name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
isPrimePow_nat_iff_bounded_log | Mathlib.Algebra.IsPrimePow | [
"Eq.mpr",
"Trans.trans",
"Nat.Prime",
"Nat.one_lt_two",
"congrArg",
"Nat.AtLeastTwo.prop",
"Nat.instMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"IsPrimePow",
"isPrimePow_nat_iff",
"Exists",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.lt_add_one._simp_1",
"Nat.log_mono",
"Monoid.to... | true |
RelSeries.append_length | Mathlib.Order.RelSeries | [
"SetRel",
"RelSeries.last",
"Membership.mem",
"RelSeries.length",
"Prod.mk",
"instOfNatNat",
"RelSeries",
"instHAdd",
"HAdd.hAdd",
"Nat",
"RelSeries.append",
"instAddNat",
"Eq.refl",
"RelSeries.head",
"Prod",
"OfNat.ofNat",
"Eq",
"Set.instMembership"
] | true |
_private.Mathlib.LinearAlgebra.Eigenspace.Basic.0.Module.End.genEigenspace_inf_le_add._proof_1_6 | Mathlib.LinearAlgebra.Eigenspace.Basic | [
"Lean.RArray.leaf",
"False",
"AddMonoid.toAddSemigroup",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Lean.Grind.not_or",
"Classical.byContradiction",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Nat.instAddMonoid",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear... | false |
Lean.Lsp.LeanModuleHierarchyImportedByParams | Lean.Data.Lsp.Extra | [
"Lean.Lsp.LeanModuleHierarchyImportedByParams.mk"
] | true |
EReal.liminf_mul_le | Mathlib.Topology.Instances.EReal.Lemmas | [
"Iff.mpr",
"Filter.limsup_const",
"Preorder.toLT",
"HMul.hMul",
"Filter.liminf",
"Or.imp_left",
"EReal.instPosMulMono",
"_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.liminf_mul_le.match_1_1",
"Filter.isBounded_le_of_top",
"Filter.map",
"Filter.NeBot",
"PartialOrder.toPreorder",
"... | true |
_private.Mathlib.CategoryTheory.Discrete.SumsProducts.0.CategoryTheory.Discrete.sumEquiv.match_1.eq_1 | Mathlib.CategoryTheory.Discrete.SumsProducts | [
"CategoryTheory.Discrete.sumEquiv.match_1",
"Sum",
"Sum.inl",
"Sum.inr",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum.isClosedEmbedding_comap_fst._simp_1_1 | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"PrimeSpectrum.isClosed_zeroLocus",
"PrimeSpectrum.zeroLocus",
"CommSemiring",
"IsClosed",
"True",
"eq_true",
"PrimeSpectrum",
"Eq",
"PrimeSpectrum.zariskiTopology",
"Set"
] | false |
TopologicalSpace.Clopens.instBooleanAlgebra._proof_9 | Mathlib.Topology.Sets.Closeds | [
"SemilatticeSup.mk",
"TopologicalSpace.Clopens.coe_bot",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"TopologicalSpace.Clopens.instMin",
"TopologicalSpace.Clopens.instSDiff",
"Compl.compl",
"Iff.rfl",
"PartialOrder.toPreorder",
"TopologicalSpace.Clopens.instPartialOrder",
"TopologicalSpace.Clop... | false |
_private.Init.Data.List.Nat.Sum.0.List.sum_eq_foldl_nat._simp_1_1 | Init.Data.List.Nat.Sum | [
"List.sum_eq_foldr",
"List.sum",
"List",
"instHAdd",
"HAdd.hAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq.symm",
"List.foldr",
"Eq",
"Add",
"Zero"
] | false |
Complex.norm_mul_sin_arg | Mathlib.Analysis.SpecialFunctions.Complex.Arg | [
"Complex.mul_im",
"Norm.norm",
"Real",
"Complex.mul_re",
"HMul.hMul",
"Complex.cos",
"sub_self",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"Complex.im",
"Real.instSub",
"MulZeroClass.zero_mul",
"AddMonoid.toAddZeroClass",
"Complex.sin",
"HSub.hSub",
"Complex.instMul",
"Add... | true |
Lean.Widget.MsgEmbed.goal | Lean.Widget.InteractiveDiagnostic | [
"Lean.Widget.MsgEmbed",
"Lean.Widget.MsgEmbed.goal",
"Lean.Widget.InteractiveGoal"
] | true |
CategoryTheory.Sheaf.imageι | Mathlib.CategoryTheory.Sites.Subsheaf | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.Subfunctor.ι",
"CategoryTheory.Sheaf.image",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.... | true |
Lean.Meta.Grind.ENode.hasLambdas | Lean.Meta.Tactic.Grind.Types | [
"Bool",
"Lean.Meta.Grind.ENode"
] | true |
_private.Init.Data.Fin.Lemmas.0.Fin.subsingleton_iff_le_one.match_1_5 | Init.Data.Fin.Lemmas | [
"False",
"Fin.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Fin.mk",
