name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
WeierstrassCurve.Δ._proof_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
Real.deriv_arccos | Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv | [
"NegZeroClass.toNeg",
"Real",
"instHDiv",
"Semiring.toModule",
"Real.pi",
"Real.arcsin",
"Real.denselyNormedField",
"congrArg",
"deriv",
"Real.instDivInvMonoid",
"Real.instSub",
"NormedSpace.toModule",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedF... | true |
Algebra.TensorProduct.instNonUnitalRing | Mathlib.RingTheory.TensorProduct.Basic | [
"Algebra.TensorProduct.instNonUnitalRing._proof_2",
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"TensorProduct.addCommGroup",
"Algebra.TensorProduct.ins... | true |
QuadraticModuleCat.Hom.mk.injEq | Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat | [
"CommRing",
"Semiring.toModule",
"Eq.propIntro",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"QuadraticModuleCat.Hom.mk.inj",
"QuadraticModuleCat.toModuleCat",
"QuadraticModuleCat",
"QuadraticModuleCat.form",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
... | true |
Std.ExtDHashMap.mem_inter_iff._simp_1 | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Membership.mem",
"LawfulHashable",
"Inter.inter",
"Std.ExtDHashMap.instInterOfEquivBEqOfLawfulHashable",
"And",
"EquivBEq",
"propext",
"Std.ExtDHashMap",
"Hashable",
"BEq",
"Eq",
"Std.ExtDHashMap.mem_inter_iff"
] | false |
CategoryTheory.Pi.closedUnit._proof_2 | Mathlib.CategoryTheory.Pi.Monoidal | [
"CategoryTheory.ihom.coev_naturality",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pi.monoidalCategory",
"congrArg",
"CategoryTheory.ihom.coev",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.comp",
"Categ... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.equiv_iff_toList_perm._simp_1_4 | Std.Data.DTreeMap.Internal.Lemmas | [
"List.Perm",
"Std.DTreeMap.Internal.Impl.Equiv",
"propext",
"Std.DTreeMap.Internal.Impl.toListModel",
"Std.DTreeMap.Internal.Impl.equiv_iff_toListModel_perm",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Sigma"
] | false |
CategoryTheory.Limits.filtered_colim_preservesFiniteLimits_of_types | Mathlib.CategoryTheory.Limits.FilteredColimitCommutesFiniteLimit | [
"CategoryTheory.Limits.Types.hasColimitsOfShape",
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.PreservesFiniteLimits",
"CategoryTheory.Limits.colimitLimitToLimitColimitCone",
"CategoryTheory.Limits.colim",
"CategoryTheory.Iso.instTransIs... | true |
_private.Mathlib.Analysis.Convex.PathConnected.0.Path.range_segment._simp_1_1 | Mathlib.Analysis.Convex.PathConnected | [
"Real",
"Semiring.toModule",
"AffineMap.instFunLike",
"ContinuousSMul",
"AddGroupWithOne.toAddGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AffineMap.lineMap",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Membership.me... | false |
LinearMap.coe_restrictScalars | Mathlib.Algebra.Module.LinearMap.Defs | [
"LinearMap.restrictScalars",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"Semiring.toMonoid",
"Semiring",
"Module.toDistribMulAction",
"SMulZero... | true |
Option.decidableForallMem._proof_1 | Init.Data.Option.Instances | [
"Option.instMembership",
"Membership.mem",
"Option.none",
"Option.decidableForallMem.match_1",
"Option"
] | false |
HomologicalComplex.mapBifunctor₁₂.D₁.congr_simp | Mathlib.Algebra.Homology.BifunctorAssociator | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.functorCategoryPreadditive",
"HomologicalComplex",
"HomologicalComplex.mapBifunctor₁₂.D₁",... | true |
Lean.MessageSeverity.recOn | Lean.Message | [
"Lean.MessageSeverity",
"Lean.MessageSeverity.warning",
"Lean.MessageSeverity.rec",
"Lean.MessageSeverity.information",
"Lean.MessageSeverity.error"
] | false |
