name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
instFiniteSym | Mathlib.Data.Finite.Vector | [
"Finite",
"inferInstance",
"Sym.instFinite",
"Nat",
"Sym"
] | true |
AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assoc | Mathlib.AlgebraicGeometry.Fiber | [
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
... | true |
CategoryTheory.Limits.Cocone.extendComp | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone.extend",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso.refl",
"CategoryTheory.Iso",
"CategoryTheory.Limits.Cocone.category",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.L... | true |
Topology.CWComplex.noConfusion | Mathlib.Topology.CWComplex.Classical.Basic | [
"Topology.CWComplex.casesOn",
"Real",
"pseudoMetricSpacePi",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Pi.topologicalSpace",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Real.instZero",
"PartialEquiv.target",
"Topology.CWComplex",
"HEq.refl",
"Finset",
"PartialEquiv",
"Set.u... | false |
AddCon.eq | Mathlib.GroupTheory.Congruence.Defs | [
"AddCon.instFunLikeForallProp",
"AddCon",
"Quotient.eq''",
"AddCon.toSetoid",
"Iff",
"AddCon.Quotient",
"Eq",
"DFunLike.coe",
"AddCon.toQuotient",
"Add"
] | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.insertListIfNew.eq_2 | Std.Data.Internal.List.Associative | [
"Std.Internal.List.insertListIfNew",
"Std.Internal.List.insertEntryIfNew",
"List.cons",
"List",
"Eq.refl",
"Sigma.mk",
"BEq",
"Eq",
"Sigma"
] | true |
HomologicalComplex.isoHomologyι_hom_inv_id_assoc | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"HomologicalComplex.isoHomologyι_hom_inv_id",
"Quiver.Hom",
"congrArg",
"HomologicalComplex.HasHomology",
"HomologicalComplex.opcycles",
"HomologicalComplex",
"CategoryTheory.Catego... | true |
Units.liftRight.congr_simp | Mathlib.RingTheory.Localization.Away.Basic | [
"Monoid",
"Units.val",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Units",
"Eq.rec",
"MulOneClass.toMulOne",
"Eq.ndrec",
"Eq.refl",
"Units.liftRight",
"Eq",
"DFunLike.coe",
"Units.instMulOneClass"
] | true |
Lean.Elab.IncrementalState.initialSnap | Lean.Elab.Frontend | [
"Lean.Elab.IncrementalState",
"Lean.Language.Lean.CommandParsedSnapshot"
] | true |
AddAction.mem_orbit_symm | Mathlib.GroupTheory.GroupAction.Defs | [
"Eq.mpr",
"AddAction.orbit_eq_iff",
"AddAction.orbit",
"AddMonoid.toAddSemigroup",
"congrArg",
"Membership.mem",
"id",
"eq_comm",
"iff_self",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"Iff",
"AddSemigroupAction.toVAdd",
"AddGroup.toSubNegMonoid",
"congr",
"True",
"... | true |
Std.DTreeMap.Internal.Impl.keysArray_filter_key | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.filter",
"Std.DTreeMap.Internal.Impl.keys_filter_key",
"id",
"instOfNatNat",
"Std.DTreeMap.Internal.Impl.WF",
"List.toArray",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Array",
"List",
"Array.filter",
"Std.DTreeMap.Internal.Impl.keys... | true |
coe_convexAddSubmonoid | Mathlib.Analysis.Convex.Basic | [
"convexAddSubmonoid",
"DistribMulAction.toDistribSMul",
"Set.addZeroClass",
"AddMonoid.toAddZeroClass",
"setOf",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"AddSubmonoid",
"AddCommMonoid",
"AddZero.toZero",
"SetLike.coe",
"Convex",
"Semiring.toMonoid",
"Semi... | true |
_private.Mathlib.Data.Set.Restrict.0.Set.injective_codRestrict._simp_1_1 | Mathlib.Data.Set.Restrict | [
"Subtype",
"Subtype.ext_iff",
"propext",
"Subtype.val",
"Eq"
] | false |
ULift.seminormedCommRing._proof_6 | Mathlib.Analysis.Normed.Ring.Basic | [
"Monoid.npow",
"Semigroup.toMul",
"HMul.hMul",
"SeminormedCommRing",
"SeminormedCommRing.toCommRing",
"ULift",
"instOfNatNat",
"instHAdd",
"ULift.commRing",
"HAdd.hAdd",
"Nat",
