name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
TrivialLieModule.instLieRingModule._proof_2 | Mathlib.Algebra.Lie.Abelian | [
"congrArg",
"AddCommGroup.toAddCommMonoid",
"TrivialLieModule.instAddCommGroup",
"AddMonoid.toAddZeroClass",
"TrivialLieModule",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"ins... | false |
RelIso.sumLexComplLeft_symm_apply | Mathlib.Order.Hom.Lex | [
"Equiv.instEquivLike",
"DecidableRel",
"Sum",
"Equiv",
"Subtype",
"Subrel",
"Std.Trichotomous",
"RelIso.sumLexComplLeft",
"IsTrans",
"RelIso",
"RelIso.instFunLike",
"Equiv.sumCompl",
"Eq",
"DFunLike.coe",
"Not",
"rfl",
"Sum.Lex",
"EquivLike.toFunLike"
] | true |
Shrink.continuousLinearEquiv | Mathlib.Topology.Algebra.Module.TransferInstance | [
"Shrink.instAddCommMonoid",
"Equiv.continuousLinearEquiv",
"AddCommMonoid",
"TopologicalSpace",
"ContinuousLinearEquiv",
"RingHomInvPair.ids",
"Shrink.instTopologicalSpace",
"Semiring",
"Shrink",
"Module",
"Equiv.symm",
"Shrink.instModule",
"equivShrink",
"RingHom.id",
"Semiring.toNonAss... | true |
_private.Init.Internal.Order.Basic.0.Lean.Order.implication_order_monotone_or.match_1_1 | Init.Internal.Order.Basic | [
"Lean.Order.ImplicationOrder",
"Or.casesOn",
"Or.inl",
"Or",
"Or.inr"
] | false |
AffineMap.comp | Mathlib.LinearAlgebra.AffineSpace.AffineMap | [
"AffineMap.mk",
"AffineMap.instFunLike",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"Function.comp",
"AddCommGroup",
"AffineMap",
"AffineMap.comp._proof_1",
"LinearMap.comp",
"AffineMap.linear",
"AddTorsor",
"AffineMap.comp._proof_2",
"Module",
"RingHom.id",
"Semiring.toN... | true |
_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.comap_isBasis_iff._simp_1_10 | Mathlib.Combinatorics.Matroid.Map | [
"HasSubset.Subset",
"Set.preimage",
"propext",
"Set.image",
"Set.image_subset_iff",
"Eq.symm",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
OrderMonoidIso.val_inv_unitsCongr_symm_apply | Mathlib.Algebra.Order.Hom.Units | [
"Monoid",
"Units.val",
"MulEquiv.instEquivLike",
"OrderMonoidIso.unitsCongr",
"Monoid.toMulOneClass",
"OrderMonoidIso.instMulEquivClass",
"Units",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Inv.inv",
"OrderMonoidIso.symm",
"OrderMonoidIso",
"MulEquiv",
"Eq.refl",
"Units.instMul",
"OrderM... | true |
Lean.Meta.instReprCoeFnType | Lean.Meta.CoeAttr | [
"Lean.Meta.CoeFnType",
"Repr.mk",
"Lean.Meta.instReprCoeFnType.repr",
"Repr"
] | true |
Lean.IR.Sorry.State.mk.inj | Lean.Compiler.IR.Sorry | [
"Lean.NameMap",
"Lean.IR.Sorry.State",
"And",
"Lean.IR.Sorry.State.mk.noConfusion",
"And.intro",
"Bool",
"Lean.Name",
"Eq",
"Lean.IR.Sorry.State.mk"
] | true |
Mathlib.Tactic.Monoidal.evalWhiskerLeft_comp | Mathlib.Tactic.CategoryTheory.Monoidal.Normalize | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"CategoryTheory.Mo... | true |
normalizationMonoidOfMonoidHomRightInverse._proof_5 | Mathlib.Algebra.GCDMonoid.Basic | [
"Units.val",
"Associates.mk",
"Associates.mk_eq_mk_iff_associated",
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"Units",
"MulOne.toMul",
"CommMonoidWithZero.toMonoidWithZero",
"if_pos",
"Units.instOne",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",... | false |
Lean.Elab.Term.tryPostponeIfHasMVars | Lean.Elab.Term.TermElabM | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Std.instToFormatString",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.indentD",
"Lean.Elab.Term.instMonadTermElabM",
"String",
"Lean.Meta.State",
"Lean.MessageData.instAppend",
"Funct... | true |
_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable._proof_11 | Init.Data.String.Pattern.String | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance._proof_1",
"Int.add_one_l... | false |
Primrec.list_flatten | Mathlib.Computability.Primrec.List | [
