name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux_map | Mathlib.CategoryTheory.Sites.CoverLifting | [
"CategoryTheory.Functor.op",
"CategoryTheory.Limits.MulticospanShape.snd",
"Eq.mpr",
"CategoryTheory.Presheaf.IsSheaf.isLimitMultifork",
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct... | true |
MeasureTheory.ofReal_lpNorm | Mathlib.MeasureTheory.Function.LpSeminorm.LpNorm | [
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"ENNReal.ofReal",
"congrArg",
"PseudoMetricSpace.toUniformSpace",
"ENNReal.ofReal_toReal",
"MeasureTheory.toReal_eLpNorm",
"SeminormedAddGroup.toContinuousENorm",
"id",
"MeasureTheory.MemLp",
"MeasurableSpace",
"SeminormedAddCommGroup.toSeminormedAd... | true |
_private.Init.Data.Nat.Lemmas.0.Nat.le_pow._proof_1_1 | Init.Data.Nat.Lemmas | [
"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",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Om... | false |
DirectSum.sigmaCurryEquiv._proof_2 | Mathlib.Algebra.DirectSum.Basic | [
"Equiv.right_inv",
"AddMonoid.toAddZeroClass",
"DFinsupp.sigmaCurryEquiv",
"AddZeroClass.toAddZero",
"Sigma.fst",
"Equiv.toFun",
"AddCommMonoid",
"AddZero.toZero",
"DFinsupp.instZero",
"Function.RightInverse",
"DFinsupp",
"AddCommMonoid.toAddMonoid",
"Sigma.snd",
"Sigma",
"Equiv.invFun",... | false |
Dilation.isClosedEmbedding | Mathlib.Topology.MetricSpace.Dilation | [
"CompleteSpace",
"Dilation.antilipschitz",
"NNReal.instInv",
"EMetricSpace.toPseudoEMetricSpace",
"NNReal",
"AntilipschitzWith.isClosedEmbedding",
"EMetricSpace",
"LipschitzWith.uniformContinuous",
"Dilation.ratio",
"Inv.inv",
"PseudoEMetricSpace.toUniformSpace",
"DilationClass",
"Dilation.l... | true |
Finmap.lookup_union_right | Mathlib.Data.Finmap | [
"Finmap.liftOn₂._proof_2",
"Finmap.induction_on₂",
"AList.mk",
"Finmap.instMembership",
"Finmap.instUnion",
"Membership.mem",
"List.Perm",
"Finmap.lookup",
"Finmap.union._proof_1",
"Finmap.liftOn._proof_2",
"AList",
"Finmap.liftOn₂._proof_1",
"Finmap.liftOn",
"AList.instUnion",
"Union.un... | true |
LE.rec | Init.Prelude | [
"LE",
"LE.mk"
] | false |
MeasureTheory.innerRegularWRT_isCompact_isOpen | Mathlib.MeasureTheory.Measure.RegularityCompacts | [
"MeasureTheory.Measure",
"SecondCountableTopology",
"MeasureTheory.Measure.InnerRegularWRT.trans",
"MeasureTheory.Measure.InnerRegularWRT",
"MeasurableSpace",
"IsClosed",
"TopologicalSpace",
"MeasureTheory.IsFiniteMeasure",
"TopologicalSpace.IsCompletelyPseudoMetrizableSpace",
"OpensMeasurableSpac... | true |
initFn._@.Mathlib.Geometry.Manifold.Notation.3092023753._hygCtx._hyg.2 | Mathlib.Geometry.Manifold.Notation | [
"Lean.Name.mkNum",
"IO",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.registerTraceClass",
"Lean.Name.anonymous",
"Unit",
"Nat",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Bool.false"
] | false |
CompletelyDistribLattice.MinimalAxioms.ctorIdx | Mathlib.Order.CompleteBooleanAlgebra | [
"Nat",
"CompletelyDistribLattice.MinimalAxioms"
] | false |
FirstOrder.Language.LHom.substructureReduct._proof_4 | Mathlib.ModelTheory.Substructures | [
"Membership.mem",
"FirstOrder.Language.Substructure.instSetLike",
"Eq.mp",
"FirstOrder.Language.Substructure.mk.injEq",
"FirstOrder.Language.Substructure",
"FirstOrder.Language.Structure",
"SetLike.coe",
"Nat",
"FirstOrder.Language.Functions",
"FirstOrder.Language.LHom.IsExpansionOn",
"FirstOrde... | false |
CategoryTheory.ComposableArrows.Exact.cokerToKer'._proof_1 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"CategoryTheory.ComposableArrows.IsComplex",
"CategoryTheory.ComposableArrows.Exact.toIsComplex",
"CategoryTheory.ComposableArrows",
"instOfNatNat",
"CategoryTheory.Preadditive",
"instHAdd",
"CategoryTheory.ComposableArrows.Exact",
"HAdd.hAdd",
"Nat",
"CategoryTheory.Preadditive.preadditiveHasZero... | false |
USize.toUInt8_ofBitVec | Init.Data.UInt.Lemmas | [
"instPowNat",
"BitVec.setWidth",
"UInt8.toNat_ofBitVec",