Lean.Meta.Grind.Arith.Cutsat.VarInfo.maxDvdCoeff._default | Lean.Meta.Tactic.Grind.Arith.Cutsat.ReorderVars | [
"id",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
AlgebraicTopology.DoldKan.Γ₀.splitting._proof_3 | Mathlib.AlgebraicTopology.DoldKan.FunctorGamma | [
"ChainComplex",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"Opposite",
"Nat.instOne",
"CategoryTheory.SimplicialObject.Splitting.IndexSet",
"CategoryTheory.Limits.hasColimitsOfShape_discrete",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"CategoryT... | false |
CategoryTheory.FreeBicategory.homCategory' | Mathlib.CategoryTheory.Bicategory.Coherence | [
"CategoryTheory.FreeBicategory.homCategory",
"CategoryTheory.FreeBicategory.Hom",
"Quiver",
"CategoryTheory.Category"
] | true |
UInt32.mul_def | Init.Data.UInt.Lemmas | [
"UInt32.toBitVec",
"HMul.hMul",
"BitVec",
"instMulUInt32",
"instOfNatNat",
"UInt32.ofBitVec",
"Nat",
"UInt32",
"OfNat.ofNat",
"Eq",
"BitVec.instMul",
"rfl",
"instHMul"
] | true |
List.findIdx_map | Init.Data.List.Find | [
"cond",
"congrArg",
"List.map",
"Function.comp",
"instOfNatNat",
"List.rec",
"List.cons",
"List",
"instHAdd",
"List.findIdx_cons",
"HAdd.hAdd",
"Nat",
"congr",
"True",
"eq_self",
"List.findIdx",
"Bool",
"of_eq_true",
"instAddNat",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Eq.tra... | true |
Lean.Meta.LazyDiscrTree.InitEntry._sizeOf_1 | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree.InitEntry",
"Lean.LocalContext._sizeOf_inst",
"Lean.LocalInstance",
"Lean.LocalInstance._sizeOf_inst",
"Lean.Expr",
"instOfNatNat",
"Lean.Meta.LazyDiscrTree.InitEntry.rec",
"Array._sizeOf_inst",
"Array",
"instHAdd",
"Lean.Meta.LazyDiscrTree.LazyEntry",
"HAdd.hAdd",
"... | false |
Lean.MonadStateCacheT | Lean.Util.MonadCache | [
"Std.HashMap",
"Hashable",
"StateT",
"BEq"
] | true |
MulHom.coe_ofDense | Mathlib.Algebra.Group.Subsemigroup.Basic | [
"Semigroup",
"MulHom",
"Semigroup.toMul",
"HMul.hMul",
"Membership.mem",
"Subsemigroup.instTop",
"Subsemigroup",
"MulHom.funLike",
"MulHom.ofDense",
"Top.top",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"rfl",
"instHMul",
"Set",
"Subsemigroup.closure"
] | true |
CategoryTheory.Arrow.w_mk_assoc | Mathlib.CategoryTheory.Comma.Arrow | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"congrArg",
"CategoryTheory.Arrow.w_mk",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"congr",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Arrow.Hom.left... | true |
_private.Init.Data.ByteArray.Lemmas.0.ByteArray.data_extract._proof_1_4 | Init.Data.ByteArray.Lemmas | [
"Nat.lt_of_not_le",
"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",
"Int.decLe",
"Lean.Omega.LinearCombo.eval",
... | false |
Submonoid.mem_divPairs | Mathlib.GroupTheory.MonoidLocalization.DivPairs | [
"instHDiv",
"Monoid.toMulOneClass",
"Iff.rfl",
"Submonoid.divPairs",
"Prod.instMulOneClass",
"Membership.mem",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"CommGroup",
"Submonoid.instTop",
"Prod.fst",
"Group.toDivInvMonoid",
"Iff",
"CommMonoid.toMonoid",
"Submonoid.LocalizationMap",
"Submono... | true |
_private.Mathlib.Algebra.Module.FinitePresentation.0.Module.finitePresentation_of_free_of_surjective._simp_1_7 | Mathlib.Algebra.Module.FinitePresentation | [
"Semiring.toModule",
"Finsupp.module",
"LinearMap.instFunLike",
"Function.comp",
"LinearMap",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Finsupp.apply_linearCombination",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"Module",
"E... | false |
_private.Lean.Level.0.Lean.Level.normLtAux._unary._proof_3 | Lean.Level | [
"invImage",
"Nat.lt_add_left_iff_pos._simp_1",
"Lean.Level._sizeOf_inst",
"PSigma.casesOn",
"id",
"Prod.mk",
"instOfNatNat",
"Lean.Level",
"sizeOfWFRel",
"Nat.lt_add_one._simp_1",