"instOfNatNat",
"Nat.le.step",
"instHAdd",
"HAdd.hAdd",
"Nat.le",
"Nat",
"LT.lt",
"Eq.ndrec",
"Nat.ctorIdx",
"instAddNat",
"Nat.zero",
"Eq.refl",
"HEq",
"Nat.le.refl",
"instLTNat",
"Nat.le.cas... | false |
Finset.prod_map_toList | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"Eq.mpr",
"MulOne.toOne",
"Multiset.map",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Finset.prod.eq_1",
"List.map",
"Multiset.prod",
"Multiset",
"id",
"MulOne.toMul",
"Finset.toList",
"Finset.coe_toList",
"Finset.val",
"Finset.prod",
"Multiset.ofList",
"MulOneClass.toMulOne",
... | true |
HomotopyGroup.homotopyGroupOfUniqueMulEquivFundamentalGroup | Mathlib.Topology.Homotopy.HomotopyGroup | [
"Monoid.toMulOneClass",
"Unique",
"instGroupFundamentalGroup",
"Equiv",
"HomotopyGroup.homotopyGroupOfUniqueMulEquivFundamentalGroup._proof_2",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"decidableEq_of_subsingleton",
"Group.toDivInvMonoid",
"TopologicalSpace",
"Unique.instSubsingleton",
"MulOne... | true |
Std.Iterators.Productive.recOn | Init.Data.Iterators.Basic | [
"Std.Iterators.Productive.mk",
"Std.Iterator",
"Std.Iterators.Productive.rec",
"Std.IterM.IsPlausibleSkipSuccessorOf",
"Std.Iterators.Productive",
"Std.IterM",
"WellFounded"
] | false |
OrderDual.instOrderTopOfOrderBot.eq_1 | Mathlib.Order.BoundedOrder.Basic | [
"OrderDual.instLE",
"OrderBot.toBot",
"OrderBot",
"OrderTop.mk",
"OrderTop",
"LE",
"OrderBot.bot_le",
"OrderDual.instOrderTopOfOrderBot",
"Eq.refl",
"OrderDual",
"Eq",
"OrderDual.instTopOfBot"
] | true |
Unitization.complex_cfcₙ_eq_cfc_inr | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic | [
"cfcₙ",
"NonUnitalCStarAlgebra.toStarModule",
"Unitization.instAlgebra",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CStarAlgebra.toNonUnitalCStarAlgebra",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"NormedRing.toRing",... | true |
_private.Mathlib.CategoryTheory.Functor.TypeValuedFlat.0.CategoryTheory.FunctorToTypes.fromOverFunctorElementsEquivalence._proof_12 | Mathlib.CategoryTheory.Functor.TypeValuedFlat | [
"CategoryTheory.categoryOfElements",
"CategoryTheory.CategoryOfElements.map_snd",
"CategoryTheory.Over",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"Subtype.mk.congr_simp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
... | false |
CategoryTheory.Sheaf.freeYonedaHomEquiv | Mathlib.CategoryTheory.Generator.Sheaf | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Sheaf.freeYoneda",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Equiv.trans",
"CategoryTheory.Presheaf.freeYonedaHomEquiv",
"CategoryTheory.Functor.category",
"Equiv",
"CategoryTheory.presheafToSheaf",
"CategoryTheory.ObjectProper... | true |
SSet.Subcomplex.Pairing.RankFunction.basicCell | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | [
"SSet.Subcomplex.toSSet",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"LinearOrder",
"SSet.Subcomplex.Pairing.RankFunction.Cell.horn",
"CategoryTheory.Functor.category",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"SSet.Subcomplex.Pairing.IsProper",
"inst... | true |
ContDiff.continuous_deriv | Mathlib.Analysis.Calculus.ContDiff.Deriv | [
"Differentiable",
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"AnalyticOn",
"Continuous",
"Semiring.toModule",
"NormedRing.toRing",
"instAddMonoidWithOneENat",
"NormedSpace",
"WithTop.instPreorder",
"congrArg",
"CommSemiring.toSemiring",
"deriv",
"Set.univ",
"No... | true |
Lean.Elab.Tactic.Omega.MetaProblem.noConfusion | Lean.Elab.Tactic.Omega.Frontend | [
"Lean.Elab.Tactic.Omega.MetaProblem.noConfusionType",
"Lean.Expr.instBEq",
"Lean.Elab.Tactic.Omega.Problem",
"Std.HashSet",
"Lean.Expr",
"Lean.Elab.Tactic.Omega.MetaProblem.casesOn",
"List",
"Eq.ndrec",
"Eq.refl",
"Lean.Expr.instHashable",
"Lean.Elab.Tactic.Omega.MetaProblem",
"Eq"
] | false |
Rep.indToCoind._proof_2 | Mathlib.RepresentationTheory.FiniteIndex | [