"Primrec.of_eq",
"congrArg",
"Primrec.snd",
"id",
"Prod.mk",
"List.rec",
"Primrec.const",
"Prod.fst",
"List.cons",
"Primcodable.prod",
"Primrec",
"instHAppendOfAppend",
"List",
"True",
"Primrec.list_foldr",
"Primrec.comp",
"eq_self",
"Primcodable",
"of_eq_true",
"Primcodable.li... | true |
Turing.ToPartrec.Code.succ | Mathlib.Computability.TuringMachine.Config | [
"Turing.ToPartrec.Code.succ",
"Turing.ToPartrec.Code"
] | true |
CategoryTheory.IsHomLift.eq_of_isHomLift | Mathlib.CategoryTheory.FiberedCategory.HomLift | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Functor.IsHomLift",
"CategoryTheory.IsHomLift.codomain_eq",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Category.comp_id",
"CategoryTheory.Functor.map",
... | true |
RootPairing.InvariantForm.isOrthogonal_reflection | Mathlib.LinearAlgebra.RootSystem.RootPositive | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RootPairing.InvariantForm",
"LinearMap.IsOrthogonal",
"AddCommGroup",
"CommRing.toCommSemiring",
"RootPairing.reflection",
"RingHomInvPair.ids",
"LinearEquiv",
"DFinsupp.instEquivLikeLinearEquiv",
"Module",
"RingHom.id",... | true |
PresheafOfModules.presheaf.eq_1 | Mathlib.Algebra.Category.ModuleCat.Presheaf.Free | [
"PresheafOfModules.map",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"PresheafOfModules.presheaf._proof_5",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Functor.... | true |
GenContFract.of_s_head | Mathlib.Algebra.ContinuedFractions.Computation.Translations | [
"GenContFract.s",
"Int.cast",
"Eq.mpr",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Int.floor",
"GenContFract.IntFractPair.stream",
"congrArg",
"Int.fract",
"LinearOrder",
"AddGroupWithOne.toAddMonoidWithOne",
"GenContFract.IntFractPair",
"DivisionSemiring.toGroupWith... | true |
Associates.is_pow_of_dvd_count | Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet | [
"Nontrivial",
"Eq.mpr",
"Associates.mk",
"instHSMul",
"Dvd.dvd",
"Associates.instInhabited",
"congrArg",
"exists_const._simp_1",
"Associates.pow_factors",
"Associates.instZero",
"Associates.count",
"eq_iff_true_of_subsingleton._simp_1",
"AddMonoid.toNSMul",
"Associates.count_some",
"Deci... | true |
Quaternion.dualNumberEquiv._proof_2 | Mathlib.Algebra.DualQuaternion | [
"TrivSqZeroExt.one",
"NegZeroClass.toNeg",
"TrivSqZeroExt.snd",
"CommRing",
"QuaternionAlgebra.imI",
"CommSemiring.toSemiring",
"DualNumber",
"AddGroupWithOne.toAddMonoidWithOne",
"QuaternionAlgebra.re",
"QuaternionAlgebra.mk",
"Prod.mk",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMo... | false |
_private.Mathlib.Util.CompileInductive.0.Mathlib.Util.replaceConst.match_1 | Mathlib.Util.CompileInductive | [
"_private.Mathlib.Util.CompileInductive.0.Mathlib.Util.replaceConst._sparseCasesOn_1",
"Lean.Expr.const",
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Level",
"List",
"Lean.Name",
"Lean.Expr.ctorIdx"
] | false |
CategoryTheory.Bicategory.associator_naturality_middle_assoc | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Eq.mp",
"CategoryTheory.Bicategory.whiskerRight",
"id",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Bicategory.associator_naturality_middle"... | true |
differentiableOn_pi'' | Mathlib.Analysis.Calculus.FDeriv.Prod | [
"Iff.mpr",
"differentiableOn_pi",
"NormedSpace",
"Pi.topologicalSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Pi.module",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"SeminormedAddCommGroup.toPseudoMetricSpa... | true |
Monoid.End.instInhabited | Mathlib.Algebra.Group.Hom.Defs | [
"Monoid.End.instOne",
"One.toOfNat1",
"Inhabited",
"MulOne",
"OfNat.ofNat",
"Monoid.End",
"Inhabited.mk"
] | true |
CategoryTheory.Grp.instMonoidalMonForget₂Mon._proof_6 | Mathlib.CategoryTheory.Monoidal.Grp | [