"Prod.Lex.right",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"SizeOf.sizeOf",
"PSigma.mk",
"of... | false |
MeasureTheory.FiniteMeasure.coeFn_def | Mathlib.MeasureTheory.Measure.FiniteMeasure | [
"MeasureTheory.FiniteMeasure",
"MeasureTheory.Measure",
"NNReal",
"ENNReal.toNNReal",
"MeasureTheory.FiniteMeasure.instFunLike",
"MeasurableSpace",
"ENNReal",
"MeasureTheory.FiniteMeasure.toMeasure",
"Eq",
"DFunLike.coe",
"rfl",
"MeasureTheory.Measure.instFunLike",
"Set"
] | true |
_private.Mathlib.RingTheory.Extension.Cotangent.Basis.0.Algebra.Generators.exists_presentation_of_basis_cotangent._simp_1_3 | Mathlib.RingTheory.Extension.Cotangent.Basis | [
"Set.range_comp",
"Function.comp",
"Set.image",
"Set.range",
"Eq.symm",
"Eq",
"Set"
] | false |
Quotient.finChoice._proof_2 | Mathlib.Data.Fintype.Quotient | [
"Iff.rfl",
"Membership.mem",
"Subtype.instSetoid_mathlib",
"Subtype",
"List",
"Iff",
"List.instMembership",
"List.isSetoid",
"Setoid.r"
] | false |
_private.Mathlib.RingTheory.Polynomial.UniversalFactorizationRing.0.MvPolynomial.universalFactorizationMapPresentation_jacobian._simp_1_2 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"CommRing",
"Polynomial.resultant.eq_def",
"Polynomial.resultant",
"CommSemiring.toSemiring",
"instDecidableEqFin",
"Polynomial",
"Fin.fintype",
"instHAdd",
"CommRing.toCommSemiring",
"Polynomial.sylvester",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.symm",
"Fin",
"Eq",
"Matrix.det"
] | false |
GrpWithZero.carrier | Mathlib.Algebra.Category.GrpWithZero | [
"GrpWithZero"
] | true |
Std.Do.SPred.exists.match_1 | Std.Do.SPred.SPred | [
"List.cons",
"List",
"List.casesOn",
"Std.Do.SPred",
"List.nil"
] | false |
IsPrimitiveRoot.toRootsOfUnity | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Nat.instMulZeroClass",
"Membership.mem",
"Units",
"Subtype",
"Subgroup",
"Units.instGroup",
"rootsOfUnity",
"CommMonoid.toMonoid",
"Nat",
"rootsOfUnity.mkOfPowEq",
"IsPrimitiveRoot",
"NeZero",
"CommMonoid",
"IsPrimitiveRoot.pow_eq_one",
"SetLike.instMembership",
"Subgroup.instSetLike"... | true |
Mathlib.Meta.NormNum.not_isSquare_of_isNNRat_rat_of_num | Mathlib.Tactic.NormNum.IsSquare | [
"Nat.gcd",
"Int.cast",
"Eq.mpr",
"Nat.Coprime",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Int.cast_natCast",
"False",
"Rat.instMul",
"Rat.num",
"Preorder.toLT",
"instHDiv",
"GroupWithZero.toDivInvMonoid",
"eq_false",
"Nat.gcd_zero_right",
"congrArg",
"Int.instLinearOrder",
"Int.isS... | true |
DFinsupp.lsum_single | Mathlib.LinearAlgebra.DFinsupp | [
"LinearMap.toAddMonoidHom",
"Pi.addCommMonoid",
"DFinsupp.sumAddHom_single",
"congrArg",
"DistribMulAction.toDistribSMul",
"DFinsupp.lsum",
"Pi.module",
"DFinsupp.single",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap... | true |
Lean.Meta.Grind.AC.MonadGetStruct.noConfusionType | Lean.Meta.Tactic.Grind.AC.Util | [
"Lean.Meta.Grind.AC.MonadGetStruct.casesOn",
"Lean.Meta.Grind.AC.MonadGetStruct",
"HEq",
"Lean.Meta.Grind.AC.Struct"
] | false |
_private.Init.Meta.Defs.0.Lean.Name.replacePrefix.match_1 | Init.Meta.Defs | [
"String",
"namedPattern",
"Nat.hasNotBit",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Lean.Name.casesOn",
"_private.Init.Meta.Defs.0.Lean.Name.getRoot._sparseCasesOn_1",
"Nat",
"Lean.Name",
"Eq.refl",
"Eq"
] | false |
Lean.Expr.replace | Lean.Util.ReplaceExpr | [
"Lean.Expr",
"Lean.Expr.replaceImpl",
"Option"
] | true |
Lean.instToJsonPrintImportResult.toJson | Lean.Elab.ParseImportsFast | [
"Lean.Json",
"Lean.Json.mkObj",
"Lean.Json.opt",
"String",
"Lean.PrintImportResult.result?",
"Lean.instToJsonString",
"Lean.ToJson.toJson",
"Prod.mk",
"Lean.PrintImportResult",
"Lean.instToJsonModuleHeader",
"List.cons",
"Array",
"List",
"Lean.ModuleHeader",
"Lean.instToJsonArray",
"Pr... | true |