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Rep.V",
"Submodule.module._proof_1",
"CommRing",
"instHSMul",
"Representation",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"Pi.addCommMonoid",
... | false |
Nat.even_xor | Mathlib.Data.Nat.Bitwise | [
"Eq.mpr",
"_private.Mathlib.Data.Nat.Bitwise.0.Nat.even_xor._proof_1_2",
"Nat.instXorOp",
"congrArg",
"_private.Mathlib.Data.Nat.Bitwise.0.Nat.even_xor._simp_1_1",
"id",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"Nat.xor_mod_two_eq",
"instHAdd",
"HMod.hMod",
"Iff",
"HAdd.hAdd",
"Nat",
... | true |
Algebra.TensorProduct.piRightHom._proof_2 | Mathlib.RingTheory.TensorProduct.Pi | [
"Algebra.to_smulCommClass",
"Pi.addCommMonoid",
"HMul.hMul",
"IsScalarTower.right",
"Algebra.TensorProduct.piRightHom_mul",
"congrArg",
"CommSemiring.toSemiring",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"Pi.module",
"LinearMap.instFunLike",
"Algebra",
"Algebra.toSMul",
"Algebra.toM... | false |
Metric.Sum.dist | Mathlib.Topology.MetricSpace.Gluing | [
"Real",
"Sum",
"Nonempty.some",
"Metric.glueDist.match_1",
"Nonempty.intro",
"Real.instAdd",
"Real.instOne",
"instHAdd",
"MetricSpace",
"HAdd.hAdd",
"One.toOfNat1",
"MetricSpace.toPseudoMetricSpace",
"Dist.dist",
"PseudoMetricSpace.toDist",
"OfNat.ofNat"
] | true |
_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.forInStep.go._unsafe_rec | Std.Data.DHashMap.Internal.AssocList.Basic | [
"Pure.pure",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.forInStep.go.match_1",
"Monad.toApplicative",
"ForInStep.done",
"Applicative.toPure",
"ForInStep",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.forInStep.go._unsa... | false |
_private.Mathlib.SetTheory.ZFC.Basic.0.ZFSet.sUnion_lem.match_1_5 | Mathlib.SetTheory.ZFC.Basic | [
"congrArg",
"Exists",
"Eq.mp",
"PSet.mk",
"PSet",
"Exists.casesOn",
"Exists.intro",
"Eq",
"PSet.Type",
"PSet.Equiv"
] | false |
Lean.Parser.Tactic.Grind.grindExact_ | Init.Grind.Interactive | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Name.mkStr5",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
Lean.Compiler.LCNF.JoinPointContextExtender.ExtendContext.currentJp? | Lean.Compiler.LCNF.JoinPoints | [
"Lean.FVarId",
"Lean.Compiler.LCNF.JoinPointContextExtender.ExtendContext",
"Option"
] | true |
_private.Mathlib.Data.Nat.Factors.0.Nat.primeFactorsList.match_1.eq_1 | Mathlib.Data.Nat.Factors | [
"Unit.unit",
"Nat.primeFactorsList.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
Nat.getElem?_toList_rco_eq_some | Init.Data.Range.Polymorphic.NatLemmas | [
"Std.Rco.size",
"GetElem?.toGetElem",
"Nat.size_rco",
"congrArg",
"Std.PRange.instHasSizeNat_1",
"HSub.hSub",
"List.instGetElem?NatLtLength",
"Option.some",
"Std.PRange.instLawfulUpwardEnumerableLTNat",
"Std.PRange.instIsAlwaysFiniteNat_1",
"instSubNat",
"Nat.getElem_toList_rco",
"GetElem.ge... | true |
Monoid.Coprod.instGroup._proof_2 | Mathlib.GroupTheory.Coprod.Basic | [
"Mul.mk",
"Semigroup.toMul",
"One.mk",
"Monoid.toMulOneClass",
"Group",
"DivInvMonoid.toMonoid",
"Int",
"npowRec",
"Group.toDivInvMonoid",
"One.one",
"Inv.inv",
"instOfNat",
"Inv.mk",
"Mul.mul",
"zpowRec",
"Monoid.toSemigroup",
"One.toOfNat1",
"Eq.refl",
"Monoid.toOne",
"Monoid... | false |
ite_eq_or_eq | Mathlib.Logic.Basic | [
"Decidable",
"if_pos",
"dite",
"Or.inl",
"Or",
"Eq",
"if_neg",
"Not",
"Or.inr",
"ite"
] | true |
OrderDual.instSemiring._proof_8 | Mathlib.Algebra.Order.Ring.Synonym | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocSemiring.toMul",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.left_distrib",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Semiring",
"Semiring.toNonUnitalSemi... | false |
CategoryTheory.Limits.ImageFactorisation.isImage | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.ImageFactorisation.F",
"CategoryTheory.Limits.ImageFactorisation",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.IsImage",
"CategoryTheory.Category"
] | true |
Lean.Lsp.Registration._sizeOf_inst | Lean.Data.Lsp.Client | [