"Monoid.npow_succ",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"instAddNat",
"CommRing.toRing",
"OfNat.ofNa... | false |
Nat.Linear.ExprCnstr.denote | Init.Data.Nat.Linear | [
"cond",
"LE.le",
"instLENat",
"Nat.Linear.ExprCnstr",
"Nat.Linear.ExprCnstr.rhs",
"Nat.Linear.Expr.denote",
"Nat",
"Nat.Linear.Context",
"Nat.Linear.ExprCnstr.eq",
"Eq",
"Nat.Linear.ExprCnstr.lhs"
] | true |
CategoryTheory.Abelian.SpectralObject.Hom.casesOn | Mathlib.Algebra.Homology.SpectralObject.Basic | [
"CategoryTheory.Abelian.SpectralObject.Hom",
"CategoryTheory.Functor",
"CategoryTheory.Abelian.SpectralObject.Hom.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Abel... | false |
Int.clog_zero_left | Mathlib.Data.Int.Log | [
"Int.instAddCommGroup",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"eq_false",
"congrArg",
"Nat.log_zero_left",
"ite_self",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddGroupWithOne.... | true |
CategoryTheory.instCreatesFiniteLimitsIndFunctorOppositeTypeInclusionOfHasFiniteLimits | Mathlib.CategoryTheory.Limits.Indization.Category | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.createsFiniteLimitsOfCreatesEqualizersAndFiniteProducts",
"CategoryTheory.instCreatesFiniteLimitsIndFunctorOppositeTypeInclusionOfHasFiniteLimits._proof_2",
"CategoryTheory.Limits.HasFiniteLimits",
... | true |
Std.TreeMap.Raw.get?_diff | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.WF.out",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"SDiff.sdiff",
"Option.none",
"Std.DTreeMap.Raw.Const.get?_diff",
"Std.TreeMap.Raw.get?",
"Std.TreeMap.Raw.instSDiff",
... | true |
Matroid.finitary_iff_forall_isCircuit_finite | Mathlib.Combinatorics.Matroid.Circuit | [
"Iff.mpr",
"Matroid.Dep.not_indep",
"Eq.mpr",
"Matroid.Dep",
"False",
"Matroid.E",
"Matroid.IsCircuit.finite",
"Set.Finite",
"Membership.mem",
"Exists",
"Eq.mp",
"Matroid.Indep",
"Matroid.indep_iff_not_dep",
"Set.instSingletonSet",
"id",
"HasSubset.Subset",
"And.casesOn",
"Matroid.... | true |
CategoryTheory.Limits.Multicoequalizer.condition | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.MultispanIndex.snd",
"CategoryTheory.Limits.WalkingMultispan",
"CategoryTheory.Limits.MultispanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.MultispanShape",
"CategoryTheory.Limits.MultispanIndex.fst",
"CategoryTheory.Limits.MultispanIn... | true |
Std.HashMap.Raw._sizeOf_inst | Std.Data.HashMap.Raw | [
"Std.HashMap.Raw",
"SizeOf.mk",
"SizeOf",
"Std.HashMap.Raw._sizeOf_1"
] | false |
_private.Mathlib.Topology.Bases.0.TopologicalSpace.isSeparable_union._simp_1_1 | Mathlib.Topology.Bases | [
"and_comm",
"And",
"propext",
"Eq"
] | false |
CategoryTheory.Abelian.SpectralObject.shortComplexMap_comp._auto_3 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Init.Data.BitVec.Bitblast.0.BitVec.toInt_umod_neg_add._proof_1_1 | Init.Data.BitVec.Bitblast | [
"instPowNat",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
... | false |
Set.zero_subset | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Set.singleton_subset_iff",
"Membership.mem",
"HasSubset.Subset",
"Set.zero",
"Iff",
"Zero.toOfNat0",
"OfNat.ofNat",
"Set.instMembership",
"Set.instHasSubset",
"Zero",
"Set"
] | true |
Lean.Server.FileWorker.NamespaceEntry.selection | Lean.Server.FileWorker.RequestHandling | [
"Lean.Server.FileWorker.NamespaceEntry",
"Lean.Syntax"
] | true |
_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod.completedLFunction_one_sub_of_one_lt_even | Mathlib.NumberTheory.LSeries.ZMod | [
"ZMod.completedLFunction",
"Iff.mpr",
"Distrib.leftDistribClass",
"Eq.mpr",
"Pi.Function.module",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"Nat.instMulZeroClass",
"_private.Mathlib.NumberTheory.LSeries.ZMod.0.ZMod.completedLFunction_one_sub_of_on... | true |