SemiNormedGrp.of.injEq | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"SeminormedAddCommGroup",
"Eq.propIntro",
"Lean.injEq_helper",
"HEq.homo_ndrec",
"And",
"SemiNormedGrp.of",
"SemiNormedGrp.of.inj",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq",
"SemiNormedGrp"
] | true |
Finset.Ioo_subset_Ioi_self | Mathlib.Order.Interval.Finset.Basic | [
"Eq.mpr",
"Set.Ioi",
"LocallyFiniteOrderTop",
"Finset.Ioi",
"congrArg",
"Finset",
"id",
"Finset.coe_Ioo",
"HasSubset.Subset",
"SetLike.coe",
"Finset.instSetLike",
"Finset.coe_Ioi",
"congr",
"Finset.instHasSubset",
"LocallyFiniteOrder",
"_private.Mathlib.Order.Interval.Finset.Basic.0.Fi... | true |
Lean.Elab.Attribute.name | Lean.Elab.Attributes | [
"Lean.Elab.Attribute",
"Lean.Name"
] | true |
Std.DHashMap.Internal.Raw₀.Const.any_toList | Std.Data.DHashMap.Internal.RawLemmas | [
"Pure.pure",
"Std.DHashMap.Raw.Const.toList",
"Eq.mpr",
"Unit.unit",
"False",
"congrArg",
"instForInOfForIn'",
"Monad.toApplicative",
"Std.DHashMap.Raw",
"Bool.false_eq_true",
"Option.some",
"Membership.mem",
"ForInStep.done",
"inferInstance",
"List.forIn'_cons",
"id",
"instDecidable... | true |
Std.Time.Timestamp.ofPlainDateTimeAssumingUTC | Std.Time.DateTime | [
"Std.Time.PlainDateTime.toTimestampAssumingUTC",
"Std.Time.Timestamp",
"Std.Time.PlainDateTime"
] | true |
CategoryTheory.Abelian.SpectralObject.leftHomologyDataShortComplex._auto_1 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CuspFormClass.rec | Mathlib.NumberTheory.ModularForms.Basic | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"chartedSpaceSelf",
"Complex.instNormedAddCommGroup",
"Matrix",
"UpperHalfPlane.instChartedSpaceComplex",
"instDecidableEqFin",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"OnePoint.IsZeroAt",
... | false |
Nat.primorial_dvd_lcmUpto | Mathlib.NumberTheory.Chebyshev | [
"Eq.mpr",
"Nat.Prime",
"Dvd.dvd",
"congrArg",
"Finset",
"Nat.prod_primeFactors_dvd",
"Nat.primesLE",
"Nat.lcmUpto",
"id",
"instOfNatNat",
"Finset.prod",
"Finset.range",
"instHAdd",
"Nat.instDvd",
"HAdd.hAdd",
"Nat",
"Nat.primeFactors_lcmUpto",
"Nat.instCommMonoid",
"Nat.primesLE_... | true |
Turing.TM1to1.trCfg.eq_1 | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Inhabited.default",
"Turing.Tape",
"instInhabitedBool",
"Turing.TM1to1.trTape",
"List.Vector",
"Turing.TM1.Cfg",
"Turing.TM1.Cfg.mk",
"Option.map",
"Turing.TM1to1.Λ'",
"Turing.TM1to1.trCfg",
"Turing.TM1to1.Λ'.normal",
"Nat",
"List.Vector.replicate",
"Bool",
"Inhabited",
"Eq.refl",
"... | true |
GroupExtension.Splitting.conjAct | Mathlib.GroupTheory.GroupExtension.Basic | [
"GroupExtension.Splitting.instMonoidHomClass",
"GroupExtension.Splitting.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"GroupExtension.Splitting",
"MulAut.instGroup",
"Group",
"MulAut",
"MulOne.toMul",
"MonoidHomClass.toMonoidHom",
"MonoidHom.comp",
"DivInvMonoid.toMonoid",
"Group.toDiv... | true |
Std.HashMap.Raw.getElem_congr | Std.Data.HashMap.RawLemmas | [
"GetElem?.toGetElem",
"Std.HashMap.Raw.WF.out",
"Membership.mem",
"Std.DHashMap.Raw.Const.get_congr",
"Std.HashMap.Raw.WF",
"LawfulHashable",
"Std.HashMap.Raw.mem_congr",
"Std.HashMap.Raw",
"GetElem.getElem",
"Bool.true",
"BEq.beq",
"EquivBEq",
"Std.HashMap.Raw.instGetElem?Mem",
"Iff.mp",
... | true |
RatFunc.irreducible_minpolyX | Mathlib.FieldTheory.RatFunc.IntermediateField | [
"Subalgebra.instSetLike",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instIsPrincipalIdealRingOfIsSemisimpleRing",
"Nat.instMulZeroClass",
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"LinearOrderedCommMonoidWithZero... | true |
WeakSpace.instModule' | Mathlib.Topology.Algebra.Module.Spaces.WeakDual | [
"WeakSpace.instModule'._proof_4",
"instSMulOfMul",
"WeakSpace.instModule'._proof_3",
"CommSemiring.toSemiring",
