name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
UpperHalfPlane.instBorelSpace | Mathlib.Analysis.Complex.UpperHalfPlane.Measure | [
"NormedCommRing.toSeminormedCommRing",
"UpperHalfPlane.instMeasurableSpace",
"MeasurableSpace.comap",
"UpperHalfPlane.coe",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"BorelSpace",
"borel",
"MeasurableSpace",
"TopologicalSpace.induced",
"UpperHalfPlane",
"BorelSpace.mk",
... | true |
FiniteArchimedeanClass.congrOrderIso.eq_1 | Mathlib.Algebra.Order.Archimedean.Class | [
"RelIso.mk",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Equiv.subtypeEquiv",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"OrderIso",
"Ne",
"OrderIso.instEquivLike",
"LE.le"... | true |
Lean.Lsp.instReprCompletionItemKind | Lean.Data.Lsp.LanguageFeatures | [
"Repr.mk",
"Lean.Lsp.instReprCompletionItemKind.repr",
"Lean.Lsp.CompletionItemKind",
"Repr"
] | true |
Std.Internal.List.DistinctKeys.filterMap | Std.Data.Internal.List.Associative | [
"List.filter_sublist",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"congrArg",
"List.map",
"List.Sublist.map",
"id",
"Sigma.fst",
"Std.Internal.List.keys_filterMap'",
"List",
"Option.map",
"List.filter",
"PartialEquivBEq",
"List.Sublist",
"Sigma.mk",
"List.filterMap",
"Option.isSome"... | true |
DividedPowers.SubDPIdeal.mk | Mathlib.RingTheory.DividedPowers.SubDPIdeal | [
"DividedPowers.SubDPIdeal",
"DividedPowers.SubDPIdeal.mk",
"Semiring.toModule",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Ne",
"Submodule.instPartialOrder",
"instOfNatNat",
"LE.le",
"Ideal",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCom... | true |
Lean.Syntax.getTailInfo | Init.Meta.Defs | [
"Lean.SourceInfo",
"Option.getD",
"Lean.Syntax",
"Lean.Syntax.getTailInfo?",
"Lean.SourceInfo.none"
] | true |
Std.Http.Trailer.toList | Std.Internal.Http.Data.Chunk | [
"Std.Http.Trailer",
"Std.Http.Header.Name",
"Std.Http.Header.Value",
"List",
"Std.Http.Headers.toList",
"Std.Http.Trailer.headers",
"Prod"
] | true |
exists_nsmul_eq_self_of_coprime | Mathlib.GroupTheory.OrderOfElement | [
"mod_addOrderOf_nsmul",
"Eq.mpr",
"Nat.Coprime",
"Nat.coprime_zero_right",
"instHSMul",
"HMul.hMul",
"congrArg",
"AddMonoid.addOrderOf_eq_one_iff",
"AddMonoid.toAddZeroClass",
"addOrderOf",
"AddMonoid.toNSMul",
"Exists",
"AddZeroClass.toAddZero",
"Eq.mp",
"nsmul_zero",
"id",
"Nat.exi... | true |
CategoryTheory.evaluationLeftAdjoint.congr_simp | Mathlib.CategoryTheory.Adjunction.Evaluation | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"Eq.rec",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.evaluationLeftAdjoint",
"CategoryTheory.Limits.HasCoproductsOfShape",
"CategoryTheory.Catego... | true |
spectrum.spectralRadius_one | Mathlib.Analysis.Normed.Algebra.Spectrum | [
"Nontrivial",
"NormedCommRing.toSeminormedCommRing",
"ENNReal.ofNNReal",
"spectrum",
"Iff.of_eq",
"congrArg",
"iSup",
"SeminormedAddGroup.toNNNorm",
"CompletelyDistribLattice.toCompleteLattice",
"nnnorm_one",
"NNNorm.nnnorm",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra",
"Membership.mem... | true |
CategoryTheory.CatCommSq.mk | Mathlib.CategoryTheory.CatCommSq | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CatCommSq.mk",
"CategoryTheory.Iso",
"CategoryTheory.CatCommSq",
"CategoryTheory.Category"
] | true |
aliasIn | Mathlib.Util.AliasIn | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.const",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
_private.Mathlib.Algebra.BigOperators.Expect.0.BigOperators.delabFinsetExpect.match_3 | Mathlib.Algebra.BigOperators.Expect | [
"of_decide_eq_true",
"Array.getLit",
"Lean.Expr",
"id",
"instOfNatNat",
"dite",
"List.toArray",
"List.cons",
"Array",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.ndrec",
"Eq.refl",
"instDecidableEqNat",
"instLTNat",
"OfNat.ofNat",
"Eq.symm",
"Decidable.decide",
"E... | false |