"UInt8.toNat.inj",
"USize.toUInt8",
"congrArg",
"BitVec",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"USize.toNat_ofBitVec",
"BitVec.toNat",
"instNatPowNat",
"System.Platform.numBits",
"HMod.hMod",
"HPow.hPow",
"USize.toNat",
... | true |
ProjectiveSpectrum.mem_vanishingIdeal | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology | [
"SetLike",
"Eq.mpr",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"Nat.instAddMonoid",
"ProjectiveSpectrum.vanishingIdeal",
"Membership.mem",
"AddSubmonoidClass",
"id",
"Set.mem_setOf_eq",
"Homo... | true |
NormedAddGroupHom.opNorm_le_bound | Mathlib.Analysis.Normed.Group.Hom | [
"Norm.norm",
"Real.instLE",
"Real",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"HMul.hMul",
"Real.instZero",
"setOf",
"NormedAddGroupHom.funLike",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"SeminormedAddCommGroup.toNorm",
"Real.instConditionallyCompleteL... | true |
List.instLawfulTraversable | Mathlib.Control.Traversable.Instances | [
"Monad.toApplicative",
"LawfulTraversable.mk",
"inferInstance",
"LawfulApplicative.toLawfulFunctor",
"LawfulMonad",
"List.instMonad",
"Applicative",
"LawfulTraversable",
"List",
"List.comp_traverse",
"List.naturality",
"List.id_traverse",
"instTraversableList",
"LawfulMonad.toLawfulApplica... | true |
_private.Mathlib.Analysis.Convex.Side.0.AffineSubspace.isPreconnected_setOf_wOppSide._simp_1_1 | Mathlib.Analysis.Convex.Side | [
"False",
"CommRing",
"Lattice.toSemilatticeSup",
"eq_false",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"CompleteLattice.toBoundedOrder... | false |
Lean.Server.instInhabitedDocumentMeta.default | Lean.Server.Utils | [
"Inhabited.default",
"Lean.Server.DocumentMeta.mk",
"Lean.FileMap",
"Lean.Lsp.instInhabitedDependencyBuildMode",
"instInhabitedNat",
"Lean.instInhabitedFileMap",
"Lean.Lsp.DocumentUri",
"String.instInhabited",
"Nat",
"Lean.Server.DocumentMeta",
"Lean.Name",
"Lean.instInhabitedName",
"Lean.Ls... | true |
Int16.toISize_ofIntLE | Init.Data.SInt.Lemmas | [
"Int16.toInt_ofIntLE",
"ISize.minValue",
"ISize.maxValue",
"congrArg",
"ISize.toInt_ofIntLE",
"Int16.iSizeMinValue_le_toInt",
"ISize.toInt.inj",
"Int",
"LE.le",
"congr",
"True",
"Int.le_trans",
"Int16.toInt_le_iSizeMaxValue",
"eq_self",
"Int16.ofIntLE",
"Int16.toInt",
"of_eq_true",
... | true |
Int64.toUInt64_or | Init.Data.SInt.Bitwise | [
"instHOrOfOrOp",
"UInt64",
"Int64",
"instOrOpInt64",
"HOr.hOr",
"instOrOpUInt64",
"Int64.toUInt64",
"Eq",
"rfl"
] | true |
Finset.sum_Ioc_consecutive | Mathlib.Algebra.BigOperators.Intervals | [
"Iff.mpr",
"Eq.mpr",
"Preorder.toLT",
"lt_irrefl",
"Finset.Ioc_union_Ioc_eq_Ioc",
"LinearOrder.toDecidableEq",
"Finset.instUnion",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Nat.instLocallyFiniteOrder",
"Membership.mem",
"... | true |
IntermediateField.map_sup | Mathlib.FieldTheory.IntermediateField.Adjoin.Defs | [
"Lattice.toSemilatticeSup",
"IntermediateField",
"AlgHom",
"Algebra",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"Field.toSemifield",
"IntermediateField.gc_map_comap",
"Semifield.toDivisionSemiring",
"Max.max",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemi... | true |
neg_lt_neg_iff | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"add_neg_cancel",
"NegZeroClass.toNeg",
"AddGroup.covconv",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddRightStrictMono",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"zero_add",
"iff_se... | true |
AddSubgroup.coe_copy | Mathlib.Algebra.Group.Subgroup.Defs | [
"AddSubgroup.copy",
"AddSubgroup",
"AddGroup",
"SetLike.coe",
"AddSubgroup.instSetLike",
"Eq.refl",
"Eq",
"Set"
] | true |
instBracketSubtypeMemLieIdeal._proof_1 | Mathlib.Algebra.Lie.Ideal | [
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"CommRing",
"LieRing.toAddCommGroup",
"LieSubmodule",
"AddCommGroup.toAddGroup",
"LieRing",
"AddGroup.toSubNegMonoid",
"LieAlgebra",
