name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.IsCofilteredOrEmpty.of_left_adjoint | Mathlib.CategoryTheory.Filtered.Basic | [
"Eq.mpr",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Exists",
"id",
"Equiv",
"CategoryTheory.IsCofilteredOrEmpty",
"CategoryTheory.IsCofilteredOrEmpty.mk",
"CategoryTheory.Functor.map",
"CategoryTheory.IsCofiltered.mi... | true |
_private.Mathlib.Data.Nat.Digits.Defs.0.Nat.toDigitsCore_length._simp_1_4 | Mathlib.Data.Nat.Digits.Defs | [
"Nat.zero_le",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"True",
"eq_true",
"OfNat.ofNat",
"Eq"
] | false |
ProbabilityTheory.geometricPMFReal | Mathlib.Probability.Distributions.Geometric | [
"Real",
"HMul.hMul",
"Real.instSub",
"HSub.hSub",
"Monoid.toPow",
"Real.instOne",
"Real.instMonoid",
"instHSub",
"HPow.hPow",
"Nat",
"Real.instMul",
"One.toOfNat1",
"instHPow",
"OfNat.ofNat",
"instHMul"
] | true |
continuousAt_jacobiTheta₂ | Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable | [
"IsModuleTopology.toContinuousSMul",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Complex.instNormedAddCommGroup",
"AddMonoid.toAddSemigroup",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.instZero",
"ContinuousAt",
"DistribMulAction.toDistr... | true |
CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone._proof_1 | Mathlib.CategoryTheory.Galois.Prorepresentability | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone._proof_12",
"Opposite",
"CategoryTheory.coyoneda",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.PreGaloisCategory.Poin... | false |
ComplexShape.down.congr_simp | Mathlib.Algebra.Homology.HomologicalComplex | [
"IsRightCancelAdd",
"One",
"ComplexShape",
"Eq.refl",
"ComplexShape.down",
"Eq",
"Add"
] | true |
ImplicitFunctionData.hasStrictFDerivAt_implicitFunction | Mathlib.Analysis.Calculus.Implicit | [
"ContinuousLinearMap.comp",
"Eq.mpr",
"ImplicitFunctionData.leftFun",
"ImplicitFunctionData.leftDeriv",
"CompleteSpace",
"NormedSpace",
"congrArg",
"and_self",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"ImplicitFunctionData.implicitFunction",
"ContinuousLinearMap.funLike",
"NormedSpace.toM... | true |
Array.back_scanl? | Batteries.Data.Array.Scan | [
"GetElem?.toGetElem",
"congrArg",
"Array.scanl",
"HSub.hSub",
"Option.some",
"Array.take",
"Array.back?_eq_getElem?",
"instSubNat",
"instOfNatNat",
"Nat.lt_add_one._simp_1",
"Array.foldl",
"Array",
"GetElem.getElem",
"instHAdd",
"instHSub",
"Array.size_scanl",
"Array.back?",
"Array... | true |
LieDerivation.mk.injEq | Mathlib.Algebra.Lie.Derivation.Basic | [
"LieAlgebra.toModule",
"CommRing",
"LieDerivation",
"LieRing.toAddCommGroup",
"Eq.propIntro",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Bracket.bracket",
"LinearMap.instFunLike",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"LieRingModule.toBracket",
"LinearMap... | true |
_private.Init.Data.UInt.Lemmas.0.UInt16.lt_of_le_of_ne._simp_1_2 | Init.Data.UInt.Lemmas | [
"UInt16.le_iff_toNat_le",
"instLEUInt16",
"LE.le",
"instLENat",
"UInt16",
"Nat",
"propext",
"UInt16.toNat",
"Eq"
] | false |
Lean.Meta.LazyDiscrTree.Key.fvar.injEq | Lean.Meta.LazyDiscrTree | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.FVarId",
"Lean.Meta.LazyDiscrTree.Key.fvar",
"And",
"Nat",
"Lean.Meta.LazyDiscrTree.Key.fvar.inj",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Lean.Meta.LazyDiscrTree.Key"
] | true |
CategoryTheory.Limits.Fork.IsLimit.lift' | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.Fork.IsLimit.lift",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"Subtype",
"CategoryTheory.Limits.Fork",
"CategoryTheory.Limits.Cone.pt",
"Subtype.mk",
"CategoryT... | true |
Polynomial.eval_mul_X_pow | Mathlib.Algebra.Polynomial.Eval.Defs | [
"Polynomial.eval",