Lean.Server.RequestHandlerCompleteness.partial.sizeOf_spec | Lean.Server.Requests | [
"Lean.Server.RequestHandlerCompleteness",
"String",
"Lean.Server.RequestHandlerCompleteness._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"String._sizeOf_inst",
"Eq.refl",
"instSizeOfNat",
"OfNat.ofNat",
"Eq",
"Lean.Server.RequestHandlerCom... | true |
Matrix.isNilpotent_toLin'_iff._simp_1 | Mathlib.RingTheory.Nilpotent.Lemmas | [
"Pi.Function.module",
"Algebra.to_smulCommClass",
"Module.End.instMonoid",
"Semiring.toModule",
"Pi.addCommMonoid",
"Matrix.module",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.isNilpotent_toLin'_iff",
"Function.smulCommClass",
"Matrix.toLin'",
"Algebra.id",
"Matrix.addCommMonoid",
"Linea... | false |
Real.norm_deriv_mulExpNegMulSq_le_one | Mathlib.Analysis.SpecialFunctions.MulExpNegMulSq | [
"mul_self_nonneg",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"Real.instIsOrderedRing",
"Norm.norm",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"mul_nonneg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.... | true |
PiTensorProduct.injectiveSeminorm_def | Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm | [
"PiTensorProduct.instModule",
"NormedCommRing.toNormedRing",
"Seminorm.instSupSet",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"PiTensorProduct.toDualContinuousMultilinearMap",
"SeminormedAddCommGroup",
"PiTensorProduct.definition._proof_2._@.Mathlib.Analysis.Normed.Module.PiTensorProduct.Inject... | true |
Equiv.Perm.swapFactors._proof_3 | Mathlib.GroupTheory.Perm.Sign | [
"Iff.mpr",
"Finset.mem_univ",
"Equiv.instEquivLike",
"Finset.univ",
"Finset.mem_sort",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"LinearOrder.toDecidableLE",
"DistribLattice.toLattice",
"Ne",
"LE.le",
"instIs... | false |
ProperVAdd.toContinuousVAdd | Mathlib.Topology.Algebra.ProperAction.Basic | [
"AddMonoid.toAddSemigroup",
"instTopologicalSpaceProd",
"ProperVAdd.isProperMap_vadd_pair",
"Prod.mk",
"Prod.fst",
"HVAdd.hVAdd",
"ProperVAdd",
"TopologicalSpace",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"ContinuousVAdd.mk",
"AddSemigroupAction.toVAdd",
"AddGroup.toSubNe... | true |
Lean.Meta.Match.Pattern.var.noConfusion | Lean.Meta.Match.Basic | [
"id",
"Lean.FVarId",
"Lean.Meta.Match.Pattern.var",
"Lean.Meta.Match.Pattern.noConfusion",
"Lean.Meta.Match.Pattern",
"Eq"
] | false |
_private.Mathlib.Data.Finset.Range.0.Finset.mem_range_le._proof_1_1 | Mathlib.Data.Finset.Range | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
"Finset",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"IntCast.intCast",
"L... | false |
CategoryTheory.ShortComplex.RightHomologyData.canonical_p | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory.ShortComplex.RightHomologyData.canonical",
"CategoryTheory.ShortComplex.pO... | true |
Polynomial.derivWithin_aeval | Mathlib.Analysis.Calculus.Deriv.Polynomial | [
"NormedCommRing.toNormedRing",
"Polynomial.derivative",
"Eq.mpr",
"Polynomial.eval",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Lin... | true |
AlgebraicGeometry.quasiCompact_iff | Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"AlgebraicGeometry.QuasiCompact.casesOn",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCa... | true |
Int8.le | Init.Data.SInt.Basic | [
"Int8",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Int8.toBitVec",
"OfNat.ofNat",
"Eq",
"BitVec.sle"
] | true |
ProbabilityTheory.stronglyMeasurable_stieltjesOfMeasurableRat | Mathlib.Probability.Kernel.Disintegration.MeasurableStieltjes | [
"Real",
"Rat",
"Measurable",
"PseudoMetricSpace.toUniformSpace",
"ProbabilityTheory.IsMeasurableRatCDF.stronglyMeasurable_stieltjesFunction",
"StieltjesFunction.toFun",
"ProbabilityTheory.isMeasurableRatCDF_toRatCDF",
"ProbabilityTheory.stieltjesOfMeasurableRat",
"ProbabilityTheory.toRatCDF",
"Mea... | true |