"Eq.mpr",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Grp.instMonoidalCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Grp.forget₂Mon",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryThe... | false |
DFinsupp.subtypeSupportEqEquiv._proof_5 | Mathlib.Data.DFinsupp.Defs | [
"Iff.mpr",
"Eq.mpr",
"DFinsupp.mk",
"dite_congr",
"Trans.trans",
"and_true",
"Iff.of_eq",
"congrArg",
"Finset",
"iff_true",
"Decidable",
"Membership.mem",
"Exists",
"DFinsupp.instDFunLike",
"Set.Elem",
"Subtype",
"Ne",
"DFinsupp.support",
"dite",
"Subtype.mk",
"iff_self",
"... | false |
ne_zero_and_ne_zero_of_mul | Mathlib.Algebra.GroupWithZero.Basic | [
"HMul.hMul",
"MulZeroClass.toMul",
"MulZeroClass",
"right_ne_zero_of_mul",
"Ne",
"And",
"And.intro",
"left_ne_zero_of_mul",
"Zero.toOfNat0",
"OfNat.ofNat",
"MulZeroClass.toZero",
"instHMul"
] | true |
_private.Mathlib.Analysis.MellinInversion.0.mellin_eq_fourier._simp_1_6 | Mathlib.Analysis.MellinInversion | [
"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 |
DivisionSemiring.mk.noConfusion | Mathlib.Algebra.Field.Defs | [
"Nontrivial",
"Semiring.toNatCast",
"Semigroup.toMul",
"instHDiv",
"Inv",
"HMul.hMul",
"NNRatCast",
"AddMonoid.toZero",
"DivisionSemiring.noConfusion",
"id",
"HDiv.hDiv",
"Div",
"NNRat",
"Ne",
"Int",
"DivInvMonoid.div_eq_mul_inv._autoParam",
"NNRat.num",
"Nat.cast",
"autoParam",
... | false |
_private.Mathlib.Probability.Distributions.Gaussian.Real.0.ProbabilityTheory.gaussianPDFReal_inv_mul._simp_1_4 | Mathlib.Probability.Distributions.Gaussian.Real | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
getElem?_eq_none_iff._simp_1 | Init.GetElem | [
"getElem?_eq_none_iff",
"GetElem?",
"Decidable",
"Option.none",
"propext",
"GetElem?.getElem?",
"Eq",
"Not",
"Option",
"LawfulGetElem"
] | false |
lowerCentralSeries_pi_of_finite | Mathlib.GroupTheory.Nilpotent | [
"Set.univ",
"Finite",
"Group",
"Pi.group",
"Subgroup",
"Subgroup.lowerCentralSeries",
"Nat",
"Subgroup.lowerCentralSeries_pi_of_finite",
"Subgroup.pi",
"Eq"
] | true |
_private.Init.Data.String.Decode.0.Char.utf8Size_eq_four_iff._proof_1_5 | Init.Data.String.Decode | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Char.toNat",
"id",
"in... | false |
Std.PRange.UpwardEnumerable.succMany?_succ?_eq_succ?_bind_succMany? | Init.Data.Range.Polymorphic.UpwardEnumerable | [
"Std.PRange.UpwardEnumerable",
"Option.bind",
"instOfNatNat",
"Std.PRange.UpwardEnumerable.succ?",
"instHAdd",
"Std.PRange.UpwardEnumerable.succMany?",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq",
"Std.PRange.UpwardEnumerable.succMany?_add_one_eq_succ?_bind_succMany?",
"Std.PRange.... | true |
Nat.add_le_add_iff_left._simp_1 | Init.Data.Nat.Basic | [
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat.add_le_add_iff_left",
"Nat",
"propext",
"instAddNat",
"Eq"
] | false |
Subfield.mk.congr_simp | Mathlib.Algebra.Field.Subfield.Basic | [
"Subring.toSubsemiring",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Ring.toNonAssocRing",
"Submonoid.toSubsemigroup",
"DivisionSemiring.toGroupWithZero",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Eq.rec",
"DivisionRing.toDivisionSemiring",
"MulOne.toMul",
... | true |
Polynomial.smeval_assoc_X_pow | Mathlib.Algebra.Polynomial.Smeval | [
"add_mul",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"HMul.hMul",
"Pow",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Modu... | true |
smul_mem_asymptoticCone_iff._simp_1 | Mathlib.Topology.Algebra.AsymptoticCone | [
"OrderTopology",
"instHSMul",
"Preorder.toLT",
"ContinuousSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"AddCommGroup.toAddGroup",
"Membership.mem",
"SemilatticeInf.toParti... | false |