"MulOne.toOne",
"Semigroup.toMul",
"Nat.recAux",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"pow_succ",
"SemigroupWithZero.toSemigroup",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"instOfNatNat",
"NonUnitalSemiring.toSemigroupWithZero",
"_private.Mathlib... | true |
_private.Mathlib.Analysis.Calculus.Taylor.0.hasDerivAt_taylorWithinEval_succ._simp_1_6 | Mathlib.Analysis.Calculus.Taylor | [
"GroupWithZero.toMonoidWithZero",
"False",
"GroupWithZero.toDivInvMonoid",
"eq_false",
"GroupWithZero",
"DivInvMonoid.toZPow",
"Ne",
"Int",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Zero.toOfNat0",
"zpow_ne_zero",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq... | false |
Std.HashMap.get?_union_of_not_mem_left | Std.Data.HashMap.Lemmas | [
"Membership.mem",
"Std.HashMap",
"Std.HashMap.instUnion",
"LawfulHashable",
"EquivBEq",
"Std.HashMap.get?",
"Std.DHashMap.Const.get?_union_of_not_mem_left",
"Hashable",
"Union.union",
"Std.HashMap.inner",
"BEq",
"Eq",
"Not",
"Std.HashMap.instMembership",
"Option"
] | true |
WeierstrassCurve.Projective.Nonsingular | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | [
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"WeierstrassCurve.Projective.Equation",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"WeierstrassCurve.Projective.polynomialY",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAs... | true |
MeasurableSpace.DynkinSystem.mk.sizeOf_spec | Mathlib.MeasureTheory.PiSystem | [
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"MeasurableSpace.DynkinSystem.mk",
"Compl.compl",
"instSizeOfDefault",
"Disjoint",
"CompleteLattice.toConditionallyCompleteLattice",
"instOfNatNat",
"Set.instCompl",
"MeasurableSpace.DynkinSystem",
"instHAdd",
"HAdd.hAdd",
... | true |
RCLike.I_to_real | Mathlib.Analysis.RCLike.Basic | [
"Real",
"Real.instZero",
"Real.instRCLike",
"RCLike.I",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
IsAddRegular.all | Mathlib.Algebra.Group.Defs | [
"IsAddRegular.mk",
"IsCancelAdd.toIsLeftCancelAdd",
"IsAddRightRegular.all",
"IsAddLeftRegular.all",
"IsAddRegular",
"IsCancelAdd",
"IsCancelAdd.toIsRightCancelAdd",
"Add"
] | true |
Int64.toISize_ofNat' | Init.Data.SInt.Lemmas | [
"Int64.toBitVec_ofNat'",
"BitVec.setWidth",
"congrArg",
"ISize.ofNat",
"BitVec",
"System.Platform.numBits_le._simp_1",
"instOfNatNat",
"LE.le",
"BitVec.ofNat",
"instLENat",
"System.Platform.numBits",
"Nat",
"congr",
"True",
"ISize.toBitVec",
"eq_self",
"BitVec.signExtend_eq_setWidth_... | true |
AffineMap.instAddCommGroup._proof_4 | Mathlib.LinearAlgebra.AffineSpace.AffineMap | [
"AffineMap.coe_smul",
"instHSMul",
"AffineMap.instFunLike",
"AffineMap.mulAction",
"DistribMulAction.toDistribSMul",
"AddMonoid.nat_smulCommClass'",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Function.hasSMu... | false |
MeasureTheory.AEEqFun.instMonoid | Mathlib.MeasureTheory.Function.AEEqFun | [
"MeasureTheory.ae",
"Monoid",
"Function.Injective.monoid",
"MulOne.toOne",
"MeasureTheory.AEEqFun.toGerm_injective",
"Semigroup.toMul",
"MeasureTheory.Measure",
"MeasureTheory.AEEqFun.toGerm",
"Monoid.toMulOneClass",
"MeasureTheory.AEEqFun.instPowNat",
"MeasureTheory.AEEqFun.instMonoid._proof_2"... | true |
CommRingCat.Colimits.descFunLift._unsafe_rec | Mathlib.Algebra.Category.Ring.Colimits | [
"NegZeroClass.toNeg",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRingCat.carrier",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"CategoryTheory.Fu... | false |
_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.insert._proof_19 | Std.Data.DTreeMap.Internal.Operations | [
"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",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.ev... | false |
ENat.iInf_toNat | Mathlib.Data.ENat.Lattice | [