Nat.exists_add_one_eq._simp_1 | Init.Data.Nat.Lemmas | [
"Exists",
"instOfNatNat",
"instHAdd",
"Nat.exists_add_one_eq",
"HAdd.hAdd",
"Nat",
"LT.lt",
"propext",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | false |
initFn._@.Mathlib.Tactic.Continuity.Init.3906107317._hygCtx._hyg.3 | Mathlib.Tactic.Continuity.Init | [
"IO",
"instOfNatNat",
"instMonadEIO",
"Unit",
"Aesop.RuleSetName",
"Array.forM",
"Nat",
"Array.mkArray1",
"Lean.Name",
"IO.Error",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1",
"Aesop.Frontend.declareRuleSetUnchecked",
"Array.size"
] | false |
CategoryTheory.Abelian.SpectralObject.d_map_fourδ₄Toδ₃ | Mathlib.Algebra.Homology.SpectralObject.EpiMono | [
"CategoryTheory.ComposableArrows.fourδ₄Toδ₃",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.E",
"instNeZeroNatHAdd_1",
"CategoryTheory.Abelian.SpectralObject.cycles",
"CategoryTheory.Abelian.SpectralObject.δToCycles_πE",
"CategoryTheory.Abelian.SpectralObject.toCycles_πE... | true |
Lean.Doc.Part._sizeOf_inst | Lean.DocString.Types | [
"Lean.Doc.Part._sizeOf_1",
"SizeOf.mk",
"Lean.Doc.Part",
"SizeOf"
] | false |
Std.ExtDHashMap.eq_empty_iff_forall_not_mem | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.ExtDHashMap.isEmpty",
"Std.ExtDHashMap.instEmptyCollection",
"Std.DHashMap.isEmpty_iff_forall_not_mem",
"Membership.mem",
"Std.ExtDHashMap.isEmpty_iff",
"Std.ExtDHashMap.inductionOn",
"LawfulHashable",
"Bool.true",
"Iff",
"EquivBEq... | true |
_private.Mathlib.Analysis.Normed.Algebra.Spectrum.0.spectrum._aux_Mathlib_Analysis_Normed_Algebra_Spectrum___unexpand_Algebra_algebraMap_2 | Mathlib.Analysis.Normed.Algebra.Spectrum | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.matchesIdent",
"Lean.Name.mkNum",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Sy... | false |
MeasureTheory.Integrable.aemeasurable | Mathlib.MeasureTheory.Function.L1Space.Integrable | [
"TopologicalSpace.PseudoMetrizableSpace",
"MeasureTheory.Integrable.aestronglyMeasurable",
"MeasureTheory.AEStronglyMeasurable.aemeasurable",
"MeasureTheory.Measure",
"AEMeasurable",
"MeasureTheory.Integrable",
"BorelSpace",
"ContinuousENorm",
"MeasurableSpace",
"TopologicalSpace"
] | true |
Tactic.ComputeAsymptotics.Monomial.mk._flat_ctor | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | [
"Tactic.ComputeAsymptotics.Monomial",
"Real",
"Tactic.ComputeAsymptotics.Monomial.mk",
"Tactic.ComputeAsymptotics.UnitMonomial"
] | false |
_private.Mathlib.Data.Sym.Sym2.0.Sym2.fromRel_irrefl.match_1_1 | Mathlib.Data.Sym.Sym2 | [
"Std.Irrefl",
"Std.Irrefl.casesOn",
"Std.Irrefl.mk",
"Not"
] | false |
_private.Lean.Level.0.Lean.Level.isMVar._sparseCasesOn_1 | 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 |
LinearIndependent.of_isLocalized_maximal | Mathlib.RingTheory.LocalProperties.Exactness | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"LinearMap.restrictScalars",
"Semiring.toModule",
"injective_of_isLocalized_maximal",
"Finsupp.module",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunL... | true |
PowerSeries.coeff_X | Mathlib.RingTheory.PowerSeries.Basic | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"congrArg",
"LinearMap.instFunLike",
"id",
"PowerSeries.coeff",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"PowerSeries.X",
"MvPowerSeries.instModule",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
... | true |
Finset.union_union_distrib_right | Mathlib.Data.Finset.Lattice.Basic | [
"Lattice.toSemilatticeSup",
"Finset.instUnion",
"Finset",
"Finset.instLattice",
"Union.union",
"sup_sup_distrib_right",
"Eq",
"DecidableEq"
] | true |
CategoryTheory.ShortComplex.instModuleHom._proof_2 | Mathlib.Algebra.Homology.ShortComplex.Linear | [
"CategoryTheory.ShortComplex.hom_ext",
"Semigroup.toMul",