"LieSubmodule.instAddSubgroupClass",
"AddSubgroupClass",
"lieRingSelfModule"
] | false |
Std.PRange.LawfulUpwardEnumerableLE.recOn | Init.Data.Range.Polymorphic.UpwardEnumerable | [
"Std.PRange.UpwardEnumerable",
"Std.PRange.UpwardEnumerable.LE",
"LE.le",
"LE",
"Iff",
"Std.PRange.LawfulUpwardEnumerableLE.mk",
"Std.PRange.LawfulUpwardEnumerableLE.rec",
"Std.PRange.LawfulUpwardEnumerableLE"
] | false |
_private.Mathlib.Tactic.GCongr.Core.0.Mathlib.Tactic.GCongr.introN.match_1 | Mathlib.Tactic.GCongr.Core | [
"Lean.TSyntax",
"Lean.MVarId",
"Prod.mk",
"List.cons",
"List",
"Lean.SyntaxNodeKind",
"Prod",
"Prod.casesOn",
"Lean.Name.mkStr1",
"List.nil"
] | false |
RingHom.Flat.ofLocalizationSpanTarget | Mathlib.RingTheory.RingHom.Flat | [
"Module.ext",
"Eq.mpr",
"RingHom.Flat",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"HEq.refl",
"Ore... | true |
Num.castNum_shiftLeft | Mathlib.Data.Num.Lemmas | [
"Nat.zero_shiftLeft",
"castPosNum",
"Nat.instMulZeroClass",
"Nat.recAux",
"HMul.hMul",
"Nat.instOne",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"HShiftLeft.hShiftLeft",
"Nat.shiftLeft_succ",
"id",
"Distrib.toAdd",
"CommMagma.toMul",
"instMulNat",
"NonUnitalCommSemiring.toNonUni... | true |
Polynomial.monic_toSubring._simp_1 | Mathlib.RingTheory.Polynomial.Subring | [
"Polynomial.monic_toSubring",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"Finset",
"Polynomial.toSubring",
"Membership.mem",
"Subtype",
"HasSubset.Subset",
"Polynomial",
"Subring.toRing",
"Polynomial.Monic",
"SetLike.coe",
"Finset.instSetLike",
"Subring",
"Polynomial.coeffs",
"prope... | false |
IsSymmetricAlgebra.lift.eq_1 | Mathlib.LinearAlgebra.SymmetricAlgebra.Basic | [
"TensorAlgebra.SymRel",
"Equiv.instEquivLike",
"AlgEquiv.toAlgHom",
"AlgEquiv.symm",
"SymmetricAlgebra",
"IsSymmetricAlgebra.lift",
"CommSemiring.toSemiring",
"AlgHom",
"IsSymmetricAlgebra",
"Algebra",
"SymmetricAlgebra.lift",
"RingQuot.instSemiring",
"SymmetricAlgebra.algHom._proof_1",
"A... | true |
IntermediateField.relrank_mul_relrank | Mathlib.FieldTheory.Relrank | [
"IntermediateField.instPartialOrder",
"HMul.hMul",
"Cardinal",
"IntermediateField",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Cardinal.instMul",
"LE.le",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"IntermediateField.toSubfield",
"Semif... | true |
HomologicalComplex.XIsoOfEq | Mathlib.Algebra.Homology.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.eqToIso",
"HomologicalComplex",
"CategoryTheory.Iso",
"ComplexShape",
"HomologicalComplex.X",
"Eq",
"HomologicalComplex.XIsoOfEq._proof_1",
"CategoryTheory.Category"
] | true |
Array.filterMap_some_fun | Init.Data.Array.Lemmas | [
"congrArg",
"Option.some",
"Array.casesOn",
"id",
"instOfNatNat",
"Array.filterMap_congr",
"List.toArray",
"Array",
"List.filterMap_some",
"funext",
"List",
"List.size_toArray",
"Array.filterMap",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"congrFun'",
"Li... | true |
CochainComplex.ιTruncLE_naturality_assoc | Mathlib.Algebra.Homology.Embedding.CochainComplex | [
"CategoryTheory.Category.assoc",
"CochainComplex.truncLEMap",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CochainComplex.truncLE",
"HomologicalComplex.HasHomology",
"AddGroupWithOne.toAddMonoidWit... | true |
LightProfinite.Extend.functorOp_map | Mathlib.Topology.Category.LightProfinite.Extend | [
"CategoryTheory.StructuredArrow.homMk",
"CategoryTheory.Functor.op",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.StructuredArrow.toCostructuredArrow",
"CategoryTheory.Limits.Cone",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"LightProfinite.Ext... | true |
Lean.Grind.AddRightCancel.mk._flat_ctor | Init.Grind.Module.Basic | [
"Lean.Grind.AddRightCancel",
"Lean.Grind.AddRightCancel.mk",
"instHAdd",
"HAdd.hAdd",
"Eq",
"Add"
] | false |
Language.mem_add | Mathlib.Computability.Language | [
"Language.instAdd",
"Iff.rfl",
"Membership.mem",