"Lean.Lsp.Registration",
"SizeOf.mk",
"Lean.Lsp.Registration._sizeOf_1",
"SizeOf"
] | false |
Array.mapFinIdx_eq_singleton_iff | Init.Data.Array.MapIdx | [
"Iff.mpr",
"List.mapFinIdx_eq_singleton_iff._proof_1",
"Iff.of_eq",
"congrArg",
"Exists",
"Array.casesOn",
"List.mapFinIdx",
"instOfNatNat",
"Array.mapFinIdx_eq_singleton_iff._proof_1",
"List.toArray",
"List.cons",
"Array",
"iff_self",
"funext",
"Array.mapFinIdx",
"List",
"Array.mk.i... | true |
Set.image_val_sInter | Mathlib.Data.Set.Subset | [
"Eq.mpr",
"congrArg",
"Subtype.val_injective",
"Function.Injective.injOn",
"Set.iInter",
"setOf",
"Membership.mem",
"Exists",
"Set.Elem",
"id",
"Subtype",
"Set.sInter_eq_biInter",
"And",
"Set.Nonempty",
"Eq.refl",
"Set.sInter_image",
"Set.image",
"Set.image.eq_1",
"Eq.symm",
"S... | true |
AddSubsemigroup.centerCongr.eq_1 | Mathlib.GroupTheory.Submonoid.Center | [
"AddSubsemigroup.instSetLike",
"AddSubsemigroup.centerCongr._proof_2",
"Membership.mem",
"AddSubsemigroup.centerCongr._proof_1",
"Equiv.mk",
"Subtype",
"AddSubsemigroup.center",
"Subtype.mk",
"AddEquiv.mk",
"AddSubsemigroup.centerCongr._proof_8",
"AddSubsemigroup",
"AddSubsemigroup.centerCongr... | true |
Joined.refl | Mathlib.Topology.Connected.PathConnected | [
"Nonempty.intro",
"TopologicalSpace",
"Path",
"Path.refl",
"Joined"
] | true |
Complement.mk.noConfusion | Init.Prelude | [
"Complement.mk",
"Complement",
"id",
"heq_of_eq",
"Eq.refl",
"HEq",
"Complement.noConfusion",
"Eq"
] | false |
WeierstrassCurve.Affine.baseChange_negY | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula | [
"Eq.mpr",
"CommRing",
"AlgHom.algHomClass",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"RingHom.coe_coe",
"AlgHom.funLike",
"WeierstrassCurve.Affine.map",
"Algebra",
"RingHom",
"Algebra.toSMul",
"id",
"WeierstrassCurve.Affine.map_baseChange",
"WeierstrassCurve.Af... | true |
IsometryEquiv.coe_mk | Mathlib.Topology.MetricSpace.Isometry | [
"Equiv.instEquivLike",
"IsometryEquiv.instEquivLike",
"Equiv",
"Equiv.toFun",
"PseudoEMetricSpace",
"IsometryEquiv.mk",
"Eq",
"DFunLike.coe",
"IsometryEquiv",
"rfl",
"Isometry",
"EquivLike.toFunLike"
] | true |
Matroid.map.congr_simp | Mathlib.Combinatorics.Matroid.Map | [
"Matroid.E",
"Eq.rec",
"Eq.ndrec",
"Eq.refl",
"Set.InjOn",
"Eq",
"Matroid",
"Matroid.map"
] | true |
NormedCommGroup.toMetricSpace | Mathlib.Analysis.Normed.Group.Defs | [
"NormedCommGroup",
"MetricSpace"
] | true |
Std.StreamMap._sizeOf_inst | Std.Sync.StreamMap | [
"Std.StreamMap._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Std.StreamMap"
] | false |
Order.Cofinal.mk.sizeOf_spec | Mathlib.Order.Ideal | [
"Order.Cofinal",
"Order.Cofinal._sizeOf_inst",
"Preorder.toLE",
"instOfNatNat",
"Order.Cofinal.mk",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"SizeOf",
"IsCofinal",
"OfNat.ofNat",
"Eq",
"Preorder",
"Set"
] | true |
CategoryTheory.Abelian.SpectralObject.shortComplex_g | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.shortComplex._auto_1",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Abelian",
"CategoryTh... | true |
Lean.Grind.CommRing.denoteTerm | Init.Grind.Ring.CommSolver | [
"cond",
"instHSMul",
"Lean.Grind.IntModule.zsmul",
"Int.instDecidableEq",
"Int",
"instBEqOfDecidableEq",
"BEq.beq",
"instOfNat",
"Lean.Grind.Ring",
"Lean.Grind.CommRing.Context",
"HSMul.hSMul",
"Lean.Grind.Ring.toSemiring",
"Lean.Grind.Ring.toIntModule",
"OfNat.ofNat",
"Lean.Grind.CommRi... | true |
le_of_isGLB_Ioi | Mathlib.Order.Bounds.Basic | [
"Iff.mpr",
"Set.Ioi",
"lowerBounds",
"le_of_lt",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"IsGLB",
"le_isGLB_iff",
"Set.instMembership",
"Preorder",
"Set"
] | true |
Mathlib.Tactic.Module.NF.eval_neg | Mathlib.Tactic.Module | [
"Eq.mpr",
"NegZeroClass.toNeg",
"neg_smul",
"instHSMul",
"Mathlib.Tactic.Module.NF",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"List.map",
"AddMonoid.toAddZeroClass",
"List.sum",
"Mathlib.Tactic.Module.NF.eval.match_1",