Char.ofOrdinal | Init.Data.Char.Ordinal | [
"Char.numCodePoints",
"_private.Init.Data.Char.Ordinal.0.Char.ofOrdinal._proof_1",
"UInt32.ofNatLT",
"instOfNatNat",
"_private.Init.Data.Char.Ordinal.0.Char.ofOrdinal._proof_4",
"Fin.val",
"dite",
"instHAdd",
"Char.mk",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Nat.decLt",
"instAddNat",
"_private.In... | true |
CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence_inverse_obj_obj | Mathlib.CategoryTheory.Sites.Descent.DescentDataAsCoalgebra | [
"Opposite",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.Pseudofunctor.DescentDataAsCoalgebra.coalgebraEquivalence",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Bicategory.Adj.Hom.l",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"Quiver.Hom.op",
"CategoryTheory.local... | true |
_private.Mathlib.Algebra.Homology.Factorizations.CM5a.0.CochainComplex.Plus.modelCategoryQuillen.cm5a_cof.step₂.epi_homologyMap_π | Mathlib.Algebra.Homology.Factorizations.CM5a | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"_private.Mathlib.Algebra.Homology.Factorizations.CM5a.0.CochainComplex.Plus.modelCategoryQuillen.cm5a_cof.step₂.S._proof_3",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pretriang... | true |
ProbabilityTheory.«_aux_Mathlib_Probability_Distributions_Poisson_Basic___macroRules_ProbabilityTheory_termPo(_)_1» | Mathlib.Probability.Distributions.Poisson.Basic | [
"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 |
CategoryTheory.Bicategory.OplaxTrans.ComonadBicat.inst._proof_21 | Mathlib.CategoryTheory.Bicategory.Monad.Basic | [
"CategoryTheory.Bicategory.OplaxTrans.ComonadBicat",
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Bicategory.OplaxTrans.ComonadBicat.inst._aux_3",
"CategoryTheory.CategoryStruct.id",... | false |
Lean.Elab.CommandContextInfo.mk.inj | Lean.Elab.InfoTree.Types | [
"Lean.Elab.CommandContextInfo",
"Lean.MetavarContext",
"Lean.FileMap",
"Lean.Elab.CommandContextInfo.mk.noConfusion",
"List",
"And",
"And.intro",
"Lean.Name",
"Lean.Elab.CommandContextInfo.mk",
"Lean.Options",
"Eq",
"Lean.Environment",
"Lean.NameGenerator",
"Lean.OpenDecl",
"Option"
] | true |
CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE_exact | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.homologyIsKernel",
"CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE",
"CategoryTheory.ShortComplex.mk",
"CategoryTheory.Sho... | true |
List.rotate'_rotate'._f | Mathlib.Data.List.Rotate | [
"List.rotate'_cons_succ",
"Eq.mpr",
"Nat.succ_eq_add_one",
"_private.Mathlib.Data.List.Rotate.0.List.rotate'_rotate'.match_1_1",
"congrArg",
"id",
"instOfNatNat",
"List.cons",
"Nat.below",
"instHAppendOfAppend",
"List",
"instHAdd",
"List.rotate'.eq_1",
"List.rotate'",
"HAdd.hAdd",
"Nat... | false |
_private.Std.Internal.Http.Internal.String.0.Std.Http.Internal.UnquoteState._sizeOf_inst | Std.Internal.Http.Internal.String | [
"_private.Std.Internal.Http.Internal.String.0.Std.Http.Internal.UnquoteState._sizeOf_1",
"_private.Std.Internal.Http.Internal.String.0.Std.Http.Internal.UnquoteState",
"SizeOf.mk",
"SizeOf"
] | false |
Path.Homotopy.reflTransSymm._proof_5 | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"False",
"Subtype.mk.congr_simp",
"Mathlib.Meta.NormNum.isNat_add",
"Real.partialOrder",
"Real.instLE",
"Mathlib.Tac... | false |
_private.Mathlib.Topology.MetricSpace.CoveringNumbers.0.Metric.packingNumber_pos_iff._simp_1_1 | Mathlib.Topology.MetricSpace.CoveringNumbers | [
"Set.not_nonempty_iff_eq_empty",
"Set.Nonempty",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Not",
"Set"
] | false |
Turing.ToPartrec.Code.prec | Mathlib.Computability.TuringMachine.Config | [
"Turing.ToPartrec.Code.nil",
"Turing.ToPartrec.Code.succ",
"Turing.ToPartrec.Code.tail",
"Turing.ToPartrec.Code.id",
"Turing.ToPartrec.Code.comp",
"Turing.ToPartrec.Code.case",
