"instMulZeroClassOfSemiring"
] | false |
instInhabitedRingInvo | Mathlib.RingTheory.RingInvo | [
"CommRing",
"RingInvo",
"CommSemiring.toSemiring",
"CommRing.toCommSemiring",
"Inhabited",
"RingInvo.id",
"Inhabited.mk"
] | true |
_private.Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong.0._auto_80 | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Mathlib.Tactic.BicategoryCoherence.liftHom₂AssociatorHom | Mathlib.Tactic.CategoryTheory.BicategoryCoherence | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.FreeBicategory.of",
"Mathlib.Tactic.BicategoryCoherence.LiftHom",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.BicategoryCoherence.LiftHom₂.mk",
"CategoryTheory.FreeBicategory.bicategory",
"Mathlib.Tactic.Bicatego... | true |
List.replace_of_not_mem | Init.Data.List.Lemmas | [
"False",
"eq_false",
"congrArg",
"False.elim",
"List.filter.match_1",
"LawfulBEq",
"Membership.mem",
"Eq.mp",
"id",
"List.rec",
"List.replace",
"List.cons",
"Bool.true",
"List",
"And",
"BEq.beq",
"Unit",
"not_or._simp_1",
"List.instMembership",
"List.mem_cons._simp_1",
"_priv... | true |
Lean.Lsp.instFromJsonResolveSupport | Lean.Data.Lsp.Basic | [
"Lean.Lsp.ResolveSupport",
"Lean.FromJson",
"Lean.FromJson.mk",
"Lean.Lsp.instFromJsonResolveSupport.fromJson"
] | true |
Lean.Elab.Term.LValResolution.projIdx | Lean.Elab.App | [
"Lean.Elab.Term.LValResolution.projIdx",
"Lean.Elab.Term.LValResolution",
"Nat",
"Lean.Name"
] | true |
pow_succ_pos._simp_1 | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"Preorder.toLT",
"MulZeroClass.toMul",
"PartialOrder.toPreorder",
"PartialOrder",
"instOfNatNat",
"Monoid.toPow",
"instHAdd",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"eq_true",
"PosMulStrictMono",
"instAddNat",
"Zero.t... | false |
FirstOrder.Language.Substructure.map_strictMono_of_injective | Mathlib.ModelTheory.Substructures | [
"StrictMono",
"PartialOrder.toPreorder",
"FirstOrder.Language.Hom",
"FirstOrder.Language.Substructure",
"FirstOrder.Language.Structure",
"GaloisCoinsertion.strictMono_l",
"FirstOrder.Language.Substructure.gciMapComap",
"FirstOrder.Language",
"FirstOrder.Language.Substructure.instPartialOrder",
"Fu... | true |
Std.Tactic.BVDecide.BVExpr.bin.injEq | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"Std.Tactic.BVDecide.BVExpr.bin",
"Std.Tactic.BVDecide.BVBinOp",
"Eq.propIntro",
"Lean.injEq_helper",
"And",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Std.Tactic.BVDecide.BVExpr",
"Std.Tactic.BVDecide.BVExpr.bin.inj",
"Eq"
] | true |
sdiff_inf_right_comm | Mathlib.Order.BooleanAlgebra.Basic | [
"Eq.mpr",
"congrArg",
"id",
"SemilatticeInf.toMin",
"GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra",
"inf_comm",
"SDiff.sdiff",
"inf_sdiff_assoc",
"GeneralizedBooleanAlgebra",
"Eq.refl",
"GeneralizedCoheytingAlgebra.toLattice",
"GeneralizedBooleanAlgebra.toSDiff",
"Eq",
"Min.min"... | true |
ISize.toNatClampNeg_pos_iff | Init.Data.SInt.Lemmas | [
"ISize.toNatClampNeg_eq_zero_iff._simp_1",
"instLTISize",
"congrArg",
"instLEISize",
"Ne",
"instOfNatNat",
"LE.le",
"_private.Init.Data.SInt.Lemmas.0.ISize.toNatClampNeg_pos_iff._simp_1_1",
"iff_self",
"Iff",
"ISize.not_le._simp_1",
"ISize.instOfNat",
"Nat",
"LT.lt",
"True",
"of_eq_tru... | true |
Int.fmod_eq_fmod_iff_fmod_sub_eq_zero | Init.Data.Int.DivMod.Lemmas | [
"Int.fmod_sub_cancel_right",
"congrArg",
"HSub.hSub",