"Eq.mpr",
"iInf",
"instCompleteLinearOrderENat",
"ENat.instNatCast",
"instTopENat",
"congrArg",
"isEmpty_or_nonempty",
"id",
"ENat.coe_iInf._simp_1",
"ENat.iInf_eq_top_of_isEmpty",
"instOfNatNat",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"IsEmpty",
"Nat.cast",
"... | true |
Int.ModEq.mul_left | Mathlib.Data.Int.ModEq | [
"HMul.hMul",
"Int.instCommSemigroup",
"CommMagma.toMul",
"Int",
"Int.ModEq.mul_left'",
"Int.instMul",
"dvd_mul_left",
"Int.ModEq",
"CommSemigroup.toCommMagma",
"Int.ModEq.of_dvd",
"instHMul"
] | true |
_private.Init.Data.ByteArray.Lemmas.0.ByteArray.extract_add_three._simp_1_3 | Init.Data.ByteArray.Lemmas | [
"List.toByteArray",
"instHAppendOfAppend",
"List",
"ByteArray.instAppend",
"ByteArray",
"List.instAppend",
"Eq.symm",
"UInt8",
"Eq",
"HAppend.hAppend",
"List.toByteArray_append"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Poly.0.Lean.Grind.CommRing.Poly.toExpr.go._sunfold | Lean.Meta.Tactic.Grind.Arith.CommRing.Poly | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Poly.0.Lean.Grind.CommRing.Poly.toExpr.go",
"_private.Lean.Meta.Tactic.Grind.Arith.CommRing.Poly.0.Lean.Grind.CommRing.Poly.toExpr.go.match_1",
"Int",
"Lean.Grind.CommRing.Expr.add",
"Unit",
"_priva... | false |
CategoryTheory.TwoSquare.mk | Mathlib.CategoryTheory.Functor.TwoSquare | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.TwoSquare",
"CategoryTheory.Category"
] | true |
Kronecker.«_aux_Mathlib_LinearAlgebra_Matrix_Kronecker___macroRules_Kronecker_term_⊗ₖₜ[_]__1» | Mathlib.LinearAlgebra.Matrix.Kronecker | [
"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.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",... | false |
Topology.WithGeneratedByTopology.isClosed_iff | Mathlib.Topology.Convenient.GeneratedBy | [
"_private.Mathlib.Topology.Convenient.GeneratedBy.0.Topology.WithGeneratedByTopology.isClosed_iff._simp_1_2",
"Equiv.instEquivLike",
"congrArg",
"iSup",
"ContinuousMap",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"inferInstance",
"_private.Mathlib.Topol... | true |
RootPairing.IsIrreducible.mk' | Mathlib.LinearAlgebra.RootSystem.Irreducible | [
"Nontrivial",
"Sublattice",
"Eq.mpr",
"Submodule",
"RootPairing.coreflection",
"RingHomSurjective.ids",
"LinearEquiv.symm",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Equiv.nontrivial",
"Submodule.Quotient.addCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddComm... | true |
BooleanSubalgebra.subtype_comp_inclusion | Mathlib.Order.BooleanSubalgebra | [
"BooleanAlgebra",
"BooleanSubalgebra",
"BooleanSubalgebra.instBooleanAlgebraCoe",
"PartialOrder.toPreorder",
"BooleanSubalgebra.subtype",
"Preorder.toLE",
"Membership.mem",
"BooleanAlgebra.toBoundedOrder",
"Subtype",
"BiheytingAlgebra.toCoheytingAlgebra",
"LE.le",
"BooleanAlgebra.toBiheytingAl... | true |
FiniteIndexNormalAddSubgroup.rec | Mathlib.GroupTheory.FiniteIndexNormalSubgroup | [
"AddSubgroup.FiniteIndex",
"FiniteIndexNormalAddSubgroup.mk",
"FiniteIndexNormalAddSubgroup",
"AddSubgroup",
"AddSubgroup.Normal",
"AddGroup"
] | false |
_private.Mathlib.Topology.Order.0.TopologicalSpace.nhds_mkOfNhds_single._simp_1_2 | Mathlib.Topology.Order | [
"Pure.pure",
"Filter.Eventually",
"Filter.instPure",
"propext",
"Filter.eventually_pure",
"Eq",
"Filter"
] | false |
continuousAt_gauge_zero | Mathlib.Analysis.Convex.Gauge | [
"Filter.instMembership",
"Eq.mpr",
"Real",
"gauge",
"ContinuousSMul",
"Real.instZero",
"congrArg",
"ContinuousAt",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Membership.mem",
... | true |
CategoryTheory.SimplicialObject.IsCoskeletal.isRightKanExtension | Mathlib.AlgebraicTopology.SimplicialObject.Coskeletal | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.SimplicialObject.IsCoskeletal",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"LE.le",