"instHSMul",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.Hom.τ₁",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"CategoryT... | false |
_private.Lean.Elab.App.0.Lean.Elab.Term.ElabAppArgs.isNextOutParamOfLocalInstanceAndResult.hasLocalInstanceWithOutParams._unsafe_rec | Lean.Elab.App | [
"Pure.pure",
"Lean.Core.instMonadEnvCoreM",
"Lean.Expr",
"IO.RealWorld",
"EIO",
"instDecidableEqBool",
"Lean.Level",
"instMonadEIO",
"Lean.hasOutParams",
"Applicative.toPure",
"Lean.BinderInfo.isInstImplicit",
"Bool.true",
"List",
"Unit",
"Lean.Core.State",
"Lean.Core.CoreM",
"StateR... | false |
Finset.map_truncatedSup | Mathlib.Combinatorics.SetFamily.AhlswedeZhang | [
"OrderIsoClass.toSupHomClass",
"Eq.mpr",
"apply_dite",
"SetLike.mem_coe._simp_1",
"LowerSet.map",
"dite_congr",
"instSubsingletonDecidable",
"lowerClosure_image",
"Iff.of_eq",
"congrArg",
"Finset",
"map_finset_sup'",
"PartialOrder.toPreorder",
"Decidable",
"Preorder.toLE",
"Finset.map"... | true |
retractionKerCotangentToTensorEquivSection._proof_16 | Mathlib.RingTheory.Smooth.Kaehler | [
"TensorProduct.instDistribMulAction",
"LinearMap.id",
"Ideal.Quotient.commSemiring",
"Eq.mpr",
"Submodule",
"RingHom.instRingHomClass",
"IsScalarTower.to_smulCommClass'",
"retractionKerCotangentToTensorEquivSection._proof_5",
"tensorKaehlerQuotKerSqEquiv._proof_3",
"tensorKaehlerQuotKerSqEquiv._pr... | false |
Cardinal.zero_toNat | Mathlib.SetTheory.Cardinal.ToNat | [
"Nat.instMulZeroOneClass",
"Nat.instMulZeroClass",
"Cardinal",
"CommSemiring.toSemiring",
"Cardinal.commSemiring",
"Cardinal.toNat",
"MonoidWithZeroHom.funLike",
"MonoidWithZeroHom.monoidWithZeroHomClass",
"map_zero",
"instOfNatNat",
"instMulZeroOneClassOfSemiring",
"MonoidWithZeroHom",
"Nat... | true |
Topology.ContinuousMapGeneratedBy.recOn | Mathlib.Topology.Convenient.ContinuousMapGeneratedBy | [
"Topology.ContinuousMapGeneratedBy.rec",
"TopologicalSpace",
"Topology.ContinuousMapGeneratedBy",
"Topology.ContinuousGeneratedBy",
"Topology.ContinuousMapGeneratedBy.mk"
] | false |
MvPolynomial.finSuccEquiv_X_zero | Mathlib.Algebra.MvPolynomial.Equiv | [
"Finsupp.instAddZeroClass",
"Polynomial.C",
"instNeZeroNatHAdd_1",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.algebra",
"Polynomial.algebraOfAlgebra",
"Finsupp.instAddMonoid",
"MvPolynomial.X",
"Ad... | true |
LaurentPolynomial.leval | Mathlib.Algebra.Polynomial.Laurent | [
"Monoid",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Module.toMulActionWithZero",
"LaurentPolynomial",
"Units",
"AddZeroClass.toAddZero",
"Int",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"LinearMap.mk",
"Semiring",
"AddCommMonoid.toAddMon... | true |
MulAction.aestabilizer_empty | Mathlib.MeasureTheory.Group.AEStabilizer | [
"MeasureTheory.ae",
"instHSMul",
"MeasureTheory.Measure",
"congrArg",
"Set.smul_set_empty",
"Filter.EventuallyEq.refl._simp_1",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"Filter.EventuallyEq",
"MulAction.aestabilizer",
"DivInvM... | true |
_private.Lean.Parser.Types.0.Lean.Parser.FirstTokens.seq._sparseCasesOn_1 | Lean.Parser.Types | [
"Lean.Parser.FirstTokens.rec",
"Lean.Parser.FirstTokens.unknown",
"Nat.ne_of_beq_eq_false",
"Lean.Parser.Token",
"Nat.shiftRight",
"Lean.Parser.FirstTokens.epsilon",
"Lean.Parser.FirstTokens.tokens",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Parser.FirstTokens.optTokens",
"Lean.Parser.FirstTokens.c... | false |
List.Pairwise.insertionSort_eq | Mathlib.Data.List.Sort | [
"List.Pairwise",
"DecidableRel",
"List.rec",
"List",
"_private.Mathlib.Data.List.Sort.0.List.Pairwise.insertionSort_eq._proof_1_2",
"Eq",
"_private.Mathlib.Data.List.Sort.0.List.Pairwise.insertionSort_eq._proof_1_1",
"List.insertionSort"
] | true |
riemannZeta_one | Mathlib.NumberTheory.Harmonic.ZetaAsymp | [