"Int.zero_fmod",
"Int",
"Int.fmod",
"iff_self",
"Iff",
"instHSub",
"instOfNat",
"True",
"Int.sub_self",
"Iff.trans",
"of_eq_true",
"Int.instSub",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Iff.symm",
"Eq.trans"
] | true |
_private.Lean.Elab.PreDefinition.WF.PackMutual.0.Lean.Elab.WF.packCalls.match_1 | Lean.Elab.PreDefinition.WF.PackMutual | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Nat",
"_private.Lean.Elab.PreDefinition.WF.PackMutual.0.Lean.Elab.WF.packCalls._sparseCasesOn_1",
"Option"
] | false |
CategoryTheory.ObjectProperty.IsTriangulated.rec | Mathlib.CategoryTheory.Triangulated.Subcategory | [
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Preadditive",
"CategoryTheory.ObjectProperty.IsStableUnderShift",
"CategoryTheory.ObjectProperty.IsTriangulated",
"CategoryTheory.ObjectProperty.IsTriangulatedClosed₂",
"CategoryTheory.Limit... | false |
_private.Mathlib.ModelTheory.Types.0.FirstOrder.Language.Theory.CompleteType.typesWith_inf._simp_1_4 | Mathlib.ModelTheory.Types | [
"And",
"propext",
"Eq.symm",
"Eq",
"forall_and"
] | false |
Std.Tactic.BVDecide.BVLogicalExpr.eval_ite | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"cond",
"Std.Tactic.BVDecide.BoolExpr",
"Std.Tactic.BVDecide.BoolExpr.ite",
"Bool",
"Std.Tactic.BVDecide.BVLogicalExpr.eval",
"Std.Tactic.BVDecide.BVExpr.Assignment",
"Eq",
"rfl",
"Std.Tactic.BVDecide.BVPred"
] | true |
TProd.instMeasurableSpace._sunfold | Mathlib.MeasureTheory.MeasurableSpace.Constructions | [
"TProd.instMeasurableSpace.match_1",
"MeasurableSpace",
"List",
"Unit",
"TProd.instMeasurableSpace",
"PUnit",
"PUnit.instMeasurableSpace",
"List.TProd",
"Prod",
"List.foldr",
"Prod.instMeasurableSpace"
] | false |
Set.functorToTypes._proof_4 | Mathlib.CategoryTheory.Types.Set | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"Set.functorToTypes.match_1",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"TypeCat.ofHom",
"Set.Elem",
"id",
"Preorder.smallCategory",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlg... | false |
FinBoolAlg._sizeOf_inst | Mathlib.Order.Category.FinBoolAlg | [
"FinBoolAlg",
"FinBoolAlg._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor.recOn | Mathlib.Tactic.Linarith.Datatypes | [
"Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor",
"Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor.mk",
"Mathlib.Tactic.Linarith.PreprocessorBase",
"Lean.MVarId",
"Lean.Expr",
"Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor.rec",
"Lean.Meta.MetaM",
"List",
"Mathlib.Tactic.Linarith.Bran... | false |
_private.Lean.Elab.BuiltinDo.For.0.Lean.Elab.Do.elabDoFor.match_9 | Lean.Elab.BuiltinDo.For | [
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn",
"Option"
] | false |
mdifferentiableWithinAt_congr_set' | Mathlib.Geometry.Manifold.MFDeriv.Basic | [
"Eq.mpr",
"NormedSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Compl.compl",
"instAddCommGroupTangentSpace",
"nhdsWithin",
"NormedField.toField",
"Exists",
"Filter.EventuallyEq",
"Set.instSingletonSet",
"id",
"instModuleTangentSpace",
"Set.instCompl",
"Field.toSemifield",
"instT... | true |
AlgebraicTopology.DoldKan.Γ₀.Obj.summand | Mathlib.AlgebraicTopology.DoldKan.FunctorGamma | [
"ChainComplex",
"Opposite",
"CategoryTheory.Epi",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SimplicialObject.Splitting.IndexSet",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