"AddCommGroup.toAddGroup",
"Functi... | true |
CategoryTheory.coherentTopology.exists_effectiveEpiFamily_iff_mem_induced | Mathlib.CategoryTheory.Sites.Coherent.SheafComparison | [
"Iff.mpr",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor.preimage",
"CategoryTheory.Functor",
"CategoryTheory.Functor.EffectivelyEnough.presentation",
"CategoryTheory.Functor.EffectivePresentation",
"CategoryTheory.Functor.finite_effectiveEpiFamily_of_map",
"CategoryTheory.Categ... | true |
Ideal.Quotient.stabilizerHom_surjective_of_profinite | Mathlib.RingTheory.Invariant.Profinite | [
"Subalgebra.instSetLike",
"MulSemiringAction.toRingAut",
"Monoid",
"Ideal.Quotient.commSemiring",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"CategoryTheory.isCofilteredOrEmpty_of_directed_ge",
"Submodule.instAddCommMonoidWithOne",
"Ideal.Quotient.algebraOfLie... | true |
MulChar.eq_one_iff | Mathlib.NumberTheory.MulChar.Basic | [
"Units.val",
"MulOne.toOne",
"_private.Mathlib.NumberTheory.MulChar.Basic.0.MulChar.eq_one_iff._simp_1_1",
"MulChar.one_apply_coe",
"MulChar.hasOne",
"congrArg",
"Units",
"MulChar",
"MulChar.instFunLike",
"CommMonoidWithZero.toMonoidWithZero",
"MulZeroOneClass.toMulOneClass",
"iff_self",
"Mu... | true |
Polynomial.coeToPowerSeries.algHom_apply | Mathlib.RingTheory.PowerSeries.Basic | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Algebra",
"RingHom",
"Algebra.id",
"MvPowerSeries.instAlgebra",
"Polynomial",
"CommSemiring",
"MvPowerSeries.instSemiring",
"PowerSeries.map",
"Unit",
"RingHom.instFunLike",
"Po... | true |
_private.Mathlib.Condensed.Light.TopCatAdjunction.0.LightCondSet.coinducingCoprod | Mathlib.Condensed.Light.TopCatAdjunction | [
"LightCondensed._proof_1",
"CategoryTheory.Functor",
"instCountablePUnit",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ConcreteCategory.hom",
"instMetricSpacePUnit",
"Quiver.Hom.op",
"SecondCountableTopology",
"instIndiscreteTopologyPUnit",
"CompHausLike.const",
"EMet... | true |
OnePoint.IsBoundedAt.add | Mathlib.NumberTheory.ModularForms.BoundedAtCusp | [
"Filter.BoundedAtFilter.add",
"OnePoint.instGLAction",
"Eq.mpr",
"OnePoint.IsBoundedAt",
"NormedCommRing.toSeminormedCommRing",
"UpperHalfPlane.IsBoundedAtImInfty",
"Real",
"instHSMul",
"OnePoint.infty",
"AddMonoid.toAddSemigroup",
"congrArg",
"Matrix",
"instDecidableEqFin",
"Complex.instN... | true |
AlgebraicClosure.instSMulOfIsScalarTower | Mathlib.FieldTheory.IsAlgClosed.AlgebraicClosure | [
"instSMulOfMul",
"IsScalarTower",
"SMul",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Field.toDivisionRing",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AlgebraicClosure.instSMulOfIsScalarTower._aux_1",
"DivisionRing.toRing",
"SMul.mk",
"Field.toSemifield",... | true |
instDecidableEqExcept_batteries.decEq._proof_4 | Batteries.Lean.Except | [
"False",
"Except.ok",
"False.elim",
"noConfusion_of_Nat",
"Except.error",
"Except.ctorIdx",
"Except",
"Eq",
"Not"
] | false |
exists_neg_mem_iff_exists_mem | Mathlib.Algebra.Group.Subgroup.Defs | [
"SetLike",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"congrArg",
"Membership.mem",
"Exists",
"neg_neg",
"SubtractionMonoid.toSubNegZeroMonoid",
"AddSubgroupClass.toNegMemClass",
"SubNegZeroMonoid.toNegZeroClass",
"And.casesOn",
"And",
"AddGr... | true |
_private.Mathlib.RingTheory.Ideal.Maximal.0.Ideal.exists_maximal.match_1_1 | Mathlib.RingTheory.Ideal.Maximal | [
"Semiring.toModule",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"Submodule.instPartialOrder",
"Bot.bot",
"LE.le",
"Ideal",
"And.casesOn",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Submodule.instBot",
"And",
"Exists.casesOn",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
... | false |
CategoryTheory.ComposableArrows.scMapIso._proof_1 | Mathlib.Algebra.Homology.ExactSequence | [
"CategoryTheory.ShortComplex.hom_ext",
"CategoryTheory.ComposableArrows.sc'._proof_7",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ComposableArrows.scMap",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.Hom.τ₁",