"List",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Or",
"Language.instMembershipList",
"Language"
] | true |
Lean.Meta.Grind.Arith.CommRing.PolyDerivation.input.injEq | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Grind.CommRing.Poly",
"Eq.propIntro",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation.input.inj",
"Eq.ndrec",
"Eq.refl",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation.input",
"Eq"
] | true |
Part.notMem_none._simp_1 | Mathlib.Data.Part | [
"Part",
"False",
"eq_false",
"Membership.mem",
"Part.instMembership",
"Part.none",
"Part.notMem_none",
"Eq"
] | false |
RingQuot.definition._proof_4._@.Mathlib.Algebra.RingQuot.3469094938._hygCtx._hyg.2 | Mathlib.Algebra.RingQuot | [
"RingQuot.add_quot",
"NonAssocSemiring.toAddCommMonoidWithOne",
"congrArg",
"AddMonoid.toAddZeroClass",
"RingQuot.instSemiring",
"AddZeroClass.toAddZero",
"Distrib.toAdd",
"RingQuot.Rel",
"RingQuot",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSemiring",
"instHAdd",
"RingQuot.mk... | false |
CategoryTheory.Square.toArrowArrowFunctor'._proof_1 | Mathlib.CategoryTheory.Square | [
"CategoryTheory.Square.category",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Square.Hom.τ₁",
"CategoryTheory.Square.X₂",
"CategoryTheory.Square",
"CategoryTheory.Square.f₁₂",
"CategoryTheory.Square.Hom.τ₂",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Square.H... | false |
Pell.pellZd_sub | Mathlib.NumberTheory.PellMatiyasevic | [
"Zsqrtd.instMul",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"MulOne.toOne",
"Nat.instOrderedSub",
"Semigroup.toMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"CommRing.toNonUnitalComm... | true |
List.pmap_attachWith | Init.Data.List.Attach | [
"List.pmap_attachWith._proof_1",
"List.ext_getElem",
"congrArg",
"List.attachWith",
"List.getElem_pmap",
"List.getElem_attachWith._proof_1",
"Membership.mem",
"Exists",
"Eq.rec",
"Subtype",
"List.getElem_attachWith",
"Subtype.mk",
"GetElem.getElem",
"forall_prop_domain_congr",
"List.pmap... | true |
Lean.protectedExt | Lean.Modifiers | [
"Inhabited.default",
"Lean.TagDeclarationExtension.instInhabited",
"Lean.TagDeclarationExtension"
] | true |
CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.IsTerminal.casesOn | Mathlib.CategoryTheory.Presentable.Directed | [
"CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Cardinal",
"CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.src",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.SmallCategory",
"CategoryTheory.IsCard... | false |
Std.Do.SPred.and_or_right | Std.Do.SPred.DerivedLaws | [
"Std.Do.SPred.or",
"Std.Do.SPred.and_congr",
"Std.Do.SPred.or_and_left",
"Std.Do.SPred.bientails",
"List",
"Std.Do.SPred.bientails.trans",
"Std.Do.SPred.or_comm",
"Std.Do.SPred",
"Std.Do.SPred.and"
] | true |
_private.Mathlib.Topology.Separation.Regular.0.IsCompact.nhdsSet_basis_isCompact_isClosed.match_1_2 | Mathlib.Topology.Separation.Regular | [
"HasSubset.Subset",
"And.casesOn",
"TopologicalSpace",
"And",
"And.intro",
"IsOpen",
"Set.instHasSubset",
"Set"
] | false |
Tactic.ComputeAsymptotics.UnitMonomial.FirstNonzeroIsPos.cons_iff | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates | [
"Real",
"Real.instZero",
"Real.instLT",
"_private.Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates.0.Tactic.ComputeAsymptotics.UnitMonomial.FirstNonzeroIsPos.cons_iff._proof_1_5",
"Tactic.ComputeAsymptotics.UnitMonomial.FirstNonzeroIsPos",
"List.cons",
"And",
"Iff",
"Tactic.ComputeA... | true |
Lean.Grind.Linarith.Expr.collectVars._f | Lean.Meta.Tactic.Grind.Arith.Linear.VarRename | [
"Lean.Grind.Linarith.Expr.zero",
"Lean.Grind.Linarith.Expr",
"Lean.Grind.Linarith.Expr.neg",
"Lean.Grind.Linarith.Expr.intMul",
"HAndThen.hAndThen",
"Lean.Grind.Linarith.Expr.natMul",
"instHAndThenOfAndThen",
"Lean.Meta.Grind.instAndThenVarCollector",
"id",
"Lean.Grind.Linarith.Expr.sub",
"Int",... | false |