"Subty... | true |
MonoidAlgebra.liftNCRingHom._proof_3 | Mathlib.Algebra.MonoidAlgebra.Lift | [
"MonoidAlgebra.addCommMonoid",
"Finsupp.instFunLike",
"Monoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"MonoidAlgebra.liftNC_mul",
"HMul.hMul",
"MonoidHom",
"AddMonoidHomClass.toAddMonoidHom",
"Monoid.toMulOneClass",
"Finset",
"Add... | false |
Std.TreeSet.min?_le_of_contains | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"Std.TreeSet.min?",
"Ordering",
"Std.TreeSet.inner",
"Std.TransCmp",
"Std.TreeSet.isSome_min?_of_contains",
"Std.TreeSet.contains",
"Bool.true",
"Unit",
"Std.TreeMap.minKey?_le_of_contains",
"Option.get",
"Bool",
"Ordering.isLE",
"Eq"
] | true |
OreLocalization.add_assoc | Mathlib.RingTheory.OreLocalization.Basic | [
"Monoid",
"Eq.mpr",
"instHSMul",
"Submonoid.mul",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Monoid.toMulOneClass",
"congrArg",
"OreLocalization.OreSet",
"DistribMulAction.toDistribSMul",
"add_assoc",
"OreLocalization",
"OreLocalization.ind",
"AddMonoid.toAddZeroClass",
"Membership.mem",
... | true |
Complex.exp_int_mul_two_pi_mul_I | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Int.cast",
"Real.pi",
"HMul.hMul",
"Complex.commRing",
"Complex.exp_zero",
"Nat.instAtLeastTwoHAddOfNat",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Complex.instMul",
"Complex.exp_periodic",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"instOfNatNat",
"Int",
"AddGroupWithOne.toInt... | true |
_private.Std.Data.DTreeMap.Internal.Balancing.0.Std.DTreeMap.Internal.Impl.balanceR.match_1.eq_4 | Std.Data.DTreeMap.Internal.Balancing | [
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.BalanceLPrecond",
"Std.DTreeMap.Internal.Impl.balanceR.match_1",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | true |
CategoryTheory.Cat.FreeRefl.instUnique._proof_3 | Mathlib.CategoryTheory.Category.ReflQuiv | [
"Inhabited.default",
"CategoryTheory.Quotient",
"Unique",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.instUniquePaths",
"CategoryTheory.Cat.FreeRefl.instUnique._aux_1",
"CategoryTheory.Cat.FreeRefl",
"CategoryTheory.ReflQuiver.toQuiver",
"CategoryTheory.ReflQuiver... | false |
_private.Mathlib.Data.Int.CardIntervalMod.0.Nat.Ico_filter_modEq_cast._simp_1_3 | Mathlib.Data.Int.CardIntervalMod | [
"Preorder.toLT",
"Finset",
"Preorder.toLE",
"Membership.mem",
"Finset.Ico",
"LE.le",
"And",
"Finset.instSetLike",
"LT.lt",
"propext",
"LocallyFiniteOrder",
"Eq",
"SetLike.instMembership",
"Preorder",
"Finset.mem_Ico"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Reproducing.0.RKHS.posSemidef_tfae.match_1_1 | Mathlib.Analysis.InnerProductSpace.Reproducing | [
"And.casesOn",
"And",
"And.intro"
] | false |
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0.CategoryTheory.ComposableArrows.homMk₄_app_three._proof_1 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonneg_of_le",
"instOfNatNat",
"Int",
"Nat.cast... | false |
_private.Lean.Elab.Extra.0.Lean.Elab.Term.elabForIn.match_1 | Lean.Elab.Extra | [
"Unit.unit",
"Lean.LOption.undef",
"Lean.Expr",
"Lean.LOption.some",
"Lean.LOption.none",
"Lean.LOption.casesOn",
"Unit",
"Lean.LOption"
] | false |
_private.Lean.PrettyPrinter.Formatter.0.Lean.PrettyPrinter.Formatter.withMaybeTag.match_4 | Lean.PrettyPrinter.Formatter | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"String.Pos.Raw",
