name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Analysis.Normed.Module.Multilinear.Basic.0.MultilinearMap.continuous_of_bound._simp_1_1 | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"One",
"ZeroLEOneClass",
"LE.le",
"LE",
"zero_le_one",
"True",
"eq_true",
"One.toOfNat1",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
StateTransition.tr_eval_rev | Mathlib.Computability.StateTransition | [
"Iff.mpr",
"Part",
"StateTransition.tr_reaches_rev",
"Option.ctorIdx",
"congrArg",
"Option.instMembership",
"HEq.refl",
"False.elim",
"Option.casesOn",
"noConfusion_of_Nat",
"Option.some",
"Membership.mem",
"Exists",
"StateTransition.Respects.match_1",
"Eq.mp",
"Eq.casesOn",
"Part.in... | true |
StarSubalgebra.ext_iff | Mathlib.Algebra.Star.Subalgebra | [
"CommSemiring.toSemiring",
"HEq.refl",
"Iff.rfl",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"Eq.casesOn",
"StarSubalgebra",
"StarSubalgebra.setLike",
"StarAddMonoid.toInvolutiveStar",
"StarSubalgebra.ext",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAd... | true |
Lean.Lsp.ParameterInformation._sizeOf_inst | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.ParameterInformation._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Lsp.ParameterInformation"
] | false |
_private.Mathlib.Algebra.Lie.Weights.Basic.0.LieModule.iSup_genWeightSpace_eq_top._simp_1_1 | Mathlib.Algebra.Lie.Weights.Basic | [
"Submodule",
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieSubmodule.toSubmodule",
"LieSubmodule",
"AddCommGroup",
"LieSubmodule.toSubmodule_inj",
"LieRing",
"CommRing.toCommSemiring",
"LieRingModule",
"propext",
"Module",
"Eq.symm",
"Eq"
] | false |
_private.Mathlib.Order.Atoms.0.IsAtom.Iic.match_1_1 | Mathlib.Order.Atoms | [
"Preorder.toLT",
"Subtype.casesOn",
"Preorder.toLE",
"Membership.mem",
"Subtype",
"LE.le",
"Subtype.mk",
"LT.lt",
"Set.Iic",
"Set.instMembership",
"Preorder",
"Subtype.preorder",
"Set"
] | false |
_private.Mathlib.Data.Finset.Basic.0.Equiv.Finset.union_symm_right._simp_1_1 | Mathlib.Data.Finset.Basic | [
"Equiv.instEquivLike",
"Equiv.symm_apply_eq",
"Equiv",
"propext",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Var.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastVar.go_get_aux._proof_1_2 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Var | [
"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.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.combo_s... | false |
Std.TreeSet.Raw.getD_minD | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.getD",
"Std.TreeSet.Raw.WF.out",
"Ordering",
"Std.TransCmp",
"Std.TreeSet.Raw",
"Unit",
"Std.TreeMap.Raw.getKeyD_minKeyD",
"Bool",
"Std.TreeSet.Raw.isEmpty",
"Bool.false",
"Std.TreeSet.Raw.inner",
"Std.TreeSet.Raw.minD",
"Eq",
"Std.TreeSet.Raw.WF"
] | true |
commGroupOfIsUnit | Mathlib.Algebra.Group.Units.Defs | [
"Semigroup.toMul",
"Inv",
"CommMonoid.mul_comm",
"DivInvMonoid.mk",
"IsUnit",
"commGroupOfIsUnit._proof_1",
"DivInvMonoid.div'",
"CommGroup",
"Div.mk",
"npowRec",
"CommGroup.mk",
"CommMonoid.toMonoid",
"commGroupOfIsUnit._proof_4",
"commGroupOfIsUnit._proof_5",
"zpowRec",
"invOfIsUnit"... | true |
_private.Lean.Meta.Tactic.Repeat.0.Lean.Meta.repeat'Core.go.match_3 | Lean.Meta.Tactic.Repeat | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
_private.Init.Data.Array.Lemmas.0.Array.back_append._simp_1_1 | Init.Data.Array.Lemmas | [
"Bool.true",
"List",
"List.isEmpty",
"List.isEmpty_iff",
"propext",
"Bool",
"Eq",
"List.nil"
] | false |
Aesop.aesop.dev.generateScript | Aesop.Options.Public | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