"instInnerProductSpaceRealComplex",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Complex.log",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.pi",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"div_right_comm",
"riemannZeta",
"DivisionC... | true |
_private.Mathlib.Analysis.Calculus.Deriv.MeanValue.0.not_differentiableWithinAt_of_deriv_tendsto_atTop_Ioi._simp_1_1 | Mathlib.Analysis.Calculus.Deriv.MeanValue | [
"Filter.instMembership",
"mem_interior_iff_mem_nhds",
"Membership.mem",
"nhds",
"TopologicalSpace",
"interior",
"propext",
"Eq.symm",
"Eq",
"Set.instMembership",
"Filter",
"Set"
] | false |
Std.Sat.CNF.mk._flat_ctor | Std.Sat.CNF.Basic | [
"Std.Sat.CNF",
"Array",
"Std.Sat.CNF.mk",
"Std.Sat.CNF.Clause"
] | false |
_private.Lean.Elab.SyntheticMVars.0.Lean.Elab.Term.synthesizeSyntheticMVars.loop._unsafe_rec | Lean.Elab.SyntheticMVars | [
"Pure.pure",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"bne",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"_private.Lean.Elab.SyntheticMVars.0.Lean.Elab.Term.synthesizeUsingDefault",
"_private.Lean.Elab.Synth... | false |
HomotopicalAlgebra.Cylinder.LeftHomotopy.refl | Mathlib.AlgebraicTopology.ModelCategory.LeftHomotopy | [
"HomotopicalAlgebra.Cylinder.LeftHomotopy",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.Cylinder",
"HomotopicalAlgebra.Cylinder.toPrecylinder",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"CategoryTheory.Category.toCategoryStruct",
"HomotopicalAlgebra.Precylinder... | true |
_private.Mathlib.InformationTheory.KullbackLeibler.ChainRule.0.InformationTheory.integral_llr_compProd_eq_add._simp_1_6 | Mathlib.InformationTheory.KullbackLeibler.ChainRule | [
"MeasureTheory.Measure",
"MeasureTheory.Integrable",
"Ne",
"ContinuousENorm",
"MeasurableSpace",
"TopologicalSpace",
"ENorm.enorm",
"ContinuousENorm.toENorm",
"MeasureTheory.IsFiniteMeasure",
"True",
"ENNReal",
"eq_true",
"MeasureTheory.integrable_const_enorm",
"ENNReal.instTop",
"Top.to... | false |
groupCohomology.cocycles₂_ρ_map_inv_sub_map_inv | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Iff.mpr",
"Pi.Function.module",
"Submodule",
"Rep.V",
"MulOne.toOne",
"CommRing",
"Representation",
"MonoidHom.instFunLike",
"inv_mul_cancel",
"Pi.addCommMonoid",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSem... | true |
NumberField.mixedEmbedding.volume_negAt_plusPart | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearEquiv.symm",
"Real",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Complex.borelSpace",... | true |
maximal_gt_iff._simp_1 | Mathlib.Order.Minimal | [
"Preorder.toLT",
"maximal_gt_iff",
"Preorder.toLE",
"And",
"LT.lt",
"propext",
"Maximal",
"Eq",
"Preorder",
"IsMax"
] | false |
_private.Aesop.Tree.TreeM.0.Aesop.mkInitialTree.match_1 | Aesop.Tree.TreeM | [
"Aesop.ForwardRuleMatch",
"Aesop.ForwardState",
"Prod.mk",
"Array",
"Prod",
"Prod.casesOn"
] | false |
AlgebraicGeometry.StructureSheaf.comap._proof_5 | Mathlib.AlgebraicGeometry.StructureSheaf | [
"AlgebraicGeometry.StructureSheaf.Localizations",
"CategoryTheory.Functor",
"CommRing",
"Semiring.toModule",
"Opposite",
"HMul.hMul",
"CommRingCat.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CommRingCat",
"AddCommGroup.toAddCommMonoid",
"TopCat.PrelocalPred... | false |
Pi.involutiveNeg.eq_1 | Mathlib.Algebra.Group.Pi.Basic | [
"Pi.instNeg",
"Pi.involutiveNeg",
"Pi.involutiveNeg._proof_1",
"InvolutiveNeg",
"InvolutiveNeg.mk",
"Eq.refl",
"InvolutiveNeg.toNeg",
"Eq"
] | true |
Lean.Meta.Simp.ConfigCtx.mk._flat_ctor | Init.MetaTypes | [
"Lean.Meta.Simp.ConfigCtx.mk",
"Lean.Meta.Simp.ConfigCtx",
"Lean.Meta.EtaStructMode",
"Nat",
"Bool",
"Lean.Meta.Simp.Config.mk",
"Option"
] | false |