"_private.Lean.PrettyPrinter.Formatter.0.Lean.PrettyPrinter.Formatter.withMaybeTag._sparseCasesOn_4",
"Option"
] | false |
_private.Mathlib.Geometry.Manifold.VectorField.Pullback.0.VectorField.mpullback_zero._simp_1_1 | Mathlib.Geometry.Manifold.VectorField.Pullback | [
"NormedSpace",
"VectorField.mpullbackWithin",
"Set.univ",
"VectorField.mpullbackWithin_univ",
"TopologicalSpace",
"ModelWithCorners",
"VectorField.mpullback",
"TangentSpace",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"Eq.symm",
"NormedAddCommGroup.toSeminormedAddCommG... | false |
CategoryTheory.Functor.mapSquare._proof_6 | Mathlib.CategoryTheory.Square | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Square.category",
"CategoryTheory.Square.f₂₄",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Square.Hom.τ₁",
"CategoryTheory.Square.Hom.τ₄",
"CategoryTheory.Functor.mapSquare._proof_4",
"CategoryTheory.Cate... | false |
PartOrdEmb.hasForgetToPartOrd._proof_4 | Mathlib.Order.Category.PartOrdEmb | [
"PartOrd.instConcreteCategoryOrderHomCarrier",
"PartOrdEmb.hasForgetToPartOrd._proof_2",
"CategoryTheory.Functor",
"PartOrdEmb.str",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartOrd.instCategory",
"CategoryTheory.Functor.mk",
"PartOrd.str",
"PartialOrder.toPreorder",
"CategoryThe... | false |
Filter.ker_surjective | Mathlib.Order.Filter.Ker | [
"PartialOrder.toPreorder",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"CompleteBooleanAlgebra.toCompleteLattice",
"Filter.principal",
"Filter.gi_principal_ker",
"Function.Surjective",
"GaloisCoinsertion.u_surjective",
"CompleteAtomicBooleanAlgebra.toComplete... | true |
MeasureTheory.Lp.smul_neg | Mathlib.MeasureTheory.Function.Holder | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"MeasureTheory.Measure",
"NormedRing.toRing",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"Module.toMulActionWithZero",
"AddCommGroup.toAddGroup... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.bicoloring_of_even._simp_4 | Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions | [
"instNeZeroNatHAdd_1",
"Fin.instSub",
"SimpleGraph.Adj",
"HSub.hSub",
"SimpleGraph.cycleGraph",
"Fin.instOfNat",
"instOfNatNat",
"SimpleGraph.cycleGraph_adj",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"propext",
"instAddNat",
"Or",
"OfNat.ofNat",
"Fin",
"E... | false |
Lean.Lsp.SymbolTag.deprecated | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolTag.deprecated",
"Lean.Lsp.SymbolTag"
] | true |
Con.subgroup_quotientGroupCon | Mathlib.GroupTheory.QuotientGroup.Defs | [
"Con.mk",
"Con.rel_mk._simp_2",
"Subgroup.instSubgroupClass",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"QuotientGroup.leftRel",
"MulOne.toM... | true |
WeierstrassCurve.map_preΨ₄ | Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Basic | [
"Polynomial.C",
"RingHom.instRingHomClass",
"CommRing",
"Polynomial.map_mul",
"RingHomClass.toAddMonoidHomClass",
"HMul.hMul",
"map_sub",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"HSub.hSub",
"WeierstrassCurve.map_b₈",
"RingHom",
"Polynomial.map_pow",
"Polynom... | true |
nsmulBinRec.go_spec | Mathlib.Algebra.Group.Defs | [
"cond",
"Nat.bit",
"Eq.mpr",
"False",
"HMul.hMul",
"_private.Mathlib.Algebra.Group.Defs.0.nsmulBinRec.go_spec._proof_1_6",
"nsmulRec'",
"congrArg",
"add_assoc",
"nsmulBinRec.go",
"False.elim",