_private.Mathlib.Data.Set.Lattice.Image.0.Set.iUnion_prod_of_monotone._simp_1_4 | Mathlib.Data.Set.Lattice.Image | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
UniformSpace.Completion.completeSpace | Mathlib.Topology.UniformSpace.Completion | [
"UniformSpace",
"CompleteSpace",
"CauchyFilter.instUniformSpace",
"UniformSpace.Completion.uniformSpace",
"CauchyFilter.instCompleteSpace",
"SeparationQuotient.instCompleteSpace",
"CauchyFilter",
"UniformSpace.Completion"
] | true |
PEquiv.injective_of_forall_ne_isSome | Mathlib.Data.PEquiv | [
"Iff.mpr",
"PEquiv.instFunLikeOption",
"Eq.mpr",
"False",
"Function.LeftInverse",
"Function.HasLeftInverse.injective",
"congrArg",
"not_imp_comm",
"Option.casesOn",
"Bool.false_eq_true",
"Option.some",
"Eq.rec",
"id",
"Option.rec",
"Ne",
"Bool.true",
"Option.none",
"PEquiv.eq_some_... | true |
Sum.Ioo_inr_inr | Mathlib.Data.Sum.Interval | [
"Sum.instLocallyFiniteOrder",
"Finset",
"Sum.instPreorderSum",
"Finset.map",
"Sum",
"Sum.inr",
"Function.Embedding.inr",
"LocallyFiniteOrder",
"Eq",
"Finset.Ioo",
"rfl",
"Preorder"
] | true |
Lean.Server.Test.Runner.Client.InteractiveGoal._sizeOf_inst | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.InteractiveGoal",
"Lean.Server.Test.Runner.Client.InteractiveGoal._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
CompleteLattice.MulticoequalizerDiagram.multispanIndex._proof_8 | Mathlib.Order.CompleteLattice.MulticoequalizerDiagram | [
"CategoryTheory.Limits.MultispanShape.prod",
"CategoryTheory.Limits.MultispanShape.L",
"PartialOrder.toPreorder",
"CompleteLattice.MulticoequalizerDiagram.multispanIndex.match_1",
"Preorder.toLE",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"Category... | false |
CategoryTheory.Limits.IsColimit.natIso | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Opposite",
"CategoryTheory.coyoneda",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Iso",
"CategoryTheory.uliftFunctor",
"Opposite.op",
"CategoryTheory.types",
"Cat... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_2 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Lean.Grind.eq_false_of_not_eq_true",
"List.pairwise_cons_cons",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Lean.Grind.not_not",
"Equiv.instEquivLike",
"List.Pairwise",
"Lean.Grind.iff_eq",
"List.nodup_iff_pairwise_ne",
"Classical.byContradiction",
"Eq.mp",
"id",
"Equiv",
"Ne",
"Lis... | false |
CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.leftHomologyData_π | Mathlib.Algebra.Homology.ShortComplex.Abelian | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.CokernelCofork",
"CategoryTheory.Limits.KernelFork",
"CategoryTheory.ShortComplex",
"Cate... | true |
inv_lt_of_neg | Mathlib.Algebra.Order.Field.Basic | [
"Iff.mpr",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"inv_lt_zero'",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"NonUnitalNonAssocSemiring.toMulZeroC... | true |
IsBezout.toGCDDomain._proof_6 | Mathlib.RingTheory.PrincipalIdealDomain | [
"CommRing",
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"IsBezout.gcd",
"CommSemiring.toSemiring",
"semigroupDvd",
"SemigroupWithZero.toSemigroup",
"IsBezout.toGCDDomain._proof_5",
"IsBezout",
"NonUnitalSemiring.toSemigroupWithZero",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"CommRing.toComm... | false |
AdjoinRoot.isAdjoinRoot._proof_1 | Mathlib.RingTheory.IsAdjoinRoot | [
"CommRing",
"Dvd.dvd",
"Semiring.toModule",
"AlgHom.algHomClass",
"CommRing.toNonUnitalCommRing",
"AdjoinRoot.mk_eq_zero._simp_1",
"AdjoinRoot",
"RingHom.mem_ker._simp_1",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial... | false |
AddGroupCone.nonneg_toAddSubmonoid | Mathlib.Algebra.Order.Group.Cone | [