"WeakSpace.instModule'._proof_7",
"Module.mk",
"WeakSpace.instModule'._proof_5",
"instAddCommMonoidWeakSpace",
"Distrib.toAdd",
"DistribMulAction.mk",
"WeakSpace.instModule'._proof_6",... | true |
CategoryTheory.Subfunctor.range | Mathlib.CategoryTheory.Subfunctor.Image | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"TypeCat.instFunLikeFun",
"CategoryTheory.Subfunctor",
"TypeCat.Fun",
"CategoryTheory.types",
"CategoryTheory.Category.toCategoryStruct",
"C... | true |
QuaternionAlgebra.equivProd | Mathlib.Algebra.Quaternion | [
"QuaternionAlgebra.imI",
"QuaternionAlgebra.re",
"QuaternionAlgebra.mk",
"QuaternionAlgebra",
"Equiv.mk",
"Equiv",
"Prod.mk",
"Prod.fst",
"QuaternionAlgebra.equivProd._proof_2",
"QuaternionAlgebra.imK",
"Prod",
"QuaternionAlgebra.equivProd._proof_1",
"Prod.snd",
"QuaternionAlgebra.imJ"
] | true |
_private.Init.Data.String.Lemmas.Pattern.Pred.0.String.Slice.Pattern.Model.CharPred.Decidable.matchesAt_iff_matchesAt_decide._simp_1_2 | Init.Data.String.Lemmas.Pattern.Pred | [
"String.Slice.Pattern.Model.CharPred.Decidable.instPatternModelForallCharPropOfDecidablePred",
"String.Slice",
"String.Slice.Pattern.Model.CharPred.Decidable.isLongestMatchAt_iff_isLongestMatchAt_decide",
"String.Slice.Pattern.Model.CharPred.instPatternModelForallCharBool",
"DecidablePred",
"propext",
"... | false |
Vector.set_mk._proof_3 | Init.Data.Vector.Lemmas | [
"congrArg",
"Array.set",
"Vector.set_mk._proof_2",
"Array.size_set",
"Array",
"Nat",
"LT.lt",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"instLTNat",
"Eq",
"Array.size",
"Eq.trans"
] | false |
ContDiffOn.pow | Mathlib.Analysis.Calculus.ContDiff.Operations | [
"NormedRing.toRing",
"NormedSpace",
"ContDiffOn",
"Membership.mem",
"NormedRing.toNonUnitalNormedRing",
"Monoid.toPow",
"NonUnitalNormedRing.toNormedAddCommGroup",
"HPow.hPow",
"NormedAlgebra.toNormedSpace",
"Nat",
"ENat",
"NormedRing.toSeminormedRing",
"Semiring.toMonoid",
"NontriviallyNo... | true |
Std.Internal.IO.Async.UDP.Socket.getPeerName | Std.Internal.Async.UDP | [
"IO",
"Std.Internal.IO.Async.UDP.Socket",
"Std.Net.SocketAddress",
"Std.Internal.IO.Async.UDP.Socket.native",
"Std.Internal.UV.UDP.Socket.getPeerName"
] | true |
Aesop.GoalOrigin | Aesop.Tree.Data | [
"Aesop.GoalOrigin.subgoal",
"Aesop.GoalOrigin.copied",
"Aesop.GoalOrigin.droppedMVar"
] | true |
Submodule.span_smul | Mathlib.LinearAlgebra.Span.Basic | [
"Monoid",
"Submodule.pointwiseDistribMulAction",
"Submodule",
"RingHomSurjective.ids",
"instHSMul",
"DistribSMul.toLinearMap",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap",
"AddComm... | true |
_private.Mathlib.Probability.Distributions.Gaussian.Real.0.ProbabilityTheory.complexMGF_id_gaussianReal._simp_1_5 | Mathlib.Probability.Distributions.Gaussian.Real | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Lean.Meta.Grind.InjectiveInfo.inv? | Lean.Meta.Tactic.Grind.Types | [
"Lean.Expr",
"Lean.Meta.Grind.InjectiveInfo",
"Prod",
"Option"
] | true |
_private.Mathlib.CategoryTheory.Triangulated.Opposite.OpOp.0.CategoryTheory.Pretriangulated.commShiftIso_opOp_hom_app._proof_3 | Mathlib.CategoryTheory.Triangulated.Opposite.OpOp | [
"Lean.RArray.leaf",
"False",
"congrArg",
"Classical.byContradiction",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"instOfNatNat",
"Int",
"Int.Linear.Poly.num",
"autoParam",
"Int.Linear.Poly.add",
"Int.Linear.norm_eq",
"Int.Linear.diseq_unsat",
"CategoryTheory.Pret... | false |
_private.Mathlib.GroupTheory.Descent.0.Group.fg_of_descent._simp_1_4 | Mathlib.GroupTheory.Descent | [
"False",
"HMul.hMul",
"eq_false",
"Mul",
"Ne",
"NoZeroDivisors",
"Zero.toOfNat0",
"mul_ne_zero",
"OfNat.ofNat",
"Eq",
"instHMul",
"Zero"
] | false |
Valuation.val_le_one_or_val_inv_lt_one | Mathlib.RingTheory.Valuation.Basic | [