"Eq.mp",
"not_true_eq_false",
"id",
"Ne",
"instMulNat",
"instOfNatNat",
"AddSemigroup",
... | true |
Std.TreeSet.insertMany_list_equiv_foldl | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"Eq.mpr",
"Unit.unit",
"Std.TreeMap.insertIfNew",
"Std.TreeMap.Equiv",
"List.foldl_hom",
"congrArg",
"instForInOfForIn'",
"Ordering",
"Std.TreeSet.insert",
"inferInstance",
"Std.TreeSet.inner",
"id",
"List.foldl",
"Id",
"Membership",
"List",
"Unit",
"List.instMembe... | true |
Plausible.Configuration.quiet | Plausible.Testable | [
"Plausible.Configuration",
"Bool"
] | true |
FixedPoints.instAlgebraSubtypeMemSubfieldSubfield | Mathlib.FieldTheory.Fixed | [
"Monoid",
"Subfield.toAlgebra",
"Subfield.instSubfieldClass",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"inferInstance",
"Subtype",
"Subfield.instSetLike",
"CommRing.toNonAssocCommRing",
"Field.toSemifield",
"Field.toCommRing",
"Semifield.toDivisionSemiring",
"FixedPoints.instAl... | true |
Std.Internal.List.getValueD_filter_not_contains_of_contains_right | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"Bool.not",
"List.contains",
"Std.Internal.List.getValueD_eq_fallback",
"Sigma.fst",
"Bool.true",
"List",
"EquivBEq",
"List.filter",
"Bool",
"Std.Internal.List.containsKey_filter_not_contains_of_contains_right",
"BEq",
"Eq",
"Std.Internal.List.getValueD",
... | true |
Units.map._proof_4 | Mathlib.Algebra.Group.Units.Hom | [
"Monoid",
"Units.val",
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Units",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Units.instGroup",
"Group.toDivInvMonoid",
"map_mul",
"MulOneClass.toMulOne",
"True",
"Units... | false |
_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_5 | Mathlib.Data.List.NodupEquivFin | [
"StrictMono",
"Lean.Grind.nestedProof",
"_private.Mathlib.Data.List.NodupEquivFin.0.List.sublist_iff_exists_fin_orderEmbedding_get_eq._proof_1_4",
"Lean.Grind.Nat.lt_eq",
"Fin.mk",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"dite",
"instLEFin",
"List",
"instHAdd",
"RelEmbedding",
"... | false |
DedekindCut.instCompleteLinearOrder._proof_7 | Mathlib.Order.Completion | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"inferInstance",
"DistribLattice.toLattice",
"DedekindCut",
"LE.le",
"CompleteLattice.toSupSet",
"CompleteLattice.isLUB_sSup",
"IsLUB",
"Semi... | false |
CategoryTheory.Equivalence.unitIso_hom_app_comp_inverse_map_η_functor_assoc | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.Equival... | true |
Lean.Meta.Grind.Arith.Cutsat.UnsatProof.ctorElimType | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"cond",
"Lean.Meta.Grind.Arith.Cutsat.UnsatProof.dvd",
"Nat.ble",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstr",
"PULift",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstr",
"Lean.Meta.Grind.Arith.Cutsat.UnsatProof.cooper",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstr",
"Nat",
"Lean.Meta.Grind.Arith.Cutsat.UnsatProof"... | false |
Std.DHashMap.getD_eq_fallback | Std.Data.DHashMap.Lemmas | [
"Eq.mpr",
"congrArg",
"LawfulBEq",
"Membership.mem",
"id",
"Std.DHashMap.instMembership",
"Bool.true",
"Std.DHashMap.contains",
"Std.DHashMap.getD_eq_fallback_of_contains_eq_false",
"implies_congr",
"Bool.not_eq_true",
"Std.DHashMap.getD",
"Bool",
"_private.Std.Data.DHashMap.Lemmas.0.Std.D... | true |