"instLENat",
"Nat",
"SimplexCategory",
"SimplexCategory.Truncated.in... | true |
Lean.Meta.SimpAll.M | Lean.Meta.Tactic.Simp.SimpAll | [
"Lean.Meta.MetaM",
"IO.RealWorld",
"StateRefT'",
"Lean.Meta.SimpAll.State"
] | true |
Differentiable.fun_add_iff_right | Mathlib.Analysis.Calculus.FDeriv.Add | [
"Differentiable",
"Differentiable.add_iff_right",
"NormedSpace",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"id",
"instHAdd",
"Iff",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"HAdd.hAdd",
"NontriviallyNormedField",
"NormedAddCommGroup.toAddCommGroup",
"NontriviallyNormed... | true |
List.untrop_prod | Mathlib.Algebra.Tropical.BigOperators | [
"AddMonoid.toAddSemigroup",
"congrArg",
"Tropical.instMulOfAdd",
"List.map",
"AddMonoid.toAddZeroClass",
"List.sum",
"AddZeroClass.toAddZero",
"List.rec",
"List.cons",
"Tropical",
"AddZero.toZero",
"List",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"True",
"eq_self",
"AddMonoid... | true |
MeasureTheory.llr.eq_1 | Mathlib.MeasureTheory.Measure.LogLikelihoodRatio | [
"Real",
"MeasureTheory.Measure",
"MeasureTheory.Measure.rnDeriv",
"MeasureTheory.llr",
"Real.log",
"MeasurableSpace",
"ENNReal.toReal",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Topology.Separation.Hausdorff.0.t2_iff_ultrafilter._simp_1_2 | Mathlib.Topology.Separation.Hausdorff | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
SemistandardYoungTableau.col_strict' | Mathlib.Combinatorics.Young.SemistandardTableau | [
"YoungDiagram",
"Membership.mem",
"Prod.mk",
"Nat",
"LT.lt",
"instLTNat",
"SemistandardYoungTableau.entry",
"Prod",
"SetLike.instMembership",
"YoungDiagram.instSetLikeProdNat",
"SemistandardYoungTableau"
] | true |
FirstOrder.Language.instUniqueStructureEmpty | Mathlib.ModelTheory.Basic | [
"FirstOrder.Language.empty",
"Unique.mk",
"Unique",
"FirstOrder.Language.instUniqueStructureEmpty._proof_1",
"FirstOrder.Language.emptyStructure",
"FirstOrder.Language.Structure",
"Inhabited.mk"
] | true |
CategoryTheory.SmallObject.SuccStruct.mk | Mathlib.CategoryTheory.SmallObject.Iteration.Basic | [
"CategoryTheory.SmallObject.SuccStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SmallObject.SuccStruct.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
ContinuousMonoidHom.comp | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"Monoid",
"Monoid.toMulOneClass",
"ContinuousMonoidHom.mk",
"MonoidHom.comp",
"TopologicalSpace",
"MulOneClass.toMulOne",
"ContinuousMonoidHom.comp._proof_1",
"ContinuousMonoidHom",
"ContinuousMonoidHom.toMonoidHom"
] | true |
Lean.JsonRpc.Message.noConfusion | Lean.Data.JsonRpc | [
"Lean.Json",
"Lean.JsonRpc.Message.casesOn",
"Lean.JsonRpc.ErrorCode",
"String",
"Lean.Json.Structured",
"Lean.JsonRpc.Message",
"Lean.JsonRpc.Message.noConfusionType",
"Eq.ndrec",
"Eq.refl",
"Lean.JsonRpc.RequestID",
"Eq",
"Option"
] | false |
MvPolynomial.restrictSupportIdeal.congr_simp | Mathlib.RingTheory.MvPolynomial.Ideal | [
"Finsupp.instLE",
"MvPolynomial.restrictSupportIdeal",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommSemiring.toSemiring",
"IsUpperSet",
"Finsupp.instAddMonoid",
"Nat.instAddMonoid",
"Eq.rec",
"instLENat",
"Ideal",
"CommSemiring",
"Nat",
"MvPolynomial",
"Eq.ndrec",
"Eq.refl... | true |
UniformSpace.Completion.mapRingEquiv_symm_apply | Mathlib.Topology.Algebra.UniformRing | [
"UniformSpace",
"UniformSpace.Completion.map",
"Continuous",
"UniformSpace.Completion.mul",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"UniformSpace.Completion.mapRingEquiv",
"RingEquiv.instEquivLike",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"IsUniformAddG... | true |
Lean.Grind.Bool.or_eq_of_eq_true_left | Init.Grind.Lemmas | [
"congrArg",
"Bool.true",
"True",
"eq_self",
"Bool",