"Turing.ToPartrec.Code.head",
"Turing.ToPartrec.Code.zero'",
"Turing.ToPartrec.Code.fix",
"Turing.ToPartrec.Code.pred",
... | true |
Aesop.elabSimpTheorems | Aesop.RuleTac.ElabRuleTerm | [
"Pure.pure",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.Elab.Tactic.ElabSimpArgsResult.simpArgs",
"Lean.Elab.Term.instMonadTermElabM",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
... | true |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.List.range'_eq_toList_rco._simp_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"List.ext_getElem_iff",
"GetElem.getElem",
"List",
"And",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"List.instGetElemNatLtLength",
"Eq",
"List.length"
] | false |
Finset.subset_insert._simp_1 | Mathlib.Data.Finset.Insert | [
"Finset",
"Insert.insert",
"HasSubset.Subset",
"Finset.instInsert",
"True",
"Finset.subset_insert",
"eq_true",
"Finset.instHasSubset",
"Eq",
"DecidableEq"
] | false |
_private.Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset.0.Finset.zero_smul_subset._simp_1_2 | Mathlib.Algebra.GroupWithZero.Action.Pointwise.Finset | [
"instHSMul",
"Finset.smul",
"Finset",
"SMul",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"propext",
"HSMul.hSMul",
"Finset.mem_smul",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
Std.ExtDHashMap.union | Std.Data.ExtDHashMap.Basic | [
"Std.ExtDHashMap.mk",
"LawfulHashable",
"EquivBEq",
"_private.Std.Data.ExtDHashMap.Basic.0.Std.ExtDHashMap.union._proof_1",
"Std.ExtDHashMap.lift₂",
"Std.DHashMap.union",
"Std.ExtDHashMap",
"Hashable",
"BEq",
"Std.DHashMap"
] | true |
Lean.Meta.LazyDiscrTree.ImportData.mk._flat_ctor | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree.ImportData.mk",
"Lean.Meta.LazyDiscrTree.ImportFailure",
"Lean.Meta.LazyDiscrTree.ImportData",
"Array",
"IO.Ref"
] | false |
_private.Mathlib.Algebra.Ring.Int.Parity.0.Int.odd_mul._simp_1_1 | Mathlib.Algebra.Ring.Int.Parity | [
"Odd",
"Int",
"Int.not_even_iff_odd",
"Even",
"propext",
"Int.instAdd",
"Eq.symm",
"Eq",
"Not",
"Int.instSemiring"
] | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Projection.0.isIdempotentElem_iff_spectrum_subset._proof_1_2 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Projection | [
"instSMulOfMul",
"IsScalarTower.right",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"Field.toSemifield",
"instDistribOfSemiring",
"Distrib.toMul",
"Semifield.toCommSemiring",
"Ring.toSemiring",
"Field",
"Ring"
] | false |
TypeVec.«term_:::_» | Mathlib.Data.TypeVec | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
List.mapWithPrefixSuffixAux._sunfold | Batteries.Data.List.Basic | [
"List.mapWithPrefixSuffixAux",
"List.concat",
"List.cons",
"List",
"List.diff.match_1",
"List.nil"
] | false |
Std.Tactic.BVDecide.LRAT.Internal.Result._sizeOf_1 | Std.Tactic.BVDecide.LRAT.Internal.LRATChecker | [
"Std.Tactic.BVDecide.LRAT.Internal.Result.rec",
"instOfNatNat",
"Nat",
"Std.Tactic.BVDecide.LRAT.Internal.Result",
"OfNat.ofNat"
] | false |
List.take_sum_flatten | Mathlib.Algebra.BigOperators.Group.List.Basic | [
"List.take_nil",
"congrArg",
"List.map",
"AddMonoid.toAddZeroClass",
"List.sum",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"instOfNatNat",
"List.rec",
"List.take_length_add_append",
"List.cons",
"Nat.casesAuxOn",
"AddZero.toZero",
"instHAppendOfAppend",
"List",
"instHAdd",
"HAdd... | true |
ULift.semiring._proof_11 | Mathlib.Algebra.Ring.ULift | [
"AddMonoid.toAddSemigroup",
"ULift",
"ULift.nonAssocSemiring",
"NonAssocSemiring.toOne",
"instOfNatNat",
"NatCast.natCast",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"Semiring",
"One.to... | false |
Lean.Meta.Grind.proveHEq? | Lean.Meta.Tactic.Grind.ProveEq | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Monad.toApplicative",
"_private.Lean.Meta.Tactic.Grind.ProveEq.0.Lean.Meta.Grind.ensureInternalized",
"Lean.Meta.Sym.Context",