CategoryTheory.Limits.CokernelCofork.isColimitMapBifunctor.exists_desc | Mathlib.CategoryTheory.Limits.Preserves.BifunctorCokernel | [
"CategoryTheory.Limits.Cofork.IsColimit.hom_ext",
"Eq.mpr",
"CategoryTheory.Functor.flip",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasBinaryCoproduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPai... | true |
CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker | Mathlib.RingTheory.Idempotents | [
"Iff.mpr",
"RingHom.instRingHomClass",
"Semiring.toModule",
"Equiv.instEquivLike",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"congrArg",
"Equiv.symm_apply_apply",
"CompleteOrthogonalIdempotents.lift_of_isNilpotent_ker_aux",
"RingHom",
"Function.comp",
"Membership.mem",
"Exists",
"Eq.mp... | true |
_private.Lean.Meta.Tactic.Grind.CasesMatch.0.Lean.Meta.Grind.casesMatch.match_6 | Lean.Meta.Tactic.Grind.CasesMatch | [
"Lean.Expr",
"Prod.mk",
"Array",
"Prod",
"Prod.casesOn"
] | false |
AddAction.instElemOrbit_1._proof_1 | Mathlib.GroupTheory.GroupAction.Defs | [
"AddMonoid.toAddSemigroup",
"AddAction.orbitRel.Quotient.orbit",
"AddSemigroupAction.add_vadd",
"Membership.mem",
"Set.Elem",
"Subtype",
"AddAction.orbitRel.Quotient.mapsTo_vadd_orbit",
"AddAction.orbitRel.Quotient",
"VAdd.mk",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"i... | false |
ContractingWith.fixedPoint_unique | Mathlib.Topology.MetricSpace.Contracting | [
"CompleteSpace",
"ContractingWith.fixedPoint_unique'",
"PseudoMetricSpace.toUniformSpace",
"NNReal",
"MetricSpace",
"ContractingWith.fixedPoint",
"ContractingWith",
"Nonempty",
"MetricSpace.toPseudoMetricSpace",
"Function.IsFixedPt",
"ContractingWith.fixedPoint_isFixedPt",
"MetricSpace.toEMetr... | true |
_private.Lean.Parser.Extension.0.Lean.Parser.compileParserDescr.visit.match_3 | Lean.Parser.Extension | [
"Unit.unit",
"Lean.Parser.ParserCategory",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
Lean.PrettyPrinter.Delaborator.State.mk._flat_ctor | Lean.PrettyPrinter.Delaborator.Basic | [
"Lean.PrettyPrinter.Delaborator.State.mk",
"Nat",
"Lean.Elab.Info",
"Lean.PrettyPrinter.Delaborator.State",
"Lean.PrettyPrinter.Delaborator.SubExpr.HoleIterator",
"Lean.SubExpr.PosMap"
] | false |
LocalizedModule.instRing._proof_9 | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"AddGroupWithOne.intCast_negSucc._autoParam",
"Semiring.toNatCast",
"Ring.toNonAssocRing",
"LocalizedModule",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"OreLocalization.instAddCommGroup",
"IntCast.intCast",
"Algebra",
"AddCommGroup.toAddGroup",
"inferInstance",
"AddCommGroup",
... | false |
MeasureTheory.Measure.rnDeriv_add_right_of_absolutelyContinuous_of_mutuallySingular | Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.ae.congr_simp",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure",
"MeasurableSet",
"MeasureTheory.Measure.restrict_add",
"Measurable.aemeasurable",
"congrArg",
"Compl.compl",
"MeasureTheory.ae_of_ae_restrict_of_ae_restrict_compl",
"Measu... | true |
Multiset.foldl_zero | Mathlib.Data.Multiset.MapFold | [
"Multiset",
"Multiset.foldl",
"Zero.toOfNat0",
"RightCommutative",
"OfNat.ofNat",
"Eq",
"rfl",
"Multiset.instZero"
] | true |
Finset.bipartiteBelow.eq_1 | Mathlib.Combinatorics.Enumerative.DoubleCounting | [
"Finset",
"Decidable",
"Eq.refl",
"Finset.bipartiteBelow",
"Finset.filter",
"Eq"
] | true |
Batteries.AssocList.findEntryP?._unsafe_rec | Batteries.Data.AssocList | [
"cond",
"Batteries.AssocList.toList.match_1",
"Option.some",
"Prod.mk",
"Batteries.AssocList",
"Batteries.AssocList.findEntryP?._unsafe_rec",
"Option.none",
"Unit",
"Bool",
"Prod",
"Option"
] | false |
not_fermatLastTheoremFor_two | Mathlib.NumberTheory.FLT.Basic | [
"False",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"Nat.instCharZero",