Lean.Grind.CommRing.Poly.pow | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Nat.brecOn",
"Lean.Grind.CommRing.Poly.pow._f",
"Nat"
] | true |
MeasureTheory.Measure.prod_sum | Mathlib.MeasureTheory.Measure.Prod | [
"Eq.mpr",
"MeasureTheory.Measure.sum_sum",
"MeasureTheory.instSFiniteSumOfCountable",
"MeasureTheory.Measure",
"congrArg",
"id",
"Prod.fst",
"MeasurableSpace",
"funext",
"MeasureTheory.SFinite",
"MeasureTheory.Measure.prod",
"MeasureTheory.Measure.prod_sum_right",
"True",
"eq_self",
"of_... | true |
instAlgebraCliffordAlgebra._proof_6 | Mathlib.LinearAlgebra.CliffordAlgebra.Basic | [
"CommRing",
"CliffordAlgebra.Rel",
"instHSMul",
"HMul.hMul",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"QuadraticForm",
"RingHom",
"AddCommGroup",
"Algebra.id",
"TensorAlgebra",
"SMul.mk",
"RingQuot.instAlgebra._proof_6",
"instSemiringTensorAlgebra",
... | false |
Module.toCentroidHom_apply_toFun | Mathlib.Algebra.Ring.CentroidHom | [
"instHSMul",
"instSMulOfMul",
"Module.toCentroidHom",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Ad... | true |
CommGrpCat.Forget₂.createsLimit._proof_8 | Mathlib.Algebra.Category.Grp.Limits | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"CategoryTheory.Limits.Cone.π",
"GrpCat.hasForgetToMonCat",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"GrpCat",
"MonoidHom.instFunLike",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"GrpCat.str",
... | false |
Submodule.IsOrtho.map | Mathlib.Analysis.InnerProductSpace.Orthogonal | [
"LinearIsometry",
"InnerProductSpace.toNormedSpace",
"Submodule",
"RingHomSurjective.ids",
"Inner.inner",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"LinearMap.instFunLike",
"LinearIsometry.inner_map_map",
"LinearIsometry.instFunLike",
"Membership.mem",
"NormedField.... | true |
Sublattice.map_bot | Mathlib.Order.Sublattice | [
"Sublattice",
"Lattice",
"Sublattice.comap",
"Sublattice.instBot",
"Sublattice.gc_map_comap",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"LatticeHom",
"Bot.bot",
"BoundedOrder.toOrderBot",
"GaloisConnection.l_bot",
"Sublattice.instPartialOrder",
"Sublatti... | true |
Std.Internal.List.getKey!_modifyKey_self | Std.Data.Internal.List.Associative | [
"Inhabited.default",
"Std.Internal.List.DistinctKeys",
"Std.Internal.List.getKey!",
"BEq.rfl",
"congrArg",
"LawfulBEq",
"instDecidableEqBool",
"ite_cond_eq_true",
"Bool.true",
"List",
"EquivBEq.toReflBEq",
"Std.Internal.List.containsKey",
"BEq.beq",
"True",
"eq_self",
"Bool",
"of_eq_... | true |
Matroid.IsNonloop.removeLoops_isNonloop | Mathlib.Combinatorics.Matroid.Loop | [
"Eq.mpr",
"id",
"Matroid.IsNonloop",
"Matroid.removeLoops",
"congrFun",
"Matroid.removeLoops_isNonloop_eq",
"Eq",
"Matroid"
] | true |
Lean.Meta.Simp.UsedSimps.contains | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.instHashableOrigin",
"Lean.Meta.instBEqOrigin",
"Lean.PersistentHashMap.contains",
"Nat",
"Bool",
"Lean.Meta.Origin",
"Lean.Meta.Simp.UsedSimps",
"Lean.Meta.Simp.UsedSimps.map"
] | true |
norm_tangentSpace_vectorSpace | Mathlib.Geometry.Manifold.Riemannian.Basic | [
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"chartedSpaceSelf",
"Inner.inner",
"Real.denselyNormedField",
"Real.instRCLike",
"congrArg",
"instAddCommGroupTangentSpace",
"instIsTopologicalAddGroupTangentSpace",
"PseudoMetricSpace.toUniformSpace",
"id",
"instModuleTange... | true |
CategoryTheory.sum.inlCompInlCompAssociator | Mathlib.CategoryTheory.Sums.Associator | [
"CategoryTheory.Functor",
"CategoryTheory.sum",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.inlCompSum'",
"Sum",
"CategoryTheory.Iso",
"CategoryTheory.Sum.inr_",
"CategoryTheory.Functor.sum'",
"CategoryTheory.Functor.isoWhiskerLeft",
"CategoryTheory.... | true |