"of_eq_true",
"Bool.or",
"Bool.true_or",
"congrFun'",
"Eq",
"Eq.trans"
] | true |
HilbertBasis.hasSum_repr_symm | Mathlib.Analysis.InnerProductSpace.l2Space | [
"LinearIsometryEquiv.instEquivLike",
"NormedCommRing.toNormedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"instHSMul",
"ENNReal.ofNat_ne_top",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"fact_one_le_two_ennreal",
"NormedRing.toR... | true |
AdjoinRoot.instCommRing._proof_3 | Mathlib.RingTheory.AdjoinRoot | [
"CommRing",
"Semiring.toModule",
"AdjoinRoot",
"CommSemiring.toSemiring",
"Add.mk",
"Submodule.Quotient.addCommGroup._proof_3",
"AdjoinRoot.instCommRing._aux_1",
"Set.instSingletonSet",
"Polynomial",
"instHAdd",
"CommRing.toCommSemiring",
"HAdd.hAdd",
"Ring.toAddCommGroup",
"Polynomial.sem... | false |
Std.Format.MonadPrettyFormat.mk | Init.Data.Format.Basic | [
"String",
"Unit",
"Nat",
"Std.Format.MonadPrettyFormat.mk",
"Std.Format.MonadPrettyFormat"
] | true |
Lean.ErrorExplanation.rec | Lean.ErrorExplanation | [
"String",
"Lean.DeclarationLocation",
"Lean.ErrorExplanation.Metadata",
"Lean.ErrorExplanation.mk",
"Option",
"Lean.ErrorExplanation"
] | false |
Real.HolderTriple.pos' | Mathlib.Data.Real.ConjExponents | [
"Real.HolderTriple.inv_add_inv_eq_inv",
"GroupWithZero.toMonoidWithZero",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"GroupWithZero.toDivisionMonoid",
"CommRing.toNonUnitalCommRing",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"Real.... | true |
Algebra.PreSubmersivePresentation.differential._proof_2 | Mathlib.RingTheory.Extension.Presentation.Submersive | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.to_smulCommClass",
"Algebra.Generators.Ring",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"Function.smulCommClass",
"Finsupp.instAddMonoid",
"AddMonoidAlgebra.commSemiring",
"Alge... | false |
AddUnits.mk_val | Mathlib.Algebra.Group.Units.Defs | [
"AddUnits.val",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"AddUnits.ext",
"instHAdd",
"HAdd.hAdd",
"AddMonoid",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"rfl",
"AddUnits",
"AddUnits.mk"
] | true |
Lean.Lsp.CompletionList.casesOn | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.CompletionList.mk",
"Lean.Lsp.CompletionList.rec",
"Lean.Lsp.CompletionItem",
"Array",
"Bool",
"Lean.Lsp.CompletionList"
] | false |
round.eq_1 | Mathlib.Algebra.Order.Round | [
"Preorder.toLT",
"HMul.hMul",
"Int.floor",
"Ring.toNonAssocRing",
"Int.fract",
"LinearOrder",
"round._proof_1",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"... | true |
_private.Init.Data.SInt.Lemmas.0.Int16.toISize_ne_minValue._proof_1_2 | Init.Data.SInt.Lemmas | [
"instPowNat",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"ISize.minValue",
"Int16",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.combo_sat'",
"... | false |
Nat.ToInt.of_eq | Init.Data.Int.OfNat | [
"congrArg",
"Eq.mp",
"Int",
"NatCast.natCast",
"Nat",
"instNatCastInt",
"Eq"
] | true |
IsValuativeTopology.hasBasis_nhds_zero' | Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | [
"subset_refl._simp_1",
"Units.val",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"False",
"ValuativeRel.instLinearOrderValueGroupWithZero",
"CommRing",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCo... | true |
MeasureTheory.«_aux_Mathlib_MeasureTheory_OuterMeasure_AE___macroRules_MeasureTheory_term∀ᵐ_∂_,__1» | Mathlib.MeasureTheory.OuterMeasure.AE | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax... | false |
pinGroup.instStarMulSubtypeCliffordAlgebraMemSubmonoid._proof_1 | Mathlib.LinearAlgebra.CliffordAlgebra.SpinGroup | [
"CommRing",
"Ring.toNonAssocRing",
"InvolutiveStar.star_involutive",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"QuadraticForm",
"Membership.mem",