"OfNat.ofNat_ne_zero._simp_1",
"instOfNatNat",
"Nat.instAddMonoidWithOne",
"Nat.instNeZeroSucc",
"Nat",
"FermatLastTheoremFor",
"True",
"eq_self",
"of_eq_true",
"Nat.instSemiring",
"Zero.toOfNat0",
"OfNat.ofNat",
... | true |
FreeLieAlgebra.liftAux_map_mul | Mathlib.Algebra.Lie.Free | [
"LieAlgebra.toModule",
"LieAlgebra.instLieRingCommutatorRing",
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"MonoidAlgebra.distribMulAction",
"FreeNonUnitalNonAssocAlgebra",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"Bracket.bracket",
"NonUnitalAlgHom.instFunLike_1",
"CommutatorRin... | true |
TypeVec.toSubtype._f | Mathlib.Data.TypeVec | [
"TypeVec.toSubtype.match_1",
"Fin2.fz",
"TypeVec.ofRepeat",
"Subtype",
"Fin2.fs",
"Nat",
"TypeVec.repeat",
"Fin2.below",
"TypeVec.Subtype_",
"TypeVec.drop",
"TypeVec.Arrow",
"Nat.succ",
"TypeVec.dropFun",
"Fin2",
"TypeVec"
] | false |
selfAdjointPart_apply_coe | Mathlib.Algebra.Star.Module | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"StarMul",
"Nat.instAtLeastTwoHAddOfNat",
"LinearMap.instFunLike",
"Invertible.invOf",
"AddCommGroup.toAddGroup",
"selfAdjointPart",
"Membership... | true |
Set.uIoo_subset_Ioo | Mathlib.Order.Interval.Set.UnorderedInterval | [
"Lattice.toSemilatticeSup",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"HasSubset.Subset",
"SemilatticeInf.toMin",
"LE.le",
"le_inf",
"Set.uIoo",
"Set.Icc",
"And.right",... | true |
AddSubgroup.unop_injective | Mathlib.Algebra.Group.Subgroup.MulOpposite | [
"AddSubgroup.unop",
"AddSubgroup.opEquiv",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddOpposite",
"OrderIso.symm",
"AddSubgroup",
"AddGroup",
"AddOpposite.instAddGroup",
"OrderIso.injective",
"Function.Injective"
] | true |
_private.Lean.Level.0.Lean.Level.geq.go._sparseCasesOn_2 | Lean.Level | [
"Lean.Level.ctorIdx",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Level.mvar",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level.imax",
"instOfNatNat",
"Lean.Level",
"Nat.land",
"Lean.Level.zero",
"Nat",
"Bool",
"Lean.Level.rec",
"Lean.Name",
"Eq.refl",
"Lean.Level.succ",
"OfN... | false |
_private.Mathlib.Topology.Algebra.Valued.ValuedField.0.Valued.valuedCompletion_surjective_iff._simp_1_1 | Mathlib.Topology.Algebra.Valued.ValuedField | [
"Membership.mem",
"SDiff.sdiff",
"And",
"Set.mem_diff",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.instSDiff",
"Set"
] | false |
List.flatten_nil | Init.Data.List.Basic | [
"List",
"Eq",
"rfl",
"List.flatten",
"List.nil"
] | true |
CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf_obj_a | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Coalgebra.instCategory",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.Endofunctor.Coalgebra.V",
"CategoryTheory.Endofunctor.Algebra.a",
"CategoryTheory.Endofunctor.Coalgebra",
"CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf",
... | true |
Submodule.mul_iSup | Mathlib.Algebra.Algebra.Operations | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Semiring.toModule",
"instSMulOfMul",
"HMul.hMul",
"iSup",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"CompleteLattice.toConditionallyCompleteLattice",
"AddZeroClass.toAddZe... | true |
Finset.univ_val_map_subtype_restrict | Mathlib.Data.Finset.BooleanAlgebra | [
"Eq.mpr",
"Finset.univ",
"Multiset.map",
"congrArg",
"Finset.univ_val_map_subtype_val",
"Function.comp",
"Multiset",
"id",
"Subtype",
"Finset.val",
"Subtype.restrict",
"Fintype",
"DecidablePred",
"Multiset.map_map",
"Eq.refl",
"Eq.symm",
"Subtype.val",
"Finset.filter",
"Eq",
"S... | true |
Nat.orderEmbeddingOfSet_range | Mathlib.Order.OrderIsoNat | [
"Membership.mem",
"Set.Elem",
"instLENat",
"DecidablePred",
"Nat",
"Nat.orderEmbeddingOfSet",
"Infinite",