"CategoryTheory.Composab... | false |
CategoryTheory.GradedObject.TriangleIndexData.h₃ | Mathlib.CategoryTheory.GradedObject.Unitor | [
"CategoryTheory.GradedObject.TriangleIndexData.p₂₃",
"Prod.mk",
"CategoryTheory.GradedObject.TriangleIndexData",
"Zero.toOfNat0",
"Prod",
"OfNat.ofNat",
"Eq",
"Zero"
] | true |
Function.Injective.divInvMonoid._proof_2 | Mathlib.Algebra.Group.InjSurj | [
"Eq.mpr",
"Function.Injective.monoid",
"MulOne.toOne",
"One",
"HMul.hMul",
"Monoid.toMulOneClass",
"Pow",
"congrArg",
"zpow_zero",
"DivInvMonoid.toZPow",
"Mul",
"id",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Int",
"DivInvMonoid",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPo... | false |
_private.Mathlib.MeasureTheory.VectorMeasure.BoundedVariation.0.BoundedVariationOn.measureAux.congr_simp | Mathlib.MeasureTheory.VectorMeasure.BoundedVariation | [
"OrderTopology",
"MeasureTheory.Measure",
"Preorder.toLT",
"CompleteSpace",
"NormedAddCommGroup.toMetricSpace",
"SecondCountableTopology",
"LinearOrder",
"Set.univ",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"SemilatticeInf.toPartialOrder",
"BorelSpace",
"Eq.rec",
"Dis... | true |
_private.Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization.0.HomogeneousLocalization.map._simp_2 | Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization | [
"Localization.mk",
"Localization.mk_eq_mk'",
"OreLocalization.instAlgebra",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Membership.mem",
"Algebra.id",
"Subtype",
"Localization",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"IsLocalization.mk'",
... | false |
OmegaCompletePartialOrder.ContinuousHom.ext_iff | Mathlib.Order.OmegaCompletePartialOrder | [
"OmegaCompletePartialOrder.ContinuousHom.ext",
"HEq.refl",
"Eq.casesOn",
"OmegaCompletePartialOrder.ContinuousHom",
"OmegaCompletePartialOrder",
"Iff",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"OmegaCompletePartialOrder.instFunLikeContinuousHom",
"Eq.symm",
"Eq",
"DFunLike.coe"
] | true |
SimplexCategory.Truncated.initial_incl._proof_2 | Mathlib.AlgebraicTopology.SimplexCategory.Truncated | [
"LE.le",
"instLENat",
"_private.Mathlib.AlgebraicTopology.SimplexCategory.Truncated.0.SimplexCategory.Truncated.initial_incl._proof_1",
"Nat"
] | false |
_private.Mathlib.MeasureTheory.PiSystem.0.piiUnionInter_singleton._simp_1_8 | Mathlib.MeasureTheory.PiSystem | [
"False",
"Membership.mem",
"propext",
"Set.instEmptyCollection",
"Set.mem_empty_iff_false",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instMembership",
"Set"
] | false |
Std.Time.Minute.instReprOffset._aux_1 | Std.Time.Time.Unit.Minute | [
"Rat.instOfNat",
"Rat",
"Std.Time.Internal.UnitVal",
"Int",
"Std.Time.Minute.Offset",
"Nat",
"Std.Format",
"Std.Time.Internal.UnitVal.val",
"OfNat.ofNat",
"Repr.reprPrec",
"Int.instRepr"
] | false |
EMetric.infEdist_singleton | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Set.instSingletonSet",
"Metric.infEDist",
"PseudoEMetricSpace",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"Metric.infEDist_singleton",
"ENNReal",
"EDist.edist",
"Singleton.singleton",
"UniformSpace.toTopologicalSpace",
... | true |
FP.Float.div.match_1 | Mathlib.Data.FP.Basic | [
"FP.Float.ctorIdx",
"FP.Float.nan",
"Nat.hasNotBit",
"Int",
"FP.FloatCfg",
"FP.Float",
"FP.Float.inf",
"Nat",
"FP.Float.casesOn",
"FP.Float.add._sparseCasesOn_1",
"FP.ValidFinite",
"Bool",
"FP.Float.finite"
] | false |
MeasureTheory.Lp.norm_const | Mathlib.MeasureTheory.Function.LpSpace.Indicator | [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"Real.instPow",
"Real",
"MeasureTheory.Measure",
"instHDiv",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.instPowReal",
"SeminormedAddGroup.toNNNorm",
"Real.instDivInvMonoid",
"Set.univ",
"AddMonoid.toAddZeroClass",
"M... | true |
CategoryTheory.FreeBicategory.Hom₂.ctorElimType | Mathlib.CategoryTheory.Bicategory.Free | [