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddCommGroup.toAddGroup",
"PartialOrder",
"AddCommGroup",
"AddGroupCone.toAddSubmonoid",
"AddSubmonoid",
"AddGroup.toSubNegMonoid",
"SubNegMonoid.toAddMonoid",
"Eq",
"AddSubmonoid.nonneg",
"IsOrderedAddMo... | true |
GenContFract.Pair.noConfusion | Mathlib.Algebra.ContinuedFractions.Basic | [
"HEq.refl",
"GenContFract.Pair.casesOn",
"GenContFract.Pair",
"GenContFract.Pair.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq"
] | false |
_private.Mathlib.Tactic.WithoutCDot.0.Lean.Elab.Term.withoutCDotContents.parenthesizer | Mathlib.Tactic.WithoutCDot | [
"Lean.Parser.optional.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.Parser.withoutPosition.parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.andthen.parenthesizer",
"Lean.Parser.symbol.parenthesizer",
"Nat",
"Lean.Parser.ppSpace.parenthesizer",
"Lean.Parser.termParser.par... | true |
Int.preimage_Ioo | Mathlib.Algebra.Order.Floor.Ring | [
"Set.ext",
"Int.cast",
"Preorder.toLT",
"Int.floor",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"_private.Mathlib.Algebra.Order.Floor.Ring.0.Int.preimage_Ioo._simp_1_1",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Int",
"AddGroupWithOne.toIntCas... | true |
Real.Angle.sign | Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle | [
"Real",
"Real.Angle",
"Real.instZero",
"PartialOrder.toPreorder",
"Real.decidableLT",
"SignType.instLinearOrder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"OrderHom.instFunLike",
"SignType",
"Real.Angle.sin",
"DFunLike.coe",
"SignType.sign",
"instDistribLatticeOfLinearO... | true |
Lean.ScopedEnvExtension.Descr._sizeOf_1 | Lean.ScopedEnvExtension | [
"IO",
"Lean.ScopedEnvExtension.Descr",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Lean.ScopedEnvExtension.Descr.rec",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Name",
"SizeOf",
"Lean.OLeanLevel",
"OfNat.ofNat",
"Lean.ImportM",
"Option"
] | false |
continuousOn_const_smul_iff₀ | Mathlib.Topology.Algebra.ConstMulAction | [
"GroupWithZero.toMonoidWithZero",
"Units.instMulAction",
"instHSMul",
"GroupWithZero",
"Units",
"Ne",
"Units.instGroup",
"ContinuousConstSMul",
"Units.mk0",
"TopologicalSpace",
"Iff",
"Units.continuousConstSMul",
"MonoidWithZero.toMulZeroOneClass",
"continuousOn_const_smul_iff",
"MulActi... | true |
Lean.Meta.Rewrites.RewriteResult.mctx | Lean.Meta.Tactic.Rewrites | [
"Lean.Meta.Rewrites.RewriteResult",
"Lean.MetavarContext"
] | true |
DirectLimit.instCommRingOfRingHomClass | Mathlib.Algebra.Colimit.DirectLimit | [
"CommRing",
"DirectLimit.instRingOfRingHomClass",
"CommSemiring.toSemiring",
"DirectLimit.instCommRingOfRingHomClass._proof_2",
"Preorder.toLE",
"LE.le",
"DirectLimit",
"CommRing.toCommSemiring",
"IsDirectedOrder",
"Nonempty",
"DirectedSystem",
"CommRing.toRing",
"Semiring.toNonAssocSemiring... | true |
Lean.initFn._@.Lean.ExtraModUses.447004708._hygCtx._hyg.2 | Lean.ExtraModUses | [
"Lean.EnvExtension.AsyncMode.sync",
"Lean.PersistentHashSet.insert",
"Lean.SimplePersistentEnvExtensionDescr.mk",
"IO",
"_private.Lean.ExtraModUses.0.Lean.extraModUses.match_1",
"Option.some",
"Lean.PersistentHashSet.contains",
"Lean.registerSimplePersistentEnvExtension",
"Lean.instBEqExtraModUse",
... | false |
_private.Init.Data.SInt.Lemmas.0.Int8.le_iff_lt_or_eq._proof_1_4 | Init.Data.SInt.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.and_not_not_of_not_or",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
... | false |
NormedGroup.toGroup | Mathlib.Analysis.Normed.Group.Defs | [
"NormedGroup",
"Group"
] | true |
Derivation.compAEval_eq | Mathlib.Algebra.Polynomial.Derivation | [