"Option.some",
"ReaderT.instMona... | true |
Nat.div.go.congr_simp | Init.Data.Nat.Div.Basic | [
"Eq.rec",
"Nat.div.go",
"instOfNatNat",
"Nat",
"LT.lt",
"Eq.ndrec",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | true |
AddActionHom.prod | Mathlib.GroupTheory.GroupAction.Hom | [
"Prod.instVAdd",
"AddActionHom.prod._proof_1",
"VAdd",
"AddActionHom",
"Prod.mk",
"AddActionHom.mk",
"instFunLikeAddActionHom",
"Prod",
"DFunLike.coe"
] | true |
Std.DHashMap.getKey_diff | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.instSDiff",
"congrArg",
"Std.DHashMap.Raw",
"Membership.mem",
"Eq.mp",
"Std.DHashMap.instMembership",
"Std.DHashMap.mem_iff_contains",
"Std.DHashMap.wf",
"instOfNatNat",
"LawfulHashable",
"Std.DHashMap.mem_diff_iff",
"Subtype.mk",
"Bool.true",
"SDiff.sdiff",
"Std.DHashMap.c... | true |
_private.Mathlib.RingTheory.Polynomial.UniversalFactorizationRing.0.MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix._proof_1_4 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"Fin.natAdd",
"HSub.hSub",
"Lean.Grind.Nat.lt_eq",
"Eq.rec",
"id",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Eq.mpr_prop",
"Eq"
] | false |
TensorProduct.prodLeft._proof_3 | Mathlib.LinearAlgebra.TensorProduct.Prod | [
"Prod.smulCommClass",
"instHSMul",
"TensorProduct.comm",
"LinearEquiv.prodCongr",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Prod.instAdd",
"IsScalarTower",
"TensorProduct.addMonoid",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Algebra",
"Alge... | false |
Vector.isSome_find? | Init.Data.Vector.Find | [
"Vector",
"congrArg",
"List.find?",
"Vector.any_toList",
"Vector.any",
"List.isSome_find?",
"Nat",
"_private.Init.Data.Vector.Find.0.Vector.isSome_find?._simp_1_1",
"True",
"eq_self",
"Bool",
"of_eq_true",
"List.any",
"congrFun'",
"Vector.find?",
"Option.isSome",
"Vector.toList",
"... | true |
Ideal.exists_disjoint_powers_of_span_eq_top | Mathlib.RingTheory.Ideal.Maximal | [
"Ideal.span_le",
"Iff.mpr",
"False",
"Preorder.toLT",
"Semiring.toModule",
"ChainCompletePartialOrder.instOfCompleteLattice",
"eq_top_iff",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Set.disjoint_left",
"PartialOrder.toP... | true |
Set.Ico_add_Icc_subset | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"Preorder.toLT",
"add_le_add",
"PartialOrder.toPreorder",
"AddRightStrictMono",
"AddLeftMono",
"Preorder.toLE",
"Membership.mem",
"Exists",
"AddRightMono",
"PartialOrder",
"addLeftMono_of_addLeftStrictMono",
"HasSubset.Subset",
"LE.le",
"Set.Ico",
"And.casesOn",
"addRightMono_of_addRig... | true |
_private.Mathlib.Topology.Compactness.Compact.0.IsClosed.exists_minimal_nonempty_closed_subset._simp_1_5 | Mathlib.Topology.Compactness.Compact | [
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.mem_compl_iff",
"Set"
] | false |
ENormedAddMonoid.rec | Mathlib.Analysis.Normed.Group.Defs | [
"ENormedAddMonoid.mk",
"ENormedAddMonoid",
"AddMonoid.toZero",
"ESeminormedAddMonoid",
"ESeminormedAddMonoid.toAddMonoid",
"TopologicalSpace",
"ESeminormedAddMonoid.toContinuousENorm",
"ENorm.enorm",
"Iff",
"ContinuousENorm.toENorm",
"ENNReal",
"Zero.toOfNat0",
"ENNReal.instZero",
"OfNat.o... | false |
eq_of_forall_lt_iff | Mathlib.Order.Basic | [
"Iff.mpr",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"LE.le.antisymm",
"le_of_forall_lt",
"Iff",
"LT.lt",
"Iff.mp",
"LinearOrder.toPartialOrder",
"Eq"
] | true |
CategoryTheory.ShortComplex.HomologyMapData.natTransApp_left | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyMapData",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.LeftHomologyData.isPreservedBy_of_preserves",
"CategoryTheory.ShortComplex.mapNatTrans",
"Category... | true |
CategoryTheory.Limits.preservesLimit_leftOp | Mathlib.CategoryTheory.Limits.Preserves.Opposites | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Functor.mapCocone",
"CategoryTheory.Limits.PreservesLimit",