"cond",
"CategoryTheory.FreeBicategory.Hom.comp",
"CategoryTheory.FreeBicategory.Hom₂.vcomp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Nat.ble",
"CategoryTheory.FreeBicategory.categoryStruct",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.FreeBicategory.Hom₂.right_unitor_inv",
... | false |
WithZero.coe_ne_zero._simp_1 | Mathlib.Algebra.Group.WithOne.Defs | [
"WithZero.coe_ne_zero",
"False",
"eq_false",
"WithZero.instZero",
"WithZero",
"WithZero.coe",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
GradedAlgHom.ctorIdx | Mathlib.RingTheory.GradedAlgebra.AlgHom | [
"Submodule",
"CommSemiring.toSemiring",
"GradedAlgHom",
"Algebra",
"Algebra.toModule",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"GradedAlgebra",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"AddMonoid",
"Semiring",
"Semiring.toNonAssocSemiring",
"DecidableEq"
... | false |
not_isUnit_prime_of_dvd_card | Mathlib.Algebra.CharP.CharAndCard | [
"Iff.mpr",
"CommRing",
"Nat.Prime",
"Dvd.dvd",
"Classical.not_not",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"IsUnit",
"prime_dvd_char_iff_dvd_card",
"mt",
"Fact",
"Fintype.card",
"AddMonoidWithOne.toNatCast",
"Finite.of_fintype",
"Nat.cast",
"isUnit_iff_not_dvd... | true |
Stream'.Seq.cons.eq_1 | Mathlib.Data.Seq.Basic | [
"Stream'.Seq",
"Option.some",
"Subtype.mk",
"Stream'",
"Stream'.IsSeq",
"Stream'.Seq.cons",
"Stream'.Seq.cons._proof_1",
"Eq.refl",
"Stream'.cons",
"Subtype.val",
"Eq",
"Option"
] | true |
Equiv.continuousLinearEquiv | Mathlib.Topology.Algebra.Module.TransferInstance | [
"ContinuousLinearEquiv.mk",
"Equiv.linearEquiv",
"Equiv",
"AddCommMonoid",
"TopologicalSpace",
"ContinuousLinearEquiv",
"RingHomInvPair.ids",
"LinearEquiv",
"Equiv.continuousLinearEquiv._proof_1",
"Semiring",
"Equiv.addCommMonoid",
"Equiv.module",
"Equiv.continuousLinearEquiv._proof_2",
"M... | true |
List.reduceOption_eq_append_iff | Mathlib.Data.List.ReduceOption | [
"List.filterMap_eq_append_iff",
"Exists",
"id",
"instHAppendOfAppend",
"List",
"And",
"Iff",
"List.reduceOption",
"List.instAppend",
"Eq",
"HAppend.hAppend",
"Option"
] | true |
CategoryTheory.Limits.inr_pushoutRightPushoutInlIso_inv | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | [
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.hasPushoutVertPaste",
"Quiver.Hom",
"CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_inv",
"CategoryTheory.Limits.pushoutRightPushoutInlIso",
"CategoryTheory.Limits.pushoutRightPushoutInlI... | true |
CategoryTheory.Limits.isLimitOfCoconeUnopOfCone | Mathlib.CategoryTheory.Limits.Opposites | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"Opposite",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Limits.isLimitConeOfCoconeUnop",
"CategoryTheory.Functor.unop",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Limits.coconeUnopOfCone",
"CategoryTheory.Category.opposite",
"Cat... | true |
_private.Batteries.Tactic.SqueezeScope.0.Batteries.Tactic._aux_Batteries_Tactic_SqueezeScope___elabRules__private_Batteries_Tactic_SqueezeScope_0_Batteries_Tactic_squeezeWrap_1.match_11 | Batteries.Tactic.SqueezeScope | [
"_private.Batteries.Tactic.SqueezeScope.0.Batteries.Tactic._aux_Batteries_Tactic_SqueezeScope___elabRules__private_Batteries_Tactic_SqueezeScope_0_Batteries_Tactic_squeezeScopeIn_1._sparseCasesOn_5",
"Option.ctorIdx",
"Option.some",
"Lean.Syntax.TSepArray",
"Nat.hasNotBit",
"List.cons",
"Lean.SyntaxNode... | false |
iteratedFDerivWithin._proof_2 | Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | [
"AddMonoid.toAddSemigroup",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"IsTopologicalAddGroup.toContinuousAdd",
"AddSemigroup.toAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"NormedAddCommGroup.toAddCommGroup",
"SubNegMonoid.toAddMonoid",
"Conti... | false |
MeasureTheory.charFunDual_prod' | Mathlib.MeasureTheory.Measure.CharacteristicFunction.Basic | [
"ContinuousLinearMap.comp",