"Derivation",
"Polynomial.derivative",
"Eq.mpr",
"instHSMul",
"Semiring.toModule",
"Module.AEval.of",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"Polynomial.mkDerivationEquiv._proof_1",
... | true |
IsPicardLindelof.mk | Mathlib.Analysis.ODE.PicardLindelof | [
"Norm.norm",
"Real.instLE",
"Real",
"HMul.hMul",
"NormedAddCommGroup.toMetricSpace",
"Real.instSub",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"IsPicardLindelof",
"Set.Elem",
"EMetricSpace.toPseudoEMetricSpace",
"NNReal",
"LE.le",
"IsPicardLindelof.mk",
"Real.i... | true |
_private.Mathlib.Tactic.Relation.Symm.0.Lean.Expr.relSidesIfSymm?.match_6 | Mathlib.Tactic.Relation.Symm | [
"_private.Mathlib.Tactic.Relation.Symm.0.Lean.Expr.relSidesIfSymm?._sparseCasesOn_1",
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"Prod.mk",
"Prod",
"Prod.casesOn",
"Option"
] | false |
RingQuot.instMonoidWithZero._proof_7 | Mathlib.Algebra.RingQuot | [
"_private.Mathlib.Algebra.RingQuot.0.RingQuot.instAddCommMonoid._simp_2",
"RingQuot.casesOn",
"HMul.hMul",
"congrArg",
"RingQuot.instMul",
"MulZeroClass.zero_mul",
"Quot.ind",
"RingQuot.mul_quot",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"RingQuot.Rel",
"RingQuot",
"RingQuot.mk",
"Distrib... | false |
_private.Mathlib.Analysis.Convex.BetweenList.0.List.sbtw_triple._simp_1_6 | Mathlib.Analysis.Convex.BetweenList | [
"forall_eq",
"propext",
"Eq"
] | false |
_private.Aesop.Search.ExpandSafePrefix.0.Aesop.expandFirstPrefixRapp | Aesop.Search.ExpandSafePrefix | [
"Inhabited.default",
"Aesop.SafeExpansionM",
"instInhabitedOfMonad",
"Aesop.SearchM.instMonad",
"Aesop.RappRef",
"instInhabitedPUnit",
"IO.RealWorld",
"Unit",
"Aesop.Queue",
"Aesop.SearchM",
"StateRefT'.instMonad",
"Aesop.SafeExpansionM.State"
] | true |
Ring.natCast._inherited_default | Mathlib.Algebra.Ring.Defs | [
"One.mk",
"Add.mk",
"id",
"Nat",
"Zero.mk",
"Nat.unaryCast"
] | false |
Lean.Meta.Grind.AC.EqData.noConfusionType | Lean.Meta.Tactic.Grind.AC.Eq | [
"Lean.Meta.Grind.AC.EqCnstr",
"Lean.Grind.AC.Expr",
"Lean.Meta.Grind.AC.EqData",
"Lean.Meta.Grind.AC.EqData.casesOn",
"Lean.Expr",
"Eq"
] | false |
Matrix.mulAction._proof_2 | Mathlib.LinearAlgebra.Matrix.Defs | [
"Monoid",
"Matrix.smul",
"MulOne.toOne",
"instHSMul",
"Matrix.mulAction._proof_1",
"Monoid.toMulOneClass",
"Matrix",
"Pi.mulAction._proof_2",
"SemigroupAction.mk",
"MulOneClass.toMulOne",
"MulAction",
"Pi.mulAction",
"Monoid.toSemigroup",
"One.toOfNat1",
"HSMul.hSMul",
"SemigroupAction... | false |
_private.Mathlib.Combinatorics.SetFamily.Shadow.0.Finset.mem_shadow_iterate_iff_exists_card._simp_1_2 | Mathlib.Combinatorics.SetFamily.Shadow | [
"Finset",
"Membership.mem",
"Exists",
"Insert.insert",
"instOfNatNat",
"Finset.instInsert",
"instHAdd",
"And",
"Finset.instSetLike",
"HAdd.hAdd",
"Nat",
"Finset.card_eq_succ",
"propext",
"Finset.card",
"instAddNat",
"OfNat.ofNat",
"Eq",
"Not",
"SetLike.instMembership",
"Decidab... | false |
SeparationQuotient.instAddGroup._proof_5 | Mathlib.Topology.Algebra.SeparationQuotient.Basic | [
"instHSMul",
"SeparationQuotient.instNSMul",
"AddMonoid.toNSMul",
"IsTopologicalAddGroup.toContinuousAdd",
"SeparationQuotient.mk_nsmul",
"TopologicalSpace",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Nat",
"SeparationQuotient",
"SeparationQuotient.mk",
"HSMul.hSMul",
"SubNegMonoid.toAddMonoid"... | false |
CategoryTheory.ComposableArrows.instIsIsoOfNatNatTwoδ₁Toδ₀ | Mathlib.CategoryTheory.ComposableArrows.Two | [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.ComposableArrows",
"CategoryTheory.CategoryStruct.id",
"inferInstance",
"id",
"Fin.instOf... | true |