_private.Mathlib.LinearAlgebra.Matrix.NonsingularInverse.0.Matrix.add_mul_mul_inv_eq_sub'._simp_1_1 | Mathlib.LinearAlgebra.Matrix.NonsingularInverse | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Matrix.instMulOfFintypeOfAddCommMonoid",
"Matrix",
"AddGroupWithOne.toAddMonoidWithOne",
"Invertible.invOf",
"Matrix.invOf_eq_nonsing_inv",
"NonUnitalNonAssocRing.toNonUnitalNon... | false |
_private.Mathlib.Algebra.Category.HopfAlgCat.Basic.0.HopfAlgCat.Hom.ext.match_1 | Mathlib.Algebra.Category.HopfAlgCat.Basic | [
"CommRing",
"Coalgebra.toCoalgebraStruct",
"HopfAlgebraStruct.toBialgebra",
"Bialgebra.toCoalgebra",
"HopfAlgCat.Hom.casesOn",
"HopfAlgCat.Hom",
"Algebra.toModule",
"HopfAlgCat",
"BialgHom",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"HopfAlgCat.instRing",
"CommRing.toCommSemiring",
"NonAs... | false |
Batteries.OrientedOrd | Batteries.Classes.Deprecated | [
"Ord",
"Ord.compare",
"Batteries.OrientedCmp"
] | true |
Ordnode.insert.eq_1 | Mathlib.Data.Ordmap.Invariants | [
"Ordnode",
"Ordnode.insert",
"LE",
"DecidableLE",
"Ordnode.singleton",
"Ordnode.nil",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Analysis.Normed.Operator.Basic.0.ball_subset_range_iff_surjective._simp_1_2 | Mathlib.Analysis.Normed.Operator.Basic | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
CartanMatrix.not_isSimplyLaced_G₂ | Mathlib.Data.Matrix.Cartan | [
"instDecidableNot",
"of_decide_eq_true",
"instDecidableEqFin",
"CartanMatrix.G₂",
"Matrix.IsSimplyLaced",
"id",
"instOfNatNat",
"Fin.fintype",
"Bool.true",
"Nat",
"CartanMatrix.instDecidablePredMatrixIntIsSimplyLacedOfFintypeOfDecidableEq",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Dec... | true |
CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.fac_assoc | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.OneHypercoverDenseData.SieveStruct.i₀",
"congrArg",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Functor.OneHypercoverDenseData.SieveSt... | true |
CategoryTheory.instInhabitedIsSplitCoequalizerId._proof_3 | Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Category.comp_id",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"CategoryTheory.Category.toCategoryStruct",
"congrFun'",
"Eq",
"Eq.trans",
"Cate... | false |
TensorProduct.rightComm._proof_17 | Mathlib.LinearAlgebra.TensorProduct.Associator | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LinearMap.instSMulCommClass",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"TensorProduct.assoc._proof_5",
"DistribSMul.toSMulZeroClass",
"SMulCommClass.symm",
"LinearMap",
"smulCommClass_self",... | false |
SheafOfModules.QuasicoherentData.bind._proof_3 | Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent | [
"CategoryTheory.Over",
"AddCommGrpCat.instCategory",
"AddMonoid.toAddZeroClass",
"RingCat.ring",
"AddCommGroup.toAddGroup",
"RingHom",
"AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier",
"AddZeroClass.toAddZero",
"RingCat.instConcreteCategoryRingHomCarrier",
"CategoryTheory.instCategoryOver",... | false |
Lean.ImportArtifacts.ofArray.inj | Lean.Setup | [
"Array",
"Lean.ImportArtifacts.ofArray.noConfusion",
"Lean.ImportArtifacts.ofArray",
"Lean.ImportArtifacts",
"Eq",
"System.FilePath"
] | true |
_private.Mathlib.NumberTheory.Harmonic.ZetaAsymp.0.ZetaAsymptotics.term_one._simp_1_11 | Mathlib.NumberTheory.Harmonic.ZetaAsymp | [
"MulOne.toOne",
"DivInvMonoid.toInv",
"instHDiv",
"Monoid.toMulOneClass",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"DivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"one_div",
"DivInvMonoid.toDiv",
"One.toOfNat1",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | false |
MvPowerSeries.instIsAdicCompleteSpanRangeXOfFinite | Mathlib.RingTheory.AdicCompletion.Completeness | [
"MvPowerSeries.instAddCommGroup",
"Eq.mpr",