CategoryTheory.CatCenter.mul_app | Mathlib.CategoryTheory.Center.Basic | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CatCenter",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CatCenter.naturality",
"CategoryTheory.CatCenter.mul_app'",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"id",
"... | true |
Int8.xor_neg_one | Init.Data.SInt.Bitwise | [
"Eq.mpr",
"instComplementInt8",
"congrArg",
"Int8.instNeg",
"Int8",
"id",
"Int8.neg_one_xor",
"instXorOpInt8",
"HXor.hXor",
"Complement.complement",
"Eq.refl",
"Int8.xor_comm",
"Int8.instOfNat",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"instHXorOfXorOp"
] | true |
Subarray.toArray_mkSlice_rio | Init.Data.Slice.Array.Lemmas | [
"Std.Rco.Sliceable.mkSlice",
"Subarray",
"Std.Slice.toArray",
"congrArg",
"Std.Rio.mk",
"instOfNatNat",
"SubarrayIterator",
"Subarray.toArray_mkSlice_rco",
"instSliceableSubarrayNat_7",
"Array.extract",
"Array",
"Std.Slice.Internal.SubarrayData",
"Nat",
"instSliceableSubarrayNat_1",
"Tru... | true |
_private.Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing.0.AlgebraicGeometry.SheafedSpace.GlueData.«term𝖣» | Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
_private.Mathlib.Algebra.Lie.LieTheorem.0.LieModule.exists_nontrivial_weightSpace_of_isSolvable.match_1_1 | Mathlib.Algebra.Lie.LieTheorem | [
"LieAlgebra.toModule",
"Nontrivial",
"Module.End.instRing",
"LieSubalgebra.lieAlgebra",
"LieSubmodule.instSetLike",
"Semiring.toModule",
"instSMulOfMul",
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"Module.End.instLieModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid"... | false |
CategoryTheory.ShortComplex.unop_f | Mathlib.Algebra.Homology.ShortComplex.Basic | [
"CategoryTheory.Limits.HasZeroMorphisms",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"Quiver.Hom.unop",
"CategoryTheory.Category.opposite",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ShortComplex.f",
"CategoryThe... | true |
TopologicalSpace.UpgradedIsCompletelyPseudoMetrizableSpace.recOn | Mathlib.Topology.Metrizable.CompletelyMetrizable | [
"CompleteSpace",
"TopologicalSpace.UpgradedIsCompletelyPseudoMetrizableSpace",
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace.UpgradedIsCompletelyPseudoMetrizableSpace.rec",
"PseudoMetricSpace",
"TopologicalSpace.UpgradedIsCompletelyPseudoMetrizableSpace.mk"
] | false |
CategoryTheory.Limits.Cocone.functoriality.eq_1 | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.NatTrans.mk'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.CoconeMorphism.hom",
"CategoryTheory.Functor.comp",
"CategoryTheor... | true |
Valuation.ltAddSubgroup._proof_3 | Mathlib.RingTheory.Valuation.Basic | [
"Units.val",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"lt_of_le_of_lt",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"AddGroupWithOne.toAddGroup",
"Valuation.map_add",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"setOf",
"... | false |
Antitone.rightLim_le | Mathlib.Topology.Order.LeftRightLim | [
"OrderDual.toDual",
"OrderTopology",
"Equiv.instEquivLike",
"Antitone.dual_right",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.comp",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Equiv",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompl... | true |
ApproximatesLinearOn.toOpenPartialHomeomorph_source | Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | [
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearEquiv.symm",
"Preorder.toLT",
"CompleteSpace",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"ApproximatesLinearOn",
"PseudoMetricSpace.to... | true |
MeasureTheory.measure_smul_eq_zero_iff | Mathlib.MeasureTheory.Group.Action | [
"Eq.mpr",
"instHSMul",
"MeasureTheory.Measure",
"congrArg",
"Iff.rfl",
"Group",
"id",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MeasurableSpace",
"Iff",
"MeasureTheory.measure_smul",
"MulAction",
"ENNReal",