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"_private.Mathlib.RingTheory.Valuation.Basic.0.Valuation.val_le_one_or_val_inv_lt_one._simp_1_1",
"Preorder.toLT",
"NeZero.one",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"LinearOrderedCo... | true |
Lean.Grind.IntInterval.lo?.eq_4 | Init.Grind.ToIntLemmas | [
"Int",
"Lean.Grind.IntInterval.lo?",
"Lean.Grind.IntInterval.ii",
"Option.none",
"Eq.refl",
"Eq",
"Option"
] | true |
AddAction.stabilizer.eq_1 | Mathlib.GroupTheory.GroupAction.Defs | [
"AddAction.stabilizer._proof_1",
"AddAction.stabilizerAddSubmonoid",
"AddSubgroup",
"AddAction",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Eq.refl",
"SubNegMonoid.toAddMonoid",
"AddAction.stabilizer",
"AddSubgroup.mk",
"Eq"
] | true |
ContinuousMultilinearMap.nnnorm_constOfIsEmpty | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"SeminormedAddCommGroup",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"NormedField.toField",
"NNReal.eq",
"NNReal",
"IsEmpty",
"Field.toSemifield",
"Co... | true |
groupCohomology.Hilbert90.aux.eq_1 | Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | [
"Units.val",
"Pi.Function.module",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"Equiv.instEquivLike",
"Finsupp.module",
"CommRing.toNonUnitalCommRing",
"LinearMap.instFunLike",
"groupCohomology.Hilbert90.aux._proof_1",
"Algebra",
"Field.toDivisionR... | true |
Polynomial.Monic.degree_pos | Mathlib.Algebra.Polynomial.Degree.Operations | [
"WithBot.instPreorder",
"Polynomial.instOne",
"Nat.instMulZeroClass",
"WithBot",
"Preorder.toLT",
"CommSemiring.toSemiring",
"WithBot.zero",
"Ne",
"instOfNatNat",
"Polynomial.degree",
"Polynomial",
"Polynomial.Monic",
"CommSemiring",
"Iff",
"Nat.instPreorder",
"Nat",
"LT.lt",
"Iff.... | true |
SeparationQuotient.instDistrib._proof_1 | Mathlib.Topology.Algebra.SeparationQuotient.Basic | [
"HMul.hMul",
"SeparationQuotient.instMul",
"SeparationQuotient.mk_mul",
"SeparationQuotient.mk_add",
"Distrib.toAdd",
"SeparationQuotient.instAdd",
"TopologicalSpace",
"instHAdd",
"ContinuousMul",
"Distrib.toMul",
"SeparationQuotient.surjective_mk",
"HAdd.hAdd",
"Distrib",
"SeparationQuoti... | false |
_private.Mathlib.Data.List.TakeDrop.0.List.takeD_eq_take.match_1_1 | Mathlib.Data.List.TakeDrop | [
"False",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.le.step",
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat.le",
"Nat",
"List.casesOn",
"Nat.ctorIdx",
"instAddNat",
"Nat.zero",
"Eq.refl",
"HEq",
"Nat.le.refl",
"Nat.le.cas... | false |
Lean.instInhabitedTheoremVal | Lean.Declaration | [
"Inhabited",
"Lean.instInhabitedTheoremVal.default",
"Lean.TheoremVal",
"Inhabited.mk"
] | true |
t1Space_iff_specializes_imp_eq | Mathlib.Topology.Separation.Basic | [
"Pure.pure",
"Filter.instMembership",
"Continuous",
"Equiv.instEquivLike",
"Specializes",
"TopologicalSpace.cofinite",
"Compl.compl",
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"List.instGetElem?NatLtLength",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"Exists",
"n... | true |
Submodule.IsOrtho.le | Mathlib.Analysis.InnerProductSpace.Orthogonal | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"Preorder.toLE",
"NormedField.toField",
"Submodule.instPartialOrder",
"LE.le",
"Field.toSemifield",
"Submodule.IsOrtho",
"Submodule.orthogonal",
"RCLike.toDensel... | true |
AdicCompletion.of_injective | Mathlib.RingTheory.AdicCompletion.Basic | [
"Iff.mpr",
"CommRing",
"IsHausdorff",
"instSMulOfMul",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup",
"AdicCompletion.instAddCommGroup",
"AdicCompletion.instModuleOfIsScalarTower",
"Ideal",
"LinearMap",
"IsScalarTower.left",
"instDistrib... | true |
MeasureTheory.Measure.pi | Mathlib.MeasureTheory.Constructions.Pi | [
"MeasureTheory.Measure",