"OrderEmbedding",
"Set.range",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"Nat.Subtype.coe_comp_ofNat_range",
"instFunLikeOrderEmbedding",
"Set"
] | true |
Filter.HasBasis.forall_mem_mem | Mathlib.Order.Filter.Bases.Basic | [
"Filter.instMembership",
"Eq.mpr",
"Filter.HasBasis.mem_iff",
"congrArg",
"_private.Mathlib.Order.Filter.Bases.Basic.0.Filter.HasBasis.forall_mem_mem._simp_1_2",
"Membership.mem",
"Exists",
"id",
"HasSubset.Subset",
"And",
"Filter.HasBasis",
"Iff",
"Set.Subset.rfl",
"implies_congr",
"Iff... | true |
HasCompactMulSupport.uniformContinuous_of_continuous | Mathlib.Topology.UniformSpace.HeineCantor | [
"UniformContinuous",
"UniformSpace",
"Continuous",
"One",
"HasCompactMulSupport",
"HasCompactMulSupport.is_one_at_infty",
"One.toOfNat1",
"OfNat.ofNat",
"UniformSpace.toTopologicalSpace",
"Continuous.uniformContinuous_of_tendsto_cocompact"
] | true |
PresheafOfModules.sections.eval | Mathlib.Algebra.Category.ModuleCat.Presheaf | [
"CategoryTheory.Functor",
"Opposite",
"AddCommGrpCat.instCategory",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.comp",
"AddCommGroup.toAddGroup",
"AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier",
"Membership.mem",
"AddZeroClass.toAddZero",
"Ab",
"AddCommGrpCat.carrier",
"RingCat... | true |
Lean.OptionDecl.mk.injEq | Lean.Data.Options | [
"Eq.propIntro",
"String",
"Lean.injEq_helper",
"Lean.OptionDecl",
"autoParam",
"And",
"Lean.OptionDecl.mk.inj",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Lean.OptionDecl.mk",
"Lean.DataValue",
"Lean.OptionDecl.declName._autoParam",
"Eq"
] | true |
Cardinal.zero_lt_lift_iff | Mathlib.SetTheory.Cardinal.Order | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
"Cardinal.lift",
"AddZeroClass.toAddZero",
"Eq.mp",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoid... | true |
Lean.Lsp.SymbolKind.boolean | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolKind",
"Lean.Lsp.SymbolKind.boolean"
] | true |
Cube.insertAt_boundary | Mathlib.Topology.Homotopy.HomotopyGroup | [
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"Homeomorph.funSplitAt_symm_apply",
"Pi.topologicalSpace",
"congrArg",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"Membership.mem",
"Cube.boundary",
"Real.semiring",
"Set.Elem",
"dif... | true |
CategoryTheory.Limits.Cofork.π.eq_1 | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingParallelPair.one",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory.Limits.Cocone.ι",
... | true |
Std.Iterators.Types.DropWhile.recOn | Std.Data.Iterators.Combinators.Monadic.DropWhile | [
"Std.Iterators.Types.DropWhile",
"ULift",
"Std.Iterators.Types.DropWhile.mk",
"Bool",
"Std.Iterators.PostconditionT",
"Std.IterM",
"Std.Iterators.Types.DropWhile.rec"
] | false |
_private.Mathlib.Algebra.Order.Group.DenselyOrdered.0.exists_mul_left_lt | Mathlib.Algebra.Order.Group.DenselyOrdered | [
"Iff.mpr",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
"Group",
"Exists",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"lt_div_iff_mul_lt",
"exists_between",
"And.casesOn",
"Group.toDivInvMonoid",
"GT.gt",
"MulOneClass.toMulOne",
"And",
"Exists.casesOn",
"MulRightStri... | true |
CategoryTheory.Limits.CategoricalPullback.comp_fst | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.CategoricalPullback.fst",
"CategoryTheory.Limits.CategoricalPullback",
"CategoryTheory.Limits.CategoricalPullback.Hom",
"CategoryTheory.Limits.CategoricalPullback.Hom.fst",
"CategoryTheory.Category... | true |
CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAgainst.isStableUnderBaseChangeAlong | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlong",
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAgainst",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