"instInnerProductSpaceRealComplex",
"WithLp",
"MeasurableEquiv.instEquivLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"ContinuousLinearEquiv.symm",
"Real",
"MeasureTheory.Measure",
"WithLp.instProdNormedAddCommGroup",
"Semiring.toModule",
"HMul.hMul",
"Conti... | true |
Lean.Parser.ParserState.errorMsg | Lean.Parser.Types | [
"Lean.Parser.Error",
"Lean.Parser.ParserState",
"Option"
] | true |
AddUnits.neg_eq_of_add_eq_zero_right | Mathlib.Algebra.Group.Units.Basic | [
"Eq.mpr",
"AddUnits.val",
"Trans.trans",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"id",
"instTransEq",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"AddMonoid",
"AddZero.toAdd",
"Zero.toOfNat0",
"Eq.refl",
"AddUnits.instNeg",
"AddUnits.neg_add_cancel_left",
"... | true |
Module.Baer.extensionOfMaxAdjoin | Mathlib.Algebra.Module.Injective | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Module.Baer.extensionOfMaxAdjoin._proof_3",
"LinearMap.instFunLike",
"Membership.mem",
"Fact",
"AddCommGroup",
"Module.Baer.ExtensionOfMaxAdjoin.extensionToFun",
"Subtype",
"Module.Baer.extensionOfMaxAdjoin._proof_2",
"Mo... | true |
MeasureTheory.integrable_finset_sum_measure | Mathlib.MeasureTheory.Function.L1Space.Integrable | [
"TopologicalSpace.PseudoMetrizableSpace",
"MeasureTheory.Measure",
"MeasureTheory.integrable_finsetSum_measure",
"Finset",
"MeasureTheory.Integrable",
"Membership.mem",
"ContinuousENorm",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.Measure.instAddCommMonoid",
"Iff",
"Finset.instSetLi... | true |
ContinuousLinearEquiv.continuousMultilinearMapCongrRight._proof_3 | Mathlib.Topology.Algebra.Module.Multilinear.Topology | [
"NormedCommRing.toNormedRing",
"Continuous",
"NormedRing.toRing",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"ContinuousMultilinearMap.instAddCommGroup",
"AddMonoid.toAddZeroClass",
"ContinuousMultilinear... | false |
ADEInequality.lt_six | Mathlib.NumberTheory.ADEInequality | [
"PNat.val",
"Rat.instOfNat",
"Eq.mpr",
"ADEInequality.sumInv_pqr",
"Trans.trans",
"Preorder.toLT",
"Mathlib.Meta.NormNum.IsNat.to_isNNRat",
"le_rfl",
"instLinearOrderPNat",
"Mathlib.Meta.NormNum.isNat_eq_true",
"MulZeroClass.toMul",
"IsStrictOrderedRing.toMulPosStrictMono",
"Nat.ble",
"con... | true |
_private.Mathlib.Topology.Semicontinuity.Basic.0.upperSemicontinuous_iff_isClosed_preimage._simp_1_1 | Mathlib.Topology.Semicontinuity.Basic | [
"Compl.compl",
"Set.instCompl",
"IsClosed",
"TopologicalSpace",
"propext",
"IsOpen",
"Eq.symm",
"Eq",
"isOpen_compl_iff",
"Set"
] | false |
Lean.JsonRpc.ErrorCode.ctorElimType | Lean.Data.JsonRpc | [
"cond",
"Lean.JsonRpc.ErrorCode.serverNotInitialized",
"Lean.JsonRpc.ErrorCode",
"Nat.ble",
"Lean.JsonRpc.ErrorCode.invalidRequest",
"Lean.JsonRpc.ErrorCode.invalidParams",
"Lean.JsonRpc.ErrorCode.parseError",
"PULift",
"Lean.JsonRpc.ErrorCode.workerExited",
"Lean.JsonRpc.ErrorCode.unknownErrorCod... | false |
Lean.Doc.Data.SyntaxCat.mk.noConfusion | Lean.Elab.DocString.Builtin | [
"Lean.Doc.Data.SyntaxCat.mk",
"id",
"Lean.Doc.Data.SyntaxCat.noConfusion",
"Lean.Name",
"Eq",
"Lean.Doc.Data.SyntaxCat"
] | false |
_private.Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate.0.RootPairing.ker_rootForm_eq_dualAnnihilator._proof_1_2 | Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate | [
"Semiring.toModule",
"CommSemiring.toSemiring",
"Field.toCommRing",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"Module.toDistribMulAction",
"Semi... | false |
Lean.Elab.Term.Do.ToTerm.Context.mk.noConfusion | Lean.Elab.Do.Legacy | [
"Lean.Elab.Term.Do.ToTerm.Context.noConfusion",
"Lean.Syntax",
"id",
"Lean.Elab.Term.Do.Var",
"Lean.Elab.Term.Do.ToTerm.Context.mk",
"Array",
"Lean.Elab.Term.Do.ToTerm.Context",
"Lean.Elab.Term.Do.ToTerm.Kind",
"Eq"
] | false |
_private.Lean.Meta.Tactic.Rfl.0.Lean.MVarId.applyRfl.match_1 | Lean.Meta.Tactic.Rfl | [
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
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