"Opposite",
"CategoryTheory.Limits.isColimitCoconeLeftOpOfCone",
"CategoryTheory.Functor.comp",
"Nonempty.intro",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Lim... | true |
UniformEquiv.coe_punitProd | Mathlib.Topology.UniformSpace.Equiv | [
"UniformSpace",
"instUniformSpacePUnit",
"instUniformSpaceProd",
"UniformEquiv.instEquivLike",
"UniformEquiv.punitProd",
"PUnit",
"Prod",
"Eq",
"Prod.snd",
"DFunLike.coe",
"UniformEquiv",
"rfl",
"EquivLike.toFunLike"
] | true |
SeminormedAddCommGroup.toSeminormedAddGroup | Mathlib.Analysis.Normed.Group.Defs | [
"SeminormedAddCommGroup",
"SeminormedAddGroup",
"SeminormedAddCommGroup.dist_eq",
"AddCommGroup.toAddGroup",
"SeminormedAddCommGroup.toNorm",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SeminormedAddGroup.mk",
"SeminormedAddCommGroup.toAddCommGroup"
] | true |
Turing.TM2Computable.mk.sizeOf_spec | Mathlib.Computability.TuringMachine.Computable | [
"Turing.FinTM2.k₀",
"Turing.TM2ComputableAux.tm",
"List.map",
"Option.some",
"Turing.TM2Computable._sizeOf_inst",
"instOfNatNat",
"Turing.TM2Computable",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Turing.TM2Computable.mk",
"Turing.FinTM2.Γ",
"Turing.FinTM2.k₁",
"Turing.T... | true |
GradedRing.projZeroRingHom._proof_3 | Mathlib.RingTheory.GradedAlgebra.Basic | [
"SetLike",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"instAddCommMonoidDirectSum",
"AddSubmonoidClass.toAddMonoid._proof_5",
"congrArg",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"GradedRing.toDecomposition",
"AddSubmonoidClass"... | false |
UInt16.one_mul | Init.Data.UInt.Lemmas | [
"UInt16.toBitVec",
"BitVec.one_mul",
"HMul.hMul",
"instMulUInt16",
"BitVec",
"instOfNatNat",
"UInt16",
"Nat",
"Iff.mp",
"OfNat.ofNat",
"UInt16.toBitVec_inj",
"Eq",
"UInt16.instOfNat",
"instHMul"
] | true |
_private.Lean.Meta.GetUnfoldableConst.0.Lean.Meta.getUnfoldableConstNoEx?._sparseCasesOn_1 | Lean.Meta.GetUnfoldableConst | [
"Lean.ConstantInfo.recInfo",
"Lean.ConstantInfo.defnInfo",
"Lean.ConstructorVal",
"Nat.ne_of_beq_eq_false",
"Lean.QuotVal",
"Lean.ConstantInfo.inductInfo",
"Lean.ConstantInfo.opaqueInfo",
"Nat.shiftRight",
"Lean.ConstantInfo.thmInfo",
"Nat.hasNotBit",
"Lean.ConstantInfo.rec",
"instOfNatNat",
... | false |
CategoryTheory.Functor.mapMon_obj_mon_mul | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.map",
"CategoryTheory.Mon",
"CategoryTheory.Functor.LaxMonoidal.μ",
"CategoryTheory.Mon.X",
"CategoryTheory.Mon.instCategory",
"CategoryTheory.MonoidalCatego... | true |
maximal_le_iff | Mathlib.Order.Minimal | [
"Eq.ge",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"id",
"LE.le",
"maximal_iff_eq",
"Iff",
"Maximal",
"Eq",
"rfl"
] | true |
differentiableAt_iteratedDerivWithin_cexp | Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra",
"Semiring.toModule",
"ContDiff.pow",
"Real.pi",
"DifferentiableOn.congr",
"instAddMonoidWithOneENat",
"HMul.hMul",
"contDiff_id",
"Complex.instNormedAddCommGroup",
"ENat.instNatCast",
"DifferentiableAt"... | true |
ProofWidgets.ExprPresentationProps.mk.inj | ProofWidgets.Presentation.Expr | [
"Lean.Server.WithRpcRef",
"ProofWidgets.ExprPresentationProps.mk",
"ProofWidgets.ExprWithCtx",
"Eq",
"ProofWidgets.ExprPresentationProps.mk.noConfusion",
"ProofWidgets.ExprPresentationProps"
] | true |
Subsemiring.instSetLike | Mathlib.Algebra.Ring.Subsemiring.Defs | [
"SetLike",
"Submonoid.toSubsemigroup",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"Subsemiring.toSubmonoid",
"Subsemiring",
"MulZeroOneClass.toMulOneClass",
"SetLike.mk",
"MulOneClass.toMulOne",
"NonAssocSemiring",
"Subsemiring.instSetLike._proof_1",
"Subsemigroup.carrier",
"Eq",
... | true |
ModularForm.instGCommRing._proof_7 | Mathlib.NumberTheory.ModularForms.Basic | [
"SlashInvariantForm",
"ModularForm",
"Int.instAddCommMonoid",
"Subgroup.HasDetPlusMinusOne",
"Real",