"AlgEquiv.instEquivLike",
"RingHom.instRingHomClass",
"MvPowerSeries.toAdicCompletion_coe",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"Algebra.algebraMap",
"LieRing... | true |
IsFractionRing.charZero_of_isFractionRing | Mathlib.Algebra.CharP.Algebra | [
"CommRing",
"IsFractionRing",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra",
"Field.toDivisionRing",
"IsFractionRing.charP_of_isFractionRing",
"DivisionRing.toRing",
"instOfNatNat",
"Field.toSemifield",
"CharZero",
"CharP.charP_to_charZero",
"CommRing.toCommSemiring",
"Semifield.toDivision... | true |
_private.Lean.Elab.PreDefinition.WF.Unfold.0.Lean.Elab.WF.rwFixEq | Lean.Elab.PreDefinition.WF.Unfold | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.MVarId.withContext",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.mkAppN",
"Lean.Expr.isApp",
"ReaderT",
"Lean.MVarId.getType'",
"instMonadControlTOfPure",
"String",
"Lean.MVarId.assign",
"Lean.Meta.State",
"Lean.... | true |
instArchimedeanRat | Mathlib.Algebra.Order.Archimedean.Basic | [
"Rat.addCommMonoid",
"Iff.mpr",
"Eq.mpr",
"le_refl",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"DivisionRing.toRatCast",
"congrArg",
"Rat",
"PartialOrder.toPreorder",
"Rat.linearOrder",
"Preorder.toLE",
"Exists",
"Field.toDivisionRing",
"Semilattice... | true |
Ctop.Realizer | Mathlib.Data.Analysis.Topology | [
"TopologicalSpace",
"Ctop.Realizer.mk"
] | true |
ProbabilityTheory.indepSets_of_indepSets_of_le_right | Mathlib.Probability.Independence.Basic | [
"Unit.unit",
"MeasureTheory.Measure",
"HasSubset.Subset",
"ProbabilityTheory.Kernel.indepSets_of_indepSets_of_le_right",
"MeasureTheory.Measure.dirac",
"MeasurableSpace",
"Unit",
"PUnit.instMeasurableSpace",
"ProbabilityTheory.IndepSets",
"ProbabilityTheory.Kernel.const",
"Set.instHasSubset",
... | true |
Submonoid.groupPowers.eq_1 | Mathlib.Algebra.Group.Submonoid.Membership | [
"Monoid",
"MulOne.toOne",
"Submonoid.groupPowers._proof_4",
"Monoid.toMulOneClass",
"SubmonoidClass.instPow",
"DivInvMonoid.mk",
"HSub.hSub",
"Group",
"Membership.mem",
"Submonoid.groupPowers._proof_2",
"Subtype",
"Submonoid.toMonoid",
"instSubNat",
"Submonoid.groupPowers._proof_3",
"Div... | true |
ContinuousLinearMap.eqOn_closure_span | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"LinearMap.eqOn_span'",
"Submodule",
"ContinuousLinearMap.funLike",
"LinearMap.instFunLike",
"RingHom",
"Set.EqOn.closure",
"ContinuousLinearMap.toLinearMap",
"Set.EqOn",
"LinearMap",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousLinearMap.continuous",
"SetLike.coe... | true |
Homeomorph.addLeft.eq_1 | Mathlib.Topology.Algebra.Group.Basic | [
"Homeomorph.mk",
"Homeomorph.addLeft._proof_1",
"AddMonoid.toAddZeroClass",
"SeparatelyContinuousAdd",
"Homeomorph.addLeft._proof_2",
"AddZeroClass.toAddZero",
"TopologicalSpace",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Homeomorph.addLeft",
"Equiv.addLeft",
"Homeomorph",
"AddZero.toAdd",
"... | true |
IsPrimitiveRoot.pow_ne_one_of_pos_of_lt | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Iff.mpr",
"MulOne.toOne",
"Dvd.dvd",
"Monoid.toMulOneClass",
"Nat.pos_iff_ne_zero",
"Function.comp",
"mt",
"Ne",
"instOfNatNat",
"LE.le",
"instLENat",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat.instDvd",
"CommMonoid.toMonoid",
"Nat.instPreorder",
"Nat",
"LT.lt",
... | true |
Std.TreeSet.Raw.insertMany_append | Std.Data.TreeSet.Raw.Lemmas | [
"Eq.mpr",
"congrArg",
"instForInOfForIn'",
"Ordering",
"inferInstance",
"id",
"List.rec",
"Id",
"Membership",
"List.cons",
"instHAppendOfAppend",
"List",
"Std.TreeSet.Raw.insert",
"Std.TreeSet.Raw",
"List.instMembership",
"Std.TreeSet.Raw.insertMany_cons",
"eq_self",
"of_eq_true",
... | true |
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