"pinGroup",
"AddCommGroup",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocSemiring.... | false |
_private.Mathlib.Tactic.Positivity.Core.0.Mathlib.Meta.Positivity.OrderRel.ne | Mathlib.Tactic.Positivity.Core | [
"_private.Mathlib.Tactic.Positivity.Core.0.Mathlib.Meta.Positivity.OrderRel.ne",
"_private.Mathlib.Tactic.Positivity.Core.0.Mathlib.Meta.Positivity.OrderRel"
] | true |
_private.Mathlib.NumberTheory.Multiplicity.0.Nat.eight_dvd_sq_sub_one_of_odd._proof_1_1 | Mathlib.NumberTheory.Multiplicity | [
"instPowNat",
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"Int.Nonneg.toPoly",
"Lean.Grind.CommRing.Mon.mult",
"Int.Linear.le_coeff",
"Int.Nonneg.add",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul"... | false |
Std.TreeMap.Raw.getElem_insertMany_list.match_1 | Std.Data.TreeMap.Raw.Lemmas | [
"Option.casesOn",
"Option.some",
"Option.none",
"Eq.refl",
"Eq",
"Option"
] | false |
WithLp.ofLp_multisetSum | Mathlib.Analysis.Normed.Lp.WithLp | [
"Multiset.sum",
"WithLp",
"map_multiset_sum",
"AddEquivClass.instAddMonoidHomClass",
"Multiset.map",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"WithLp.instAddCommGroup",
"AddCommGroup",
"Multiset",
"AddGroup.toSubNegMonoid",
"ENNReal",
"AddEquiv... | true |
AlgebraicGeometry.Scheme.kerFunctor._proof_4 | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"CategoryTheory.Over",
"AlgebraicGeometry.Scheme.kerFunctor._proof_2",
"CategoryTheory.Comma.right",
"AlgebraicGeometry.Scheme",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"CategoryTheory.Comma.left",
"Preorder.toLE",
"CategoryTheory.Functor.id... | false |
CategoryTheory.bifunctorComp₂₃FunctorObj_obj | Mathlib.CategoryTheory.Functor.Trifunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.bifunctorComp₂₃FunctorObj",
"CategoryTheory.bifunctorComp₂₃",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
EuclideanDomain.toNontrivial | Mathlib.Algebra.EuclideanDomain.Defs | [
"Nontrivial",
"EuclideanDomain"
] | true |
BoxIntegral.TaggedPrepartition.noConfusionType | Mathlib.Analysis.BoxIntegral.Partition.Tagged | [
"Real",
"BoxIntegral.Prepartition",
"BoxIntegral.Box.Icc",
"Membership.mem",
"Set.instLE",
"BoxIntegral.TaggedPrepartition.casesOn",
"BoxIntegral.Box.instLE",
"HEq",
"OrderEmbedding",
"Set.instMembership",
"DFunLike.coe",
"BoxIntegral.TaggedPrepartition",
"BoxIntegral.Box",
"instFunLikeOrd... | false |
ContinuousMap.instCompactSpaceElemCoeCompacts | Mathlib.Topology.ContinuousMap.Compact | [
"Membership.mem",
"Set.Elem",
"TopologicalSpace.Compacts.instCompactSpaceSubtypeMem",
"CompactSpace",
"TopologicalSpace",
"SetLike.coe",
"TopologicalSpace.Compacts.instSetLike",
"instTopologicalSpaceSubtype",
"Set.instMembership",
"TopologicalSpace.Compacts",
"Set"
] | true |
FloatArray.instEmptyCollection | Init.Data.FloatArray.Basic | [
"FloatArray",
"FloatArray.empty",
"EmptyCollection.mk",
"EmptyCollection"
] | true |
ProbabilityTheory.defaultRatCDF | Mathlib.Probability.Kernel.Disintegration.MeasurableStieltjes | [
"Rat.instOfNat",
"Real",
"Real.instZero",
"Rat",
"Real.instOne",
"Rat.instDecidableLt",
"LT.lt",
"One.toOfNat1",
"Zero.toOfNat0",
"Rat.instLT",
"OfNat.ofNat",
"ite"
] | true |
Real.rpowIntegrand₀₁_eqOn_pow_div | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation | [
"Real.instPow",
"Real.instLE",
"Real",
"Set.Ioi",
"instHDiv",
"HMul.hMul",
"Real.instZero",
"congrArg",
"Real.instDivInvMonoid",
"Real.instSub",
"HSub.hSub",
"le_of_lt",
"Membership.mem",
"HDiv.hDiv",
"Set.EqOn",
"LE.le",
"Real.rpowIntegrand₀₁",
"Real.instAdd",
"Real.instOne",
... | true |
_private.Mathlib.Algebra.Module.LocalizedModule.Basic.0.IsLocalizedModule.instLiftOfLE._simp_3 | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"IsLocalizedModule",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"DistribSMul.toSMulZeroClass",