"ModularForm.toSlashInvariantForm",
"ModularForm.instGMulIntOfHasDetPlusMinusOneFinOfNatNatReal",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"GradedMonoid.GOne.toOne",
"Matrix",
"AddMonoid.toAddZ... | false |
_private.Mathlib.Data.Stream.Init.0.Stream'.cons.match_1.eq_2 | Mathlib.Data.Stream.Init | [
"Stream'.cons.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
Nat.toArray_toList_roo | Init.Data.Range.Polymorphic.NatLemmas | [
"Std.PRange.instIsAlwaysFiniteNat_1",
"List.toArray",
"Std.Roo.toArray_toList",
"Array",
"Std.PRange.instUpwardEnumerableNat",
"Nat",
"Std.PRange.instLawfulUpwardEnumerableNat",
"Nat.decLt",
"Std.Roo.toArray",
"instLTNat",
"Eq",
"Std.Roo.toList",
"Std.Roo.mk"
] | true |
LDL.lowerInv_eq_gramSchmidtBasis | Mathlib.Analysis.Matrix.LDL | [
"NormedCommRing.toNormedRing",
"LDL.lowerInv",
"Eq.mpr",
"Pi.Function.module",
"LDL.lowerInv.eq_1",
"InnerProductSpace.toNormedSpace",
"Preorder.toLT",
"Semiring.toModule",
"Pi.addCommMonoid",
"NormedRing.toRing",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Matr... | true |
_private.Mathlib.Algebra.Homology.CochainComplexOpposite.0.CochainComplex.exactAt_op._proof_1_2 | Mathlib.Algebra.Homology.CochainComplexOpposite | [
"Int.instAddCommGroup",
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"AddMonoid.toAddSemigroup",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Int.instLinearOrder",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"PartialOr... | false |
String.Pos.Raw.IsValidForSlice | Init.Data.String.Defs | [
"String.Slice",
"String.Pos.Raw",
"String.Pos.Raw.IsValidForSlice.mk"
] | true |
ChartedSpace.sum_of_nonempty.congr_simp | Mathlib.Geometry.Manifold.ChartedSpace | [
"Sum",
"instTopologicalSpaceSum",
"TopologicalSpace",
"ChartedSpace.sum_of_nonempty",
"Nonempty",
"Eq.refl",
"Eq",
"ChartedSpace"
] | true |
SimpleGraph.Walk.IsHamiltonian.congr_simp | Mathlib.Combinatorics.SimpleGraph.Hamiltonian | [
"instSubsingletonDecidable",
"Decidable",
"SimpleGraph.Walk",
"Eq.rec",
"Pi.instSubsingleton",
"SimpleGraph",
"Eq.ndrec",
"Eq.refl",
"Subsingleton.elim",
"Eq",
"SimpleGraph.Walk.IsHamiltonian",
"DecidableEq"
] | true |
BilinForm.toMatrixAux | Mathlib.LinearAlgebra.Matrix.BilinearForm | [
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Matrix.module",
"LinearMap.BilinForm.toMatrixAux",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matrix",
"LinearMap.instSMulCommClass",
"Algebra.id",
"Matrix.addCommMonoid",
"LinearMap.module",
"LinearM... | true |
_private.Mathlib.Data.Fin.SuccPred.0.Fin.castSucc_lt_or_lt_succ._simp_1_1 | Mathlib.Data.Fin.SuccPred | [
"Fin.val",
"Fin.lt_def",
"Nat",
"LT.lt",
"instLTFin",
"propext",
"instLTNat",
"Fin",
"Eq"
] | false |
Array.find?_eq_bind_findIdx?_getElem? | Init.Data.Array.Find | [
"List.getElem?_toArray",
"congrArg",
"List.find?",
"List.instGetElem?NatLtLength",
"Option.bind",
"Array.casesOn",
"List.findIdx?",
"List.findIdx?_toArray",
"List.toArray",
"Array",
"funext",
"List",
"Nat",
"List.find?_eq_bind_findIdx?_getElem?",
"congr",
"LT.lt",
"True",
"eq_self"... | true |
_private.Mathlib.LinearAlgebra.RootSystem.Reduced.0.RootPairing.pairing_neg_one_neg_four_iff'._simp_1_1 | Mathlib.LinearAlgebra.RootSystem.Reduced | [
"neg_eq_iff_eq_neg",
"InvolutiveNeg",
"propext",
"InvolutiveNeg.toNeg",
"Eq.symm",
"Eq",
"Neg.neg"
] | false |
MvPowerSeries.rescale_rescale | Mathlib.RingTheory.MvPowerSeries.Substitution | [
"Nat.instMulZeroClass",
"Semigroup.toMul",
"MvPowerSeries.rescale",
"Semiring.toModule",
"HMul.hMul",
"Monoid.toMulOneClass",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"_private.Mathlib.RingTheory.MvPowerSeries.Substitution.0.MvPowerSeries.rescale._simp_4",
"... | true |
CategoryTheory.Subobject.factors_of_le | Mathlib.CategoryTheory.Subobject.FactorThru | [
"CategoryTheory.Subobject.Factors",
"Eq.mpr",
"CategoryTheory.Subobject.ofLE_arrow",