Lean.Grind.CommRing.Poly.mulC_nc.go._unsafe_rec | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly.combineC",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.mulConstC",
"Lean.Grind.CommRing.Poly.mulC_nc.go._unsafe_rec",
"Lean.Grind.CommRing.Poly.denote.match_1",
"Int",
"Lean.Grind.CommRing.Poly.mulMonC_nc",
"Nat",
"Lean.Grind.CommRing.Mon"
] | false |
CategoryTheory.Limits.MulticospanIndex.sections.property | Mathlib.CategoryTheory.Limits.Types.Multiequalizer | [
"CategoryTheory.Limits.MulticospanShape.snd",
"CategoryTheory.Limits.MulticospanIndex.sections.val",
"CategoryTheory.Limits.MulticospanIndex",
"CategoryTheory.Limits.MulticospanIndex.fst",
"CategoryTheory.Limits.MulticospanShape.fst",
"CategoryTheory.Limits.MulticospanIndex.sections",
"CategoryTheory.ty... | true |
PrimeMultiset.coe_coePNatMonoidHom | Mathlib.Data.PNat.Factors | [
"AddMonoid.toAddZeroClass",
"instAddCommMonoidPrimeMultiset",
"PrimeMultiset.toPNatMultiset",
"PrimeMultiset.coePNatMonoidHom",
"Multiset.instAddCancelCommMonoid",
"AddZeroClass.toAddZero",
"Multiset",
"AddCancelCommMonoid.toAddCommMonoid",
"AddCommMonoid.toAddMonoid",
"AddMonoidHom",
"AddMonoid... | true |
_private.Lean.Meta.Tactic.Grind.0.Lean.initFn._@.Lean.Meta.Tactic.Grind.3036382584._hygCtx._hyg.2 | Lean.Meta.Tactic.Grind | [
"Lean.Name.mkNum",
"IO",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.registerTraceClass",
"Lean.Name.anonymous",
"Unit",
"Nat",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr4"
] | false |
Submodule.LinearDisjoint.rank_le_one_of_commute_of_flat_of_self | Mathlib.LinearAlgebra.LinearDisjoint | [
"Eq.mpr",
"Submodule",
"le_refl",
"CommRing",
"Submodule.LinearDisjoint",
"Cardinal.instOne",
"Ring.toNonAssocRing",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"inf_of_le_left",
"Submodule.addCommMonoid",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"Algebra",
"Commu... | true |
WithLp.fstₗ_apply | Mathlib.Analysis.Normed.Lp.ProdLp | [
"WithLp",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"WithLp.fstₗ",
"WithLp.instAddCommGroup",
"AddCommGroup",
"LinearMap",
"WithLp.fst",
"ENNReal",
"Semiring",
"Eq.refl",
"WithLp.instModule",
"Module",
"Prod",
"Prod.instModule",
"RingHom.id",
"Semiring.toNonAssocSemiri... | true |
LindelofSpace | Mathlib.Topology.Compactness.Lindelof | [
"TopologicalSpace",
"LindelofSpace.mk"
] | true |
chudnovskySum._proof_1 | Mathlib.Analysis.Real.Pi.Chudnovsky | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
Finset.prod_ite_index | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"Finset",
"Decidable",
"apply_ite",
"Finset.prod",
"Eq",
"CommMonoid",
"ite"
] | true |
Nat.strongRec._unsafe_rec | Batteries.Data.Nat.Basic | [
"Nat",
"LT.lt",
"Nat.strongRec._unsafe_rec",
"instLTNat"
] | false |
CategoryTheory.Cokleisli.Adjunction.adj._proof_6 | Mathlib.CategoryTheory.Monad.Kleisli | [
"CategoryTheory.Comonad",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Cokleisli.Adjunction.adj._proof_1",
"CategoryTheory.Cokleisli.category",
"CategoryTheory.Cokleisli.Hom.of",
"CategoryTheory.Comonad.δ",
"CategoryTheory.Functor.comp"... | false |
OrderedFinpartition.partSize_pos | Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | [
"OrderedFinpartition",
"instOfNatNat",
"Nat",
"LT.lt",
"OrderedFinpartition.partSize",
"instLTNat",
"OfNat.ofNat",
"Fin",
"OrderedFinpartition.length"
] | true |
Lean.Firefox.ProfileMeta.interval._default | Lean.Util.Profiler | [
"id",
"OfScientific.ofScientific",
"Bool.true",
"Lean.Firefox.Milliseconds",
"Lean.Firefox.instOfScientificMilliseconds"
] | false |
univLE_iff_exists_embedding | Mathlib.SetTheory.Cardinal.UnivLE | [
"Eq.mpr",
"UnivLE",
"Cardinal",