"NonAssocSemiring.toMulZeroOneClass",
"LinearMap",
"AddCommMonoid",
"MulZeroOneClas... | false |
List.attach_filterMap | Init.Data.List.Attach | [
"Iff.mpr",
"Eq.mpr",
"False",
"List.map_cons",
"_private.Init.Data.List.Attach.0.List.attach_filterMap._simp_1_2",
"Iff.of_eq",
"Option.ctorIdx",
"congrArg",
"List.filterMap_map",
"List.map",
"List.attach_cons.match_1",
"False.elim",
"_private.Init.Data.List.Attach.0.List.attach_filterMap._s... | true |
UniformContinuousConstVAdd.uniformContinuous_const_vadd | Mathlib.Topology.Algebra.UniformMulAction | [
"UniformContinuous",
"UniformSpace",
"VAdd",
"UniformContinuousConstVAdd",
"HVAdd.hVAdd",
"instHVAdd"
] | true |
Batteries.RBNode.upperBound? | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode",
"Batteries.RBNode.below",
"Option.some",
"Ordering",
"Batteries.RBNode.nil",
"Option.none",
"Batteries.RBNode.brecOn",
"Batteries.RBNode.upperBound?.match_1",
"Unit",
"Batteries.RBColor",
"optParam",
"Batteries.RBNode.ins.match_1",
"Batteries.RBNode.node",
"Option"
] | true |
WithTop.mul_eq_top_iff | Mathlib.Algebra.Order.Ring.WithTop | [
"Eq.mpr",
"False",
"Decidable.casesOn",
"WithTop.mul_def",
"HMul.hMul",
"eq_false",
"and_true",
"MulZeroClass.toMul",
"congrArg",
"true_or",
"False.elim",
"Decidable",
"WithTop.map₂",
"WithTop.decidableEq",
"WithTop.map₂_eq_top_iff._simp_1",
"MulZeroClass",
"Eq.mp",
"id",
"WithTo... | true |
CategoryTheory.Presieve.singleton.rec | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.Presieve.singleton.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve.singleton",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | false |
Submonoid.LocalizationMap.map | Mathlib.GroupTheory.MonoidLocalization.Maps | [
"MonoidHom.instFunLike",
"Submonoid.LocalizationMap.lift",
"MonoidHom",
"Monoid.toMulOneClass",
"Membership.mem",
"Subtype",
"MonoidHom.comp",
"Submonoid.LocalizationMap.toMonoidHom",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"Submonoid.LocalizationMap",
"Submonoid.instSetLike",
"Subtyp... | true |
Lean.Meta.Grind.Arith.Linear.Case.fvarId | Lean.Meta.Tactic.Grind.Arith.Linear.SearchM | [
"Lean.FVarId",
"Lean.Meta.Grind.Arith.Linear.Case"
] | true |
_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.go._unsafe_rec | Std.Sat.AIG.CNF | [
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.match_16",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.State.IsExtensionBy_trans_right",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Fanin.gate",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.State.addGate",
"_private.Std.Sat.AIG.CNF.0.Std.Sat.AIG.toCNF.Cache.hmarks",
... | false |
AlgebraicGeometry.IsAffineOpen.isoSpec_hom | Mathlib.AlgebraicGeometry.AffineScheme | [
"AlgebraicGeometry.IsAffineOpen.isoSpec",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"PartialOrder.toPreorder",
"A... | true |
CategoryTheory.Comma.mapLeftIso | Mathlib.CategoryTheory.Comma.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.mapLeftIso._proof_2",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.Comma",
"CategoryTheory.Comma... | true |
_private.Mathlib.CategoryTheory.ConnectedComponents.0.CategoryTheory.instIsConnectedComponent._proof_10 | Mathlib.CategoryTheory.ConnectedComponents | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"Int.Linear.norm_le",
"Lean.Grind.nestedProof",
"Lean.Grind.CommRing.Expr.var",
"Int.Linear.Expr.eq_of_norm_eq",
"Lean.Grind.Order.eq_of_le_of_l... | false |
TopModuleCat.instIsRightAdjointTopCatForget₂ContinuousLinearMapIdCarrierContinuousMapCarrier | Mathlib.Algebra.Category.ModuleCat.Topology.Basic | [
"TopModuleCat.instCategory",
"CategoryTheory.Functor",
"TopCat.instCategory",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"ContinuousMap",