"MeasureTheory.Measure.wrapped._@.Mathlib.MeasureTheory.Constructions.Pi.668077722._hygCtx._hyg.2",
"MeasurableSpace",
"Fintype",
"MeasurableSpace.pi"
] | true |
Std.Internal.IO.Async.Signal.sigxfsz.elim | Std.Internal.Async.Signal | [
"PULift.up",
"Std.Internal.IO.Async.Signal.sigxfsz",
"Std.Internal.IO.Async.Signal.ctorIdx",
"Nat",
"Std.Internal.IO.Async.Signal",
"Eq.symm",
"Std.Internal.IO.Async.Signal.ctorElim",
"Eq"
] | false |
MonoidWithZeroHom | Mathlib.Algebra.GroupWithZero.Hom | [
"MulZeroOneClass",
"MonoidWithZeroHom.mk"
] | true |
_private.Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise.0.SubMulAction.instMulOneClass._simp_1 | Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise | [
"SubMulAction.instSetLike",
"Monoid",
"instSMulOfMul",
"HMul.hMul",
"IsScalarTower",
"SubMulAction.mem_mul",
"Mul",
"Membership.mem",
"Exists",
"And",
"SubMulAction.instMul",
"MulAction",
"propext",
"Monoid.toSemigroup",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
... | false |
Std.DTreeMap.Internal.Impl.Const.get!_insertIfNew! | Std.Data.DTreeMap.Internal.Lemmas | [
"instDecidableNot",
"instDecidableEqOrdering",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.insertIfNew_eq_insertIfNew!",
"Std.DTreeMap.Internal.Impl.Const.get!_insertIfNew",
"Membership.mem",
"Ordering",
"Std.DTreeMap.Intern... | true |
Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVExpr.mkBVConst | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.ReifiedBVExpr | [
"Pure.pure",
"Lean.Elab.Tactic.BVDecide.Frontend.ReifiedBVExpr",
"StateRefT'.instAlternativeOfMonad",
"Lean.Name.mkStr5",
"Lean.Elab.Tactic.BVDecide.Frontend.State",
"BitVec",
"Lean.mkApp2",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Level",
"Applicative.toPure",
"Lean.mkConst",
... | true |
ContDiffOn.continuousOn_fderivWithin_apply | Mathlib.Analysis.Calculus.ContDiff.Comp | [
"Set.instSProd",
"Prod.normedSpace",
"instAddMonoidWithOneENat",
"Prod.normedAddCommGroup",
"NormedSpace",
"UniqueDiffOn",
"SProd.sprod",
"WithTop.instPreorder",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"Set.univ",
"NormedSpace.toModule",
"P... | true |
MultiplierAlgebra.«_aux_Mathlib_Analysis_CStarAlgebra_Multiplier___macroRules_MultiplierAlgebra_term𝓜(_,_)_1» | Mathlib.Analysis.CStarAlgebra.Multiplier | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad"... | false |
iteratedFDerivWithin_insert | Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | [
"False",
"NormedSpace",
"eq_false",
"eventually_mem_nhdsWithin",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"iteratedFDerivWithin_congr_set'",
"Filter.Eventually.set_eq",
"Compl.compl",
"nhdsWithin",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"... | true |
Finite.ciInf_le_of_le | Mathlib.Data.Fintype.Order | [
"iInf",
"SemilatticeInf.instIsCodirectedOrder",
"Finite",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"ciInf_le_of_le",
"LE.le",
"Finite.bddBelow_range",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyCompleteLattice.toConditionallyCompletePa... | true |
AddActionHom.inverse._proof_2 | Mathlib.GroupTheory.GroupAction.Hom | [
"instAddActionSemiHomClassAddActionHom",
"congrArg",
"map_vadd",
"VAdd",
"id",
"AddActionHom",
"HVAdd.hVAdd",
"instFunLikeAddActionHom",
"True",
"eq_self",
"instHVAdd",
"of_eq_true",
"Eq",
"DFunLike.coe",
"Eq.trans"
] | false |
Lean.Meta.Simp.debug.simp.check.have | Lean.Meta.Tactic.Simp.Main | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
_private.Aesop.Script.Step.0.Aesop.Script.LazyStep.runFirstSuccessfulTacticBuilder.tryTacticBuilder.match_4 | Aesop.Script.Step | [
"Lean.Meta.SavedState",
"Option.ctorIdx",
"Option.some",
"Lean.MVarId",
"Nat.hasNotBit",
"Prod.mk",
"_private.Aesop.Script.Step.0.Aesop.Script.LazyStep.runFirstSuccessfulTacticBuilder.tryTacticBuilder._sparseCasesOn_1",