"congrArg",
"Cardinal.univ",
"univLE_iff_cardinal_le",
"id",
"LE.le",
"Cardinal.instLE",
"Function.Embedding",
"Iff",
"propext",
"Cardinal.lift_mk_le'",
"Nonempty",
"Eq",
"Ordinal"
] | true |
_private.Mathlib.LinearAlgebra.LinearIndependent.Basic.0.LinearMap.linearIndependent_iff._simp_1_1 | Mathlib.LinearAlgebra.LinearIndependent.Basic | [
"disjoint_bot_right",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"PartialOrder",
"Bot.bot",
"True",
"eq_true",
"Eq"
] | false |
_private.Std.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap.0.Std.IterM.stepAsHetT_filterMapWithPostcondition._simp_1_1 | Std.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Std.Iterators.HetT.Property",
"Exists",
"Eq.rec",
"LawfulMonad",
"Std.Iterators.HetT",
"Std.Iterators.HetT.ext_iff",
"propext",
"Std.Iterators.HetT.prun",
"Eq.symm",
"Monad",
"Eq"
] | false |
SSet.Truncated.Path₁.ext_iff | Mathlib.AlgebraicTopology.SimplicialSet.Path | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"HEq.refl",
"SSet.Truncated",
"SSet.Truncated.Path₁._proof_2",
"Eq.casesOn",
"SSet.Truncated.Path₁.vertex",
"instOfNatNat",
"SSet.Truncated.Path₁.ext",
"LE.le",
"instLENat",
"And.casesOn",
"SSet.Truncated.Path₁",
"instHAdd",
... | true |
LinearMap.norm_map_iff_inner_map_map | Mathlib.Analysis.InnerProductSpace.LinearMap | [
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"Real",
"LinearIsometry.norm_map",
"SeminormedAddCommGroup",
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"LinearIsometry.mk",
"LinearIsometry.inner_map_map",
"NormedField.toField",
"LinearMapClass.linearMap",
"Field.t... | true |
CategoryTheory.Equivalence.sheafCongrPrecoherent_inverse_obj_obj_obj | Mathlib.CategoryTheory.Sites.Coherent.Equivalence | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence.sheafCongrPrecoherent",
"CategoryTheory.Equivalence",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"Opposite.op",
"CategoryTheory.Equivalence.precoherent... | true |
Finset.card_inter_smul | Mathlib.Combinatorics.Additive.Convolution | [
"instHSMul",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"inv_one",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"DivInvOneMonoid.toDivInvMonoid",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Finset.smulFinset",
"Eq.mp",
"Finset.convolut... | true |
Submodule.torsionBySet_isTorsionBySet | Mathlib.Algebra.Module.Torsion.Basic | [
"Submodule",
"Module.IsTorsionBySet",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Submodule.mem_torsionBySet_iff",
"Membership.mem",
"AddZeroClass.toAddZero",
"Set.Elem",
"Subtype",
"DistribSMul.toSMulZeroC... | true |
CategoryTheory.AddMon.monMonoidal._proof_3 | Mathlib.CategoryTheory.Monoidal.Mon_ | [
"CategoryTheory.AddMon.Hom.ext'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.AddMon.monMonoidalStruct",
"CategoryTheory.AddMon.instCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.MonoidalCategory.id_whiskerRig... | false |
SimplicialObject.Split.Hom.f | Mathlib.AlgebraicTopology.SimplicialObject.Split | [
"CategoryTheory.CategoryStruct.toQuiver",
"SimplicialObject.Split.X",
"Quiver.Hom",
"SimplicialObject.Splitting.N",
"SimplicialObject.Split",
"SimplicialObject.Split.Hom",
"Nat",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category",
"SimplicialObject.Split.s"
] | true |
Filter.Eventually.and_frequently | Mathlib.Order.Filter.Basic | [
"congrArg",
"Filter.Eventually",
"_private.Mathlib.Order.Filter.Basic.0.Filter.Eventually.and_frequently._simp_1_1",
"Eq.mp",
"Filter.Frequently",
"funext",
"Filter.Frequently.and_eventually",
"And",
"congrFun'",
"Filter"
] | true |
LatticeHom.fst | Mathlib.Order.Hom.Lattice | [