TensorProduct.Algebra.module._proof_7 | Mathlib.RingTheory.TensorProduct.Basic | [
"instHSMul",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Algebra",
"TensorProduct.Algebra.moduleAux",
"RingHom",... | false |
Lean.Compiler.LCNF.instInhabitedFunDecl.default_1 | Lean.Compiler.LCNF.Basic | [
"Inhabited.default",
"Lean.Compiler.LCNF.instInhabitedCode",
"Lean.Expr",
"Lean.Compiler.LCNF.FunDecl",
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.FunDecl.mk",
"Array",
"Lean.instInhabitedExpr",
"Lean.Compiler.LCNF.Code",
"Array.instInhabited",
"Lean.instInhabitedFVarId",
... | true |
CategoryTheory.Bicategory.InducedBicategory.forget._proof_9 | Mathlib.CategoryTheory.Bicategory.InducedBicategory | [
"CategoryTheory.Bicategory.InducedBicategory.forget._proof_5",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Bicategory.InducedBicategory.Hom₂.hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.whiskerRight",
"Category... | false |
ModuleCat.smul._proof_10 | Mathlib.Algebra.Category.ModuleCat.Basic | [
"instHSMul",
"AddCommGrpCat.ext",
"ModuleCat.smul._proof_9",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"... | false |
AlgebraicGeometry.ExistsHomHomCompEqCompAux.exists_eq | Mathlib.AlgebraicGeometry.AffineTransitionLimit | [
"AlgebraicGeometry.ExistsHomHomCompEqCompAux.hc",
"CategoryTheory.Functor.Initial.isLimitWhiskerEquiv",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Over.pullback._proof_2",
"CategoryTheory.Over",
"AlgebraicGeometry.Exis... | true |
SemiRingCat.forget₂AddCommMonPreservesLimitsAux | Mathlib.Algebra.Category.Ring.Limits | [
"SemiRingCat.instConcreteCategoryRingHomCarrier",
"CategoryTheory.Functor",
"AddCommMonCat.instCategory",
"AddMonoid.toAddZeroClass",
"AddCommMonCat.limitConeIsLimit",
"CategoryTheory.Functor.comp",
"RingHom",
"AddCommMonCat",
"AddZeroClass.toAddZero",
"Set.Elem",
"SemiRingCat.carrier",
"SemiR... | true |
QuadraticForm.toMatrix._proof_2 | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instSMulCommClass",
"QuadraticForm.toMatrix'._proof_3",
"AddCommGroup",
"LinearMap",
"smulCommClass_self",
"QuadraticForm.toMatrix'._proof_1",
"CommRing.toCo... | false |
Finset.mulAction._proof_1 | Mathlib.Algebra.Group.Action.Pointwise.Finset | [
"Monoid",
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"id",
"one_smul",
"funext",
"MulOneClass.toMulOne",
"Finset.image_id'",
"MulAction",
"True",
"eq_self",
"Monoid.toSemigroup",
"of_eq_true",
"One.toOfNat1",
"HSMul.hSMul",
"SemigroupAc... | false |
ContinuousWithinAt.congr_of_eventuallyEq | Mathlib.Topology.ContinuousOn | [
"Iff.mpr",
"ContinuousWithinAt",
"nhdsWithin",
"Filter.EventuallyEq",
"TopologicalSpace",
"Filter.EventuallyEq.congr_continuousWithinAt",
"Eq",
"Set"
] | true |
Std.TreeMap.Raw.le_maxKeyD_of_contains | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.contains",
"Std.DTreeMap.Raw.le_maxKeyD_of_contains",
"Std.TreeMap.Raw.WF.out",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw.maxKeyD",
"Std.TreeMap.Raw",
"Bool.true",
"Bool",
"Ordering.isLE",
"Eq"
] | true |
CategoryTheory.SpectralSequence.Hom.noConfusion | Mathlib.Algebra.Homology.SpectralSequence.Basic | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.SpectralSequence.Hom.casesOn",
"Quiver.Hom",
"CategoryTheory.SpectralSequence.Hom._proof_12",
"HEq.refl",
"CategoryTheory.SpectralSequence"... | false |
PadicInt.mahlerSeries._proof_1 | Mathlib.NumberTheory.Padics.MahlerBasis | [
"AddMonoid.toAddSemigroup",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"IsTopologicalAddGroup.toContinuousAdd",
"AddSemigroup.toAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"NormedAddCommGroup.toAddCommGroup",
"SubNegMonoid.toAddMonoid",
"Conti... | false |