"Monoid.toSemigroup",
"Zero.toOfNat0",
"HSMul.hSMul",
"SemigroupAct... | true |
Subfield.charP | Mathlib.Algebra.CharP.Algebra | [
"Subfield.subtype",
"Subfield.toDivisionRing",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"DivisionRing.toDivisionSemiring",
"Subtype",
"DivisionRing.toRing",
"Subfield.instSetLike",
"Subfield.instRingSubtypeMem",
"Nat",
"RingHom.charP",
"DivisionSemiring.toSemiring",
"CharP",
... | true |
Lean.instToJsonImport.toJson | Lean.Setup | [
"Lean.Json",
"Lean.Import.importAll",
"Lean.Json.mkObj",
"Lean.Import",
"String",
"Lean.instToJsonBool",
"Lean.instToJsonName",
"Lean.Import.isMeta",
"Lean.ToJson.toJson",
"Prod.mk",
"List.cons",
"Lean.Import.module",
"List",
"Lean.Import.isExported",
"Bool",
"Lean.Name",
"Prod",
"... | true |
SimplexCategory.orderIsoOfIso.eq_1 | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"SimplexCategory.orderIsoOfIso._proof_2",
"PartialOrder.toPreorder",
"Equiv.mk",
"CategoryTheory.Iso",
"OrderIso",
"instOfNatNat",
"SimplexCategory.orderIsoOfIso._proof_4",
"SimplexCategory.orderIsoOfIso._proof_3",
"instLEFin",
"instHAdd",
"OrderHom.instFunLike",
"Fin.instPartialOrder",
"HAd... | true |
CochainComplex.ConnectData.mk.sizeOf_spec | Mathlib.Algebra.Homology.Embedding.Connect | [
"CategoryTheory.Limits.HasZeroMorphisms",
"ChainComplex",
"CochainComplex.ConnectData.mk",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddRightCancelSemigroup.toAddSemigroup",
"instSizeOfDefault",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
... | true |
ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_fun_add | Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Basic | [
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"ProbabilityTheory.IsGaussianProcess",
"AddCommGroup.toAddCommMonoid",
"SecondCountableTopology",
"NormedSpace.toModule",
"ProbabilityTheory.IsGaussianProcess.hasGaussianLaw_add",
"PseudoMetricSpace.toUniformSpace",
"BorelSpace",
"ProbabilityTheory... | true |
NONote.instMul | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.NF",
"ONote.instMul",
"Mul.mk",
"HMul.hMul",
"NONote.instMul._proof_1",
"Mul",
"NONote.mk",
"NONote",
"Subtype.val",
"ONote",
"instHMul"
] | true |
MeasureTheory.IsLocallyFiniteMeasure.recOn | Mathlib.MeasureTheory.Measure.Typeclasses.Finite | [
"MeasureTheory.Measure",
"MeasureTheory.IsLocallyFiniteMeasure.rec",
"nhds",
"MeasureTheory.Measure.FiniteAtFilter",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.IsLocallyFiniteMeasure.mk",
"MeasureTheory.IsLocallyFiniteMeasure"
] | false |
Algebra.Presentation.instCommRingCore._proof_45 | Mathlib.RingTheory.Extension.Presentation.Core | [
"Algebra.Presentation.instCommRingCore._proof_11",
"Semiring.toNatCast",
"Mul.mk",
"Algebra.Presentation.instCommRingCore._proof_7",
"CommRing",
"One.mk",
"Subring.instSetLike",
"Algebra.Presentation.instCommRingCore._aux_13",
"AddGroupWithOne.intCast_ofNat._autoParam",
"Algebra.Presentation.instC... | false |
Lean.Server.Test.Runner.Client.MsgEmbed.brecOn_3.go | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.MsgEmbed.below",
"Lean.Widget.TaggedText.tag",
"Lean.Server.Test.Runner.Client.MsgEmbed.trace",
"PProd.mk",
"String",
"Lean.Server.Test.Runner.Client.SubexprInfo",
"Lean.Server.Test.Runner.Client.InteractiveGoal",
"Lean.Server.Test.Runner.Client.MsgEmbed.expr",
"Lean.... | true |
_private.Batteries.Data.Fin.Coding.0.Fin.decodeSigma_encodeSigma.match_1_1 | Batteries.Data.Fin.Coding | [
"False",
"Fin.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Fin.mk",
"instOfNatNat",
"Nat.le.step",
"Nat.le",
"Nat",
"LT.lt",
"Nat.ctorIdx",
"Eq.refl",
"HEq",
"Nat.le.refl",
"Sigma.casesOn",
"instLTNat",
"Nat.le.casesOn",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Eq",... | false |
UInt32.le_trans | Init.Data.UInt.Lemmas | [
"UInt32.toBitVec",
"instOfNatNat",
"LE.le",
"BitVec.le_trans",
"Nat",
"instLEUInt32",
"UInt32",
"OfNat.ofNat"
] | true |