"LatticeHom.fst._proof_2",
"LatticeHom.fst._proof_1",
"Lattice",
"Lattice.toSemilatticeSup",
"SemilatticeSup.toMax",
"Prod.instLattice",
"LatticeHom",
"Prod.fst",
"LatticeHom.mk",
"Prod",
"SupHom.mk"
] | true |
PseudoMetric._sizeOf_inst | Mathlib.Topology.MetricSpace.BundledFun | [
"PseudoMetric",
"PseudoMetric._sizeOf_1",
"LE",
"SizeOf.mk",
"SizeOf",
"Add",
"Zero"
] | false |
Lean.Meta.Grind.instBEqEMatchTheoremKind.beq | Lean.Meta.Tactic.Grind.Extension | [
"Decidable",
"Lean.Meta.Grind.EMatchTheoremKind.ctorIdx",
"instDecidableEqBool",
"instBEqOfDecidableEq",
"Bool.true",
"Lean.Meta.Grind.EMatchTheoremKind",
"BEq.beq",
"Unit",
"_private.Lean.Meta.Tactic.Grind.Extension.0.Lean.Meta.Grind.instBEqEMatchTheoremKind.beq.match_1",
"Nat",
"Bool",
"inst... | true |
PUnit.commGroup.eq_1 | Mathlib.Algebra.Group.PUnit | [
"Mul.mk",
"PUnit.commGroup._proof_1",
"One.mk",
"PUnit.commGroup._proof_2",
"DivInvMonoid.mk",
"Semigroup.mk",
"PUnit.commGroup._proof_4",
"PUnit.commGroup._proof_8",
"Int",
"Monoid.mk",
"CommGroup",
"Div.mk",
"CommGroup.mk",
"PUnit.commGroup._proof_9",
"PUnit",
"Inv.mk",
"Nat",
"P... | true |
Vector.mapFinIdxM._proof_7 | Init.Data.Vector.Basic | [
"List.toArray",
"Nat",
"Eq",
"Array.size",
"rfl",
"List.nil"
] | false |
Nat.div2_bit1 | Mathlib.Data.Nat.Bits | [
"HMul.hMul",
"Nat.div2_bit",
"Nat.div2",
"instMulNat",
"instOfNatNat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq",
"instHMul"
] | true |
TotalComplexShape.symm.match_1 | Mathlib.Algebra.Homology.ComplexShapeSigns | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Batteries.PairingHeap.deleteMin | Batteries.Data.PairingHeap | [
"Batteries.PairingHeapImp.Heap.foldM.match_1",
"Batteries.PairingHeapImp.Heap.WF",
"Batteries.PairingHeapImp.Heap.deleteMin",
"Option.some",
"Prod.mk",
"Subtype.mk",
"Option.none",
"Batteries.PairingHeapImp.Heap",
"Bool",
"Batteries.PairingHeap.deleteMin._proof_1",
"Prod",
"Subtype.val",
"Eq... | true |
PProd | Init.Prelude | [
"PProd.mk"
] | true |
TrivSqZeroExt.addGroup | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"TrivSqZeroExt.sub",
"TrivSqZeroExt",
"TrivSqZeroExt.addGroup._proof_4",
"SubNegMonoid.mk",
"TrivSqZeroExt.addGroup._proof_6",
"TrivSqZeroExt.addMonoid",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid... | true |
GroupAlgebra.mul_average_left | Mathlib.RepresentationTheory.Invariants | [
"MonoidAlgebra.semiring",
"MonoidAlgebra.addCommMonoid",
"Eq.mpr",
"Finset.mul_sum",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra.mul_smul_comm",
"instHSMul",
"MonoidHom.instFunLike",
"HMul.hMul",
"GroupAlgebra.average",
"Finset.univ",
"Function.Bijective.sum_comp",
"MonoidHom",
"Mo... | true |
Lean.Widget.eraseWidgetSpec | Lean.Widget.Commands | [
"Lean.Name.mkStr3",
"Lean.ParserDescr.nodeWithAntiquot",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"Lean.Name.mkStr1"
] | true |
_private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.Expr.toPolyC.go.match_4.eq_7 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Expr",
"Lean.Grind.CommRing.Expr.mul",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.CommRing.Expr.sub",
"Lean.Grind.CommRing.Expr.natCast",
"Lean.Grind.CommRing.Expr.neg",
"Int",
"Lean.Grind.CommRing.Expr.add",
"Lean.Grind.CommRing.Var",
"Nat",
"Lean.Grind.CommRing.Expr.toPol... | true |
Quaternion.instDivisionRing._proof_8 | Mathlib.Algebra.Quaternion | [
"GroupWithZero.zpow",
"NegZeroClass.toNeg",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"GroupWithZero.toInv",
"CommRing.toNonUnitalCommRing",
"Quaternion.instGroupWithZero",
"LinearOrder",
"AddGroupWithOne.toAddMonoidWithOne",
"IsStrictOrderedRing",