"List",
"Prod",
"Prod.casesOn",
"Option"
] | false |
_private.Mathlib.Order.Cover.0.LT.lt.exists_disjoint_Iio_Ioi._proof_1_1 | Mathlib.Order.Cover | [
"instLawfulOrderLT_mathlib",
"Lean.Grind.eq_false_of_not_eq_true",
"of_eq_false",
"False",
"Preorder.toLT",
"Lean.Grind.not_and",
"eq_false",
"congrArg",
"LinearOrder",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"SemilatticeInf.toPartialOrder",
"Eq... | false |
String.Slice.getUTF8Byte.eq_1 | Init.Data.String.Basic | [
"String.instLTRaw",
"String.Slice.getUTF8Byte._proof_3",
"String.Slice.rawEndPos",
"String.Slice",
"String.getUTF8Byte",
"String.Slice.startInclusive",
"String.Pos.Raw",
"String.Slice.str",
"String.Pos.Raw.offsetBy",
"LT.lt",
"Eq.refl",
"String.Slice.getUTF8Byte",
"UInt8",
"Eq",
"String.... | true |
Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaries.recOn | Mathlib.Tactic.Translate.UnfoldBoundary | [
"Lean.NameMap",
"Lean.NameSet",
"Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaries",
"Lean.Meta.SimpTheorem",
"Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaries.mk",
"Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaries.rec",
"Lean.Name",
"Prod"
] | false |
ContinuousMap.HomotopicRel.symm | Mathlib.Topology.Homotopy.Basic | [
"ContinuousMap.HomotopyRel.symm",
"ContinuousMap.HomotopyRel",
"ContinuousMap",
"ContinuousMap.HomotopicRel",
"TopologicalSpace",
"Nonempty.map",
"Set"
] | true |
CategoryTheory.StrictlyUnitaryLaxFunctorCore._proof_2 | Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"Eq"
] | false |
Polynomial.roots_map_of_injective_of_card_eq_natDegree | Mathlib.Algebra.Polynomial.Roots | [
"Eq.mpr",
"IsDomain",
"CommRing",
"Polynomial.roots",
"Multiset.map",
"congrArg",
"CommSemiring.toSemiring",
"RingHom",
"Multiset",
"id",
"LE.le",
"instLENat",
"Polynomial",
"Polynomial.map_roots_le_of_injective",
"CommRing.toCommSemiring",
"Polynomial.card_roots_map_le_natDegree",
"... | true |
Unitization.mk_toProd | Mathlib.Algebra.Algebra.Unitization | [
"Unitization.mk",
"Unitization.toProd",
"Unitization",
"Eq",
"rfl"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_21 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"Lean.Grind.Nat.lt_eq",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"instOfNatNat",
"LE.le",
"instLENat",
"SimpleGraph",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"List.length"
] | false |
Int8.ofUInt8.sizeOf_spec | Init.Data.SInt.Basic | [
"Int8",
"UInt8._sizeOf_inst",
"instOfNatNat",
"Int8._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Int8.ofUInt8",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"UInt8",
"Eq"
] | true |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.String.0._regBuiltin.String.reducePush.declare_28._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.String.1574800046._hygCtx._hyg.14 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.String | [
"String.reducePush",
"IO",
"Lean.Meta.DiscrTree.Key.star",
"Lean.Meta.DiscrTree.Key",
"instOfNatNat",
"List.toArray",
"List.cons",
"Unit",
"Nat",
"Lean.Meta.Simp.registerBuiltinDSimproc",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Lean.Meta.DiscrTree.Key.const",
"List.nil"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.ReorderVars.0.Lean.Meta.Grind.Arith.Cutsat.updateVarCoeff | Lean.Meta.Tactic.Grind.Arith.Cutsat.ReorderVars | [
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.ReorderVars.0.Lean.Meta.Grind.Arith.Cutsat.CollectM",
"Int",
"Int.Linear.Var",
"Int.instLTInt",
"Unit",
"instOfNat",
"LT.lt",
"Int.natAbs",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.ReorderVars.0.Lean.Meta.Grind.Arith.Cutsat.updateUpper",
"_private... | true |
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