AddOreLocalization.instAddMonoid | Mathlib.GroupTheory.OreLocalization.Basic | [
"AddOreLocalization.instZero",
"AddOreLocalization.instAddMonoid._proof_2",
"AddMonoid.toAddZeroClass",
"AddMonoid.mk",
"AddZeroClass.toAddZero",
"AddSubmonoid",
"AddOreLocalization.add_zero",
"AddSemigroup.mk",
"AddOreLocalization.nsmul",
"AddOreLocalization",
"AddZero.toZero",
"AddOreLocaliz... | true |
Std.DTreeMap.Raw.getKey_eq | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.instMembership",
"Std.DTreeMap.Internal.Impl.getKey_eq",
"Ord.mk",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.Raw.getKey",
"Std.DTreeMap.Raw.WF.out",
"Std.LawfulEqCmp",
"Std.DTreeMap.Raw.inner",
"Eq",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] | true |
Lean.Widget.instAppendInteractiveGoals | Lean.Widget.InteractiveGoal | [
"Lean.Widget.InteractiveGoals",
"Append",
"Lean.Widget.InteractiveGoals.append",
"Append.mk"
] | true |
Std.Internal.List.contains_insertList_iff | Std.Data.Internal.List.Associative | [
"Eq.mpr",
"Std.Internal.List.containsKey_eq_contains_map_fst",
"Std.Internal.List.insertList",
"congrArg",
"List.map",
"List.contains",
"_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.contains_insertList_iff._simp_1_1",
"List.contains_map",
"Membership.mem",
"Exists",
"id",
"S... | true |
instInhabitedTensorAlgebra | Mathlib.LinearAlgebra.TensorAlgebra.Basic | [
"CommSemiring.toSemiring",
"TensorAlgebra",
"instInhabitedTensorAlgebra._aux_1",
"AddCommMonoid",
"CommSemiring",
"Inhabited",
"Module",
"Inhabited.mk"
] | true |
_private.Mathlib.Data.TypeVec.0.TypeVec.toSubtype'.match_1.eq_1 | Mathlib.Data.TypeVec | [
"Fin2.fz",
"TypeVec.ofRepeat",
"TypeVec.prod.mk",
"Subtype",
"instOfNatNat",
"Prod.fst",
"TypeVec.prod",
"Fin2.fs",
"instHAdd",
"HAdd.hAdd",
"Nat",
"TypeVec.toSubtype'.match_1",
"instAddNat",
"Eq.refl",
"TypeVec.repeat",
"Prod",
"OfNat.ofNat",
"TypeVec.Arrow",
"Eq",
"Prod.snd",... | true |
List.eraseIdx_eq_take_drop_succ | Init.Data.List.Erase | [
"List.brecOn",
"List.eraseIdx",
"instOfNatNat",
"instHAppendOfAppend",
"List",
"instHAdd",
"List.drop",
"HAdd.hAdd",
"Nat",
"instAddNat",
"List.instAppend",
"OfNat.ofNat",
"List.eraseIdx_eq_take_drop_succ._f",
"Eq",
"List.take",
"HAppend.hAppend"
] | true |
AntitoneOn._to_dual_cast_1 | Mathlib.Order.Monotone.Defs | [
"Preorder.toLE",
"Membership.mem",
"LE.le",
"Eq.refl",
"AntitoneOn",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
_private.Lean.Elab.BuiltinEvalCommand.0.Lean.Elab.Command.mkDeltaInstProj._unsafe_rec | Lean.Elab.BuiltinEvalCommand | [
"guard",
"Lean.Meta.mkAppOptM",
"Lean.Meta.trySynthInstance",
"_private.Lean.Elab.BuiltinEvalCommand.0.Lean.Elab.Command.mkDeltaInstProj._unsafe_rec",
"Lean.Meta.State",
"Option.some",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"_private.Lean.Elab.BuiltinEvalCommand.0... | false |
UniformContinuousConstSMul.mk | Mathlib.Topology.Algebra.UniformMulAction | [
"UniformContinuous",
"UniformSpace",
"instHSMul",
"UniformContinuousConstSMul.mk",
"SMul",
"HSMul.hSMul",
"UniformContinuousConstSMul"
] | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.unsat_of_encounteredBoth._proof_1_5 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound | [
"False",
"Std.Tactic.BVDecide.LRAT.Internal.ReduceResult.reducedToUnit",
"eq_false",
"congrArg",
"Std.Tactic.BVDecide.LRAT.Internal.Unsatisfiable",
"False.elim",
"Classical.byContradiction",
"Lean.Grind.Nat.lt_eq",
"noConfusion_of_Nat",
"id",
"instDecidableEqBool",
"Prod.mk",
"instOfNatNat",... | false |
Char.ofUInt8.eq_1 | Std.Internal.Http.Data.URI.Encoding | [
"Char.ofUInt8",
"UInt8.toUInt32",
"Char.ofUInt8._proof_2",
"Char.mk",
"Eq.refl",
"Char",
"UInt8",
"Eq"
] | true |
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