"NonUnitalNonAssocSemiring.toMulZeroClass"... | false |
Semiring.toGrindSemiring._proof_12 | Mathlib.Algebra.Ring.GrindInstances | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instNeZeroNatHAdd_1",
"AddMonoid.toAddSemigroup",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"inferInstance",
"Semiring.toGrindSemiring.match_1",
"id",
"AddMonoidWithOne.toNatCast",
"NonUnitalSemi... | false |
HomologicalComplex.homologyπ_extendHomologyIso_inv_assoc | Mathlib.Algebra.Homology.Embedding.ExtendHomology | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.homologyπ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomologicalComplex.homologyπ_extendHomologyIso_inv",
"HomologicalComplex.HasHomology",
"HomologicalComplex",
"Eq.mp",
"i... | true |
Bundle.TotalSpace.mk' | Mathlib.Data.Bundle | [
"Bundle.TotalSpace.mk",
"Bundle.TotalSpace"
] | true |
_private.Mathlib.Algebra.Lie.Nilpotent.0.LieModule.iterate_toEnd_mem_lowerCentralSeries._simp_1_1 | Mathlib.Algebra.Lie.Nilpotent | [
"LieSubmodule.instSetLike",
"CommRing",
"LieSubmodule.instTop",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieSubmodule",
"Membership.mem",
"AddCommGroup",
"LieRing",
"CommRing.toCommSemiring",
"LieRingModule",
"True",
"eq_true",
"LieSubmodule.mem_top",
"Module",
"Top.... | false |
IsBaseChange.equiv._proof_2 | Mathlib.RingTheory.IsTensorProduct | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra.to_smulCommClass",
"CommSemiring.toSemiring",
"instDistribSMul",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"CommSemiring",
"Add... | false |
_private.Mathlib.LinearAlgebra.Basis.VectorSpace.0.exists_basis_of_pairing_eq_zero._simp_1_3 | Mathlib.LinearAlgebra.Basis.VectorSpace | [
"Submodule",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Insert.insert",
"DistribSMul.toSMulZeroClass",
"Submodule.mem_span_insert'... | false |
«_aux_Mathlib_Algebra_Star_StarAlgHom___macroRules_term_→⋆ₐ__1» | Mathlib.Algebra.Star.StarAlgHom | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",... | false |
Unitization.instNeg | Mathlib.Algebra.Algebra.Unitization | [
"Unitization.equiv",
"Equiv.Neg",
"Neg",
"Prod.instNeg",
"Unitization",
"Prod"
] | true |
List.SortedGE.isChain | Mathlib.Data.List.Sort | [
"List.sortedGE_iff_isChain",
"Preorder.toLE",
"GE.ge",
"List.IsChain",
"List",
"Iff.mp",
"List.SortedGE",
"Preorder"
] | true |
Mathlib.Tactic.BicategoryLike.MonadMor₁.mk.noConfusion | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.MonadMor₁.noConfusion",
"id",
"Mathlib.Tactic.BicategoryLike.Obj",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"Mathlib.Tactic.BicategoryLike.MonadMor₁",
"heq_of_eq",
"Mathlib.Tactic.BicategoryLike.MonadMor₁.mk",
"Eq.refl",
"HEq",
"Eq"
] | false |
HomologicalComplex.instHasColimitDiscreteWalkingPairCompPairEval | Mathlib.Algebra.Homology.HomologicalComplexBiprod | [
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"HomologicalComplex",
"HomologicalComplex.eval",
"CategoryTheory.Limits.hasColimit_of_iso",
"CategoryTheory.Limits.HasBinaryBiproduct",
"CategoryTheory.Iso",
"ComplexShape... | true |
_private.Lean.Meta.InferType.0.Lean.Meta.inferConstType | Lean.Meta.InferType | [
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Core.instantiateTypeLevelParams",
"Lean.ConstantVal",
"Lean.ConstantVal.levelParams",
"ReaderT",
"Lean.Meta.throwIncorrectNumberOfLevels",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"instMonadL... | true |
CategoryTheory.Endofunctor.Coalgebra.ctorIdx | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Coalgebra",
"Nat",
"CategoryTheory.Category"
] | false |
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