"CategoryTheory.Category.assoc",
"_private.Mathlib.CategoryTheory.Subobject.FactorThru.0.CategoryTheory.Subobject.factors_of_le.match_1_2",
"CategoryTheory.Over",
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Mono... | true |
_private.Mathlib.LinearAlgebra.RootSystem.Base.0.RootPairing.Base.root_mem_span_int._simp_1_2 | Mathlib.LinearAlgebra.RootSystem.Base | [
"Submodule",
"Submodule.toAddSubmonoid",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoid",
"AddCommMonoid",
"Submodule.mem_toAddSubmonoid",
"Submodule.setLike",
"propext",
"Semiring",
"AddCommMonoid.toAddMonoid",
"Module",
"AddSubmonoid.instSetLike",
"Eq",
"SetLike.instMember... | false |
lt_mul_inv_iff_mul_lt._simp_2 | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"lt_mul_inv_iff_mul_lt",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"MulRightStrictMono",
"L... | false |
instWeaklyLawfulMonadAttachStateRefT'OfLawfulMonad | Init.Control.Lawful.MonadAttach.Instances | [
"StateRefT'.instMonadAttachOfMonad",
"WeaklyLawfulMonadAttach",
"LawfulMonad",
"_private.Init.Control.Lawful.MonadAttach.Instances.0.instWeaklyLawfulMonadAttachStateRefT'OfLawfulMonad._proof_1",
"StateRefT'",
"StateRefT'.instMonad",
"MonadAttach",
"Monad"
] | true |
Real.logb_nonneg_iff_of_base_lt_one | Mathlib.Analysis.SpecialFunctions.Log.Base | [
"Eq.mpr",
"Real.instLE",
"Real",
"Preorder.toLT",
"Real.instZero",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Real.instLT",
"Preorder.toLE",
"id",
"Real.logb_neg_iff_of_base_lt_one",
"LE.le",
"Real.instOne",
"Real.logb",
"Iff",
"not_lt",
"LT.lt",
"propext",
"One.toOfNat... | true |
MvPowerSeries.instAlgebra | Mathlib.RingTheory.MvPowerSeries.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Algebra",
"MvPowerSeries",
"MvPowerSeries.map",
"AddZeroClass.toAddZero",
"Algebra.toModule",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid... | true |
_private.Mathlib.Probability.Independence.Integration.0.ProbabilityTheory.IndepFun.integral_bilin_comp_comp'.match_1_3 | Mathlib.Probability.Independence.Integration | [
"MeasureTheory.Measure",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Integrable",
"SeminormedAddGroup.toContinuousENorm",
"And.casesOn",
"MeasurableSpace",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"And",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"And.intro",
"NormedAddCommGroup.... | false |
PresheafOfModules.Hom.app | Mathlib.Algebra.Category.ModuleCat.Presheaf | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"RingCat",
"PresheafOfModules.obj",
"PresheafOfModules",
"PresheafOfModules.Hom",
"ModuleCat.moduleCategory",
"RingCat.instCategory",
"CategoryTheory.Category.opposite",
"CategoryTheory... | true |
_private.Mathlib.Data.ENNReal.Operations.0.ENNReal.toNNReal_iInf._simp_1_1 | Mathlib.Data.ENNReal.Operations | [
"ENNReal.ofNNReal",
"iInf",
"NNReal",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"NNReal.instConditionallyCompleteLinearOrderBot",
"CompleteLinearOrder.toConditionallyCompleteLinearOrderBot",
"ENNReal",
"ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder",
... | false |
_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.Sum.dist_comm | Mathlib.Topology.MetricSpace.Gluing | [
"Real",
"add_left_comm",
"congrArg",
"Sum.casesOn",
"Sum",
"Nonempty.some",
"dist_comm",
"Sum.inl",
"Nonempty.intro",
"Real.instAddCommSemigroup",
"add_comm",
"Real.instAdd",
"Real.instOne",
"instHAdd",
"MetricSpace",
"HAdd.hAdd",
"Sum.inr",
"congr",
"True",
"eq_self",
"of_eq... | true |
Mathlib.Meta.NormNum.asc_factorial_aux | Mathlib.Tactic.NormNum.NatFactorial | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Nat.ascFactorial",
"id",
"instMulNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.symm",
"Eq",
"Nat.ascFactorial_mul_ascFactorial",
"instHMul"
] | true |
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