HasFDerivWithinAt.finset_prod | Mathlib.Analysis.Calculus.FDeriv.Mul | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NormedCommRing.toCommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedRing.toRing",
"NormedSpace",
"NormedCommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMon... | true |
SSet.sd._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.Subdivision | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.HasLeftKanExtension",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.functorCategoryHasColimit",
"CategoryTheory.CostructuredArrow",
"UnivLE.small",
"SSet",
"SSe... | false |
Nat.Linear.Expr.rec | Init.Data.Nat.Linear | [
"Nat.Linear.Expr.mulL",
"Nat.Linear.Expr",
"Nat.Linear.Expr.num",
"Nat.Linear.Var",
"Nat",
"Nat.Linear.Expr.add",
"Nat.Linear.Expr.mulR",
"Nat.Linear.Expr.var"
] | false |
Lean.Server.GoToKind.ctorElimType | Lean.Server.GoTo | [
"cond",
"Lean.Server.GoToKind.declaration",
"Nat.ble",
"Lean.Server.GoToKind.type",
"PULift",
"Nat",
"Lean.Server.GoToKind",
"Lean.Server.GoToKind.definition"
] | false |
AddOpposite.instNonUnitalNonAssocSemiring._proof_4 | Mathlib.Algebra.Ring.Opposite | [
"HMul.hMul",
"MulZeroClass.toMul",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddOpposite",
"MulZeroClass.mul_zero",
"Zero.toOfNat0",
"AddOpposite.instMulZeroClass",
"NonUnitalNonAssocSemiring",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero",
"instHMul"
] | false |
CategoryTheory.ShortComplex.LeftHomologyMapData.mk.inj | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyMapData",
"CategoryTheory.ShortComplex.LeftHomologyMapData.mk.noConfusion",
"CategoryTheory.ShortComplex.LeftHomologyData.f'",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Qui... | true |
CategoryTheory.HasCardinalFilteredGenerator.toLocallySmall | Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | [
"Cardinal.IsRegular",
"Cardinal",
"CategoryTheory.LocallySmall",
"Fact",
"CategoryTheory.HasCardinalFilteredGenerator",
"CategoryTheory.Category"
] | true |
CategoryTheory.Equivalence.symmEquivInverse.eq_1 | Mathlib.CategoryTheory.Equivalence.Symmetry | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence",
"CategoryTheory.Equivalence.asNatTrans",
"CategoryTheory.Equivalence.symmEquivInverse._proof_... | true |
NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"Real",
"Prod.normedSpace",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"Prod.normedAddCommGr... | true |
_private.Mathlib.Analysis.InnerProductSpace.Orthonormal.0.Orthonormal.inner_right_finsupp._simp_1_1 | Mathlib.Analysis.InnerProductSpace.Orthonormal | [
"eq_comm",
"propext",
"Eq"
] | false |
CategoryTheory.CountableCategory.recOn | Mathlib.CategoryTheory.Countable | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CountableCategory.mk",
"Countable",
"CategoryTheory.CountableCategory.rec",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.CountableCategory",
"CategoryTheory.Category"
] | false |
Algebra.Presentation.instCommRingCore._proof_62 | Mathlib.RingTheory.Extension.Presentation.Core | [
"Algebra.Presentation.instCommRingCore._proof_55",
"Mul.mk",
"CommRing",
"One.mk",
"Algebra.Presentation.instCommRingCore._aux_13",
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"Algebra.Presentation.instCommRingCore._proof_48",
"Algebra.Presentation.Core",
"Add.mk",
"AddMonoidWithOne.n... | false |
LieAlgebra.SemiDirectSum.neg_eq_mk | Mathlib.Algebra.Lie.SemiDirect | [
"LieHom",
"LieAlgebra.toModule",
"NegZeroClass.toNeg",
"CommRing",
"LieDerivation",
"LieRing.toAddCommGroup",
"LieAlgebra.SemiDirectSum.instAddCommGroup",
"lieAlgebraSelfModule",
"SubtractionMonoid.toSubNegZeroMonoid",
"LieAlgebra.SemiDirectSum.mk",
"SubNegZeroMonoid.toNegZeroClass",
"Subtract... | true |
Lean.Elab.MacroStackElem.after | Lean.Elab.Util | [
"Lean.Syntax",
"Lean.Elab.MacroStackElem"
] | true |
Real.rpowIntegrand₀₁_eq_sub | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation | [
"Eq.mpr",
"Real.instPow",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.rpow_neg_one",
"_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation.0.Real.rpowIntegrand₀₁_eq_sub._proof_1_3",
"HMul.hMul",
"mul_sub",
"Real.instZero",
"congrArg... | true |
instSubsingletonAddMonoidHom | Mathlib.Algebra.Group.Hom.Defs | [
"AddMonoidHom.instAddMonoidHomClass",
"AddZero.toZero",
"AddZero",
"Subsingleton.of_zeroHomClass",
"Subsingleton",
"AddMonoidHomClass.toZeroHomClass",
"AddMonoidHom",
"AddMonoidHom.instFunLike"
] | true |
ProbabilityTheory.Kernel.parallelComp_self_comp_copy | Mathlib.Probability.Kernel.Deterministic | [
"ProbabilityTheory.Kernel.comp",
"ProbabilityTheory.IsDeterministic",
"MeasurableSpace",
"ProbabilityTheory.Kernel.parallelComp",
"ProbabilityTheory.IsDeterministic.parallelComp_self_comp_copy'",
"Prod",
"Eq",
"ProbabilityTheory.Kernel",
"ProbabilityTheory.Kernel.copy",
"Prod.instMeasurableSpace"
... | true |
CategoryTheory.Subobject.mapIsoToOrderIso._proof_1 | Mathlib.CategoryTheory.Subobject.Basic | [
"CategoryTheory.Mono",
"CategoryTheory.Iso",
"CategoryTheory.mono_of_strongMono",
"CategoryTheory.Iso.isIso_hom",
"CategoryTheory.strongMono_of_isIso",
"CategoryTheory.Iso.hom",
"CategoryTheory.Category"
] | false |
Std.ExtDTreeMap.le_maxKey?_of_mem | Std.Data.ExtDTreeMap.Lemmas | [
"Std.DTreeMap.le_maxKey?_of_mem",
"Std.DTreeMap",
"Membership.mem",
"Ordering",
"Std.ExtDTreeMap.maxKey?",
"Std.TransCmp",
"Bool.true",
"Option.get",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Bool",
"Std.ExtDTreeMap.isSome_maxKey?_of_mem",
"Ordering.isLE",
"Eq",
"Std.ExtDTreeMap... | true |
selfAdjoint.val_mul | Mathlib.Algebra.Star.SelfAdjoint | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"selfAdjoint.instMulSubtypeMemAddSubgroup",
"NonUnitalCommRing",
"AddSubgroup",
"Star... | true |
MvPolynomial.eval_eq' | Mathlib.Algebra.MvPolynomial.Eval | [
"Finsupp.instAddZeroClass",
"Finsupp.instFunLike",
"Nat.instMulZeroClass",
"HMul.hMul",
"Finset.univ",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"RingHom",
"MvPolynomial.eval₂_eq'",
"MvPolynomial.support",
"instDistribOfSemiring",
"MvPolynomial.coeff",
"Fi... | true |
Algebra.TensorProduct.basisAux_map_smul | Mathlib.RingTheory.TensorProduct.Free | [
"Finsupp.instAddZeroClass",
"Finsupp.smulZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Algebra.to_smulCommClass",
"TensorProduct.leftHasSMul",
"instHSMul",
"Semiring.toModule",
"Finsupp.module",
"SemilinearMapClass.distribMulActionSemiHomClass",
"smul_assoc"... | true |
IsAlgClosed.mk | Mathlib.FieldTheory.IsAlgClosed.Basic | [
"Field.toSemifield",
"Polynomial",
"Semifield.toDivisionSemiring",
"IsAlgClosed",
"DivisionSemiring.toSemiring",
"Polynomial.Splits",
"Field",
"IsAlgClosed.mk"
] | true |
Monoid.Coprod.instGroup._proof_3 | Mathlib.GroupTheory.Coprod.Basic | [
"Mul.mk",
"Semigroup.toMul",
"One.mk",
"HMul.hMul",
"Monoid.toMulOneClass",
"Group",
"DivInvMonoid.toMonoid",
"Int",
"npowRec",
"Nat.cast",
"Group.toDivInvMonoid",
"One.one",
"Inv.inv",
"Inv.mk",
"Mul.mul",
"Nat",
"zpowRec",
"Monoid.toSemigroup",
"Eq.refl",
"Monoid.toOne",
"i... | false |
Std.Iterators.HetT.property_bind | Std.Data.Iterators.Lemmas.Equivalence.HetT | [
"Std.Iterators.HetT.Property",
"Exists",
"Std.Iterators.HetT.bind",
"LawfulMonad",
"Std.Iterators.HetT",
"And",
"eq_self",
"of_eq_true",
"Monad",
"Eq"
] | true |
Lean.Name.toStringWithSep | Init.Data.ToString.Name | [
"String",
"Lean.Name.toStringWithSep._f",
"Lean.Name.brecOn",
"Bool",
"Lean.Name",
"optParam",
"Bool.false"
] | true |
Std.Http.Trailer._sizeOf_1 | Std.Internal.Http.Data.Chunk | [
"Std.Http.Trailer.rec",
"Std.Http.Headers._sizeOf_inst",
"instOfNatNat",
"Std.Http.Trailer",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Std.Http.Headers",
"OfNat.ofNat"
] | false |
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