AlgebraicGeometry.PresheafedSpace.isIso_of_components | Mathlib.Geometry.RingedSpace.PresheafedSpace | [
"CategoryTheory.IsIso",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopCat.instCategory",
"TopCat.instCategoryPresheaf",
"TopCat.Presheaf",
"CategoryTheory.Iso.isIso_hom",
"CategoryTheory.Iso.symm",
"AlgebraicGeometry.PresheafedSpace.isoOfC... | true |
Lean.Meta.Grind.SavedState | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.SavedState.mk"
] | true |
WithLp.toLp_zero | Mathlib.Analysis.Normed.Lp.WithLp | [
"WithLp",
"WithLp.instAddCommGroup",
"WithLp.toLp",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"ENNReal",
"Zero.toOfNat0",
"AddCommGroup.toDivisionAddCommMonoid",
"OfNat.ofNat",
"NegZeroClass.toZero",
... | true |
HasCompactMulSupport.sup | Mathlib.Topology.Algebra.Order.Support | [
"Eq.mpr",
"mulTSupport.eq_1",
"One",
"congrArg",
"HasCompactMulSupport",
"Set.instUnion",
"SemilatticeSup.toMax",
"id",
"closure_mono",
"isClosed_mulTSupport",
"HasSubset.Subset",
"closure_union",
"TopologicalSpace",
"IsCompact.of_isClosed_subset",
"closure",
"Pi.instMaxForall_mathlib"... | true |
IsLUB.exists_between_sub_self' | Mathlib.Algebra.Order.Group.Bounds | [
"IsLUB.exists_between'",
"Preorder.toLT",
"AddCommGroup.toAddCommMonoid",
"instIsLeftCancelAddOfAddLeftReflectLE",
"sub_lt_self",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"Semi... | true |
Lean.Meta.SparseCasesOnInfo.rec | Lean.Meta.Constructions.SparseCasesOn | [
"Lean.Meta.SparseCasesOnInfo",
"Array",
"Nat",
"Lean.Meta.SparseCasesOnInfo.mk",
"Lean.Name"
] | false |
_private.Lean.Elab.DocString.0.Lean.Doc.initFn._@.Lean.Elab.DocString.2101956971._hygCtx._hyg.2 | Lean.Elab.DocString | [
"Pure.pure",
"Lean.instBEqFVarId",
"Lean.TSyntax",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Inhabited.default",
"Lean.findInternalDocString?",
"Array.mkEmpty",
"Lean.NameMap",
"Lean.VersoDocString",
"Lean.Syntax.matchesIdent",
"Lean.Name.mkNum",
"L... | false |
fderiv_tsum_apply | Mathlib.Analysis.Calculus.SmoothSeries | [
"Differentiable",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"NormedAddCommGroup.toMetricSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoi... | true |
_private.Init.Data.Array.Find.0.Array.idxOf?.eq_1 | Init.Data.Array.Find | [
"Fin.val",
"Array",
"Option.map",
"Nat",
"Array.finIdxOf?",
"Eq.refl",
"Array.idxOf?",
"Fin",
"BEq",
"Eq",
"Array.size",
"Option"
] | true |
DirectSum.decompose_of_mem_same | Mathlib.Algebra.DirectSum.Decomposition | [
"Subtype.coe_mk",
"SetLike",
"Eq.mpr",
"DirectSum.Decomposition",
"Equiv.instEquivLike",
"instAddCommMonoidDirectSum",
"DirectSum.decompose_of_mem",
"congrArg",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
"DFinsupp.instDFunLike",
"id",
"Eq... | true |
CategoryTheory.Functor.Faithful.of_comp_eq | Mathlib.CategoryTheory.Functor.FullyFaithful | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.comp",
"Eq.rec",
"CategoryTheory.Functor.Faithful.of_comp",
"Eq.symm",
"Eq",
"CategoryTheory.Functor.Faithful",
"CategoryTheory.Category"
] | true |
Lean.indentExpr | Lean.Message | [
"Lean.MessageData",
"Lean.indentD",
"Lean.Expr",
"Lean.MessageData.ofExpr"
] | true |
CategoryTheory.CostructuredArrow.ofCostructuredArrowProjEquivalence._proof_1 | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Over.forget",
"CategoryTheory.Iso.refl... | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.