"CategoryTheory.Functor.IsRightAdjoint",
"TopModuleCat.freeAdj",
"TopModuleCat.topologicalSpace",
"TopModuleCat.toModuleCat",
"Nonempty.in... | true |
Complex.UnitDisc | Mathlib.Analysis.Complex.UnitDisc.Basic | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"Complex.instNormedField",
"Complex.instZero",
"Set.Elem",
"Metric.ball",
"Real.instOne",
"SeminormedCommRing.toSeminormedRing",
"One.toOfNat1",
"Zero.toOfNat0",
"SeminormedRing.toPseudoMetricSpace",
"NormedField.toNormedCommRing",
"Complex",
... | true |
CochainComplex.HomComplex.Cochain.rightShift._proof_3 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | [
"IsRightCancelAdd",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Int",
"AddSemigroup.toAdd",
"Int.instAddGroup",
"AddRightCancelMonoid.toAddRightCancelSemigroup",
"AddGroup.toAddCancelMonoid",
"AddRightCancelSemigroup.toIsRightCancelAdd"
] | false |
Lean.Meta.Grind.TopSort.State.recOn | Lean.Meta.Tactic.Grind.EqResolution | [
"Lean.Meta.Grind.TopSort.State",
"Lean.Meta.Grind.TopSort.State.mk",
"Lean.Expr.instBEq",
"Std.HashSet",
"Lean.Expr",
"Array",
"Lean.Expr.instHashable",
"Lean.Meta.Grind.TopSort.State.rec"
] | false |
cfc_const._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Std.Packages.LinearPreorderOfLEArgs.rec | Init.Data.Order.PackageFactories | [
"Std.Packages.LinearPreorderOfLEArgs.mk",
"Std.Packages.LinearPreorderOfLEArgs",
"Ord",
"LE.le",
"Ord.compare",
"LE",
"Std.Packages.PreorderOfLEArgs.decidableLE",
"Bool.true",
"DecidableLE",
"Iff",
"Bool",
"Ordering.isGE",
"Or",
"Ordering.isLE",
"Eq",
"Std.Packages.PreorderOfLEArgs.le"... | false |
ENNReal.mul_div_cancel_right | Mathlib.Data.ENNReal.Inv | [
"False",
"instHDiv",
"HMul.hMul",
"eq_false",
"CommSemiring.toSemiring",
"HDiv.hDiv",
"Ne",
"ENNReal.instCommSemiring",
"instZeroENNReal",
"Distrib.toMul",
"implies_congr",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"True",
"ENNReal",
"ENNReal.instDivInvMonoid",
"DivInvMonoid.toDi... | true |
Lean.Parser.Term.let._regBuiltin.Lean.Parser.Term.letDecl.parenthesizer_137 | Lean.Parser.Term | [
"Lean.Parser.Term.letDecl.parenthesizer",
"Lean.Name.mkStr5",
"IO",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.parenthesizerAttribute",
"Unit",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
_private.Std.Data.DHashMap.Internal.AssocList.Lemmas.0.Std.DHashMap.Internal.AssocList.getEntryD.eq_def | Std.Data.DHashMap.Internal.AssocList.Lemmas | [
"Eq.mpr",
"Std.DHashMap.Internal.AssocList.below",
"congrArg",
"Std.DHashMap.Internal.AssocList.brecOn.eq",
"Std.DHashMap.Internal.AssocList.nil",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.toList.match_1",
"id",
"instDecidableEqBool",
"_private.Std.Data.D... | true |
Lean.Lsp.DidSaveTextDocumentParams.rec | Lean.Data.Lsp.TextSync | [
"Lean.Lsp.DidSaveTextDocumentParams.mk",
"String",
"Lean.Lsp.TextDocumentIdentifier",
"Lean.Lsp.DidSaveTextDocumentParams",
"Option"
] | false |
Set.swap_mem_addAntidiagonal | Mathlib.Data.Set.MulAntidiagonal | [
"Set.addAntidiagonal",
"congrArg",
"AddCommMagma",
"Membership.mem",
"Set.mem_addAntidiagonal",
"and_left_comm",
"add_comm",
"Prod.fst",
"iff_self",
"instHAdd",
"And",
"Iff",
"HAdd.hAdd",
"congr",
"True",
"propext",
"of_eq_true",
"congrFun'",
"Prod.swap",
"Prod",
"Eq",
"Set... | true |
Polynomial.coeff_comp_degree_mul_degree | Mathlib.Algebra.Polynomial.Eval.Degree | [
"zero_le",
"Eq.mpr",
"Polynomial.C",
"Nat.instCanonicallyOrderedAdd",
"RingHom.instRingHomClass",
"MulOne.toOne",
"Nat.instMulZeroClass",
"Preorder.toLT",
"Polynomial.le_natDegree_of_mem_supp",
"HMul.hMul",
"Polynomial.comp.eq_1",
"Classical.not_not._simp_1",
"IsStrictOrderedRing.toMulPosStr... | true |
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