name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Init.Data.Iterators.Lemmas.Consumers.Loop.0.Std.Iter.forIn'_toList.aux | Init.Data.Iterators.Lemmas.Consumers.Loop | [
"HEq.refl",
"Membership.mem",
"Eq.rec",
"inferInstance",
"Eq.casesOn",
"ForIn'.forIn'",
"Membership",
"ForInStep",
"ForIn'",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Monad",
"Eq"
] | true |
CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit._proof_10 | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | [
"CategoryTheory.Over.map",
"CategoryTheory.Over",
"CategoryTheory.Over.OverMorphism.ext",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryToUnit._proof_8",
"CategoryTheory.Functor.mk",
"CategoryTheory.CartesianMonoidal... | false |
LinearEquiv.domMulActCongrRight._proof_4 | Mathlib.Algebra.Module.Equiv.Basic | [
"DomMulAct",
"instHSMul",
"Equiv.instEquivLike",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"RingHomCompTriple",
"Equiv",
"DistribSMul.toSMulZeroClass",
"LinearMap.instAdd",
"Equiv.toFun",
"DomMulAct.mk",
"LinearMap",
"AddCommMonoid... | false |
TopologicalSpace.IrreducibleCloseds.orderIsoOfIsOpenEmbedding._proof_5 | Mathlib.Topology.Sets.Closeds | [
"nonempty_preimage_closure_image",
"IsPreirreducible",
"Equiv.instEquivLike",
"SetLike.coe_subset_coe._simp_1",
"congrArg",
"PartialOrder.toPreorder",
"setOf",
"Topology.IsOpenEmbedding.isEmbedding",
"Preorder.toLE",
"IsClosed.closure_eq",
"Membership.mem",
"TopologicalSpace.IrreducibleCloseds... | false |
_private.Init.Data.Nat.Fold.0.Nat.dfold.loop._proof_3 | Init.Data.Nat.Fold | [
"_private.Init.Data.Nat.Fold.0.Nat.dfold._proof_1",
"HSub.hSub",
"instSubNat",
"LE.le",
"instLENat",
"instHSub",
"Nat",
"Decidable.byContradiction",
"Nat.succ",
"Not",
"Nat.decLe"
] | false |
RatFunc.valuedRatFunc._proof_1 | Mathlib.FieldTheory.RatFunc.AsPolynomial | [
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"IsOrderedMonoid",
"Int.instLinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Multiplicative.commMonoid",
"Int",
"Multiplicative",
"Multiplicative.isOrderedMonoid",
"Multiplicative.preor... | false |
Poly.instAddCommGroup._proof_6 | Mathlib.NumberTheory.Dioph | [
"Poly.instAdd",
"Poly",
"Add.mk",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"nsmulRec",
"Nat",
"Zero.mk",
"instAddNat",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Poly.instZero"
] | false |
Aesop.UnfoldRule.instHashable | Aesop.Rule | [
"Aesop.UnfoldRule",
"Hashable.mk",
"Hashable.hash",
"Lean.Name",
"Hashable",
"Aesop.UnfoldRule.decl",
"Lean.instHashableName"
] | true |
MeasureTheory.integral_pos_iff_support_of_nonneg | Mathlib.MeasureTheory.Integral.Bochner.Basic | [
"MeasureTheory.ae",
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"Real.instZero",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"MeasureTheory.Integrable",
"SeminormedAddGroup.toContinuousENorm",
"Meas... | true |
_private.Mathlib.Algebra.QuadraticAlgebra.Basic.0.QuadraticAlgebra.instField._simp_9 | Mathlib.Algebra.QuadraticAlgebra.Basic | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
CategoryTheory.Oplax.OplaxTrans.Modification.id._proof_2 | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Category.comp_id",
"CategoryTheory.PrelaxFunc... | false |
Fin.preimage_castLE_uIoc_castLE | Mathlib.Order.Interval.Set.Fin | [
"Fin.castLE",
"Set.uIoc",
"LE.le",
"instLENat",
"Fin.instLinearOrder",
"Set.preimage",
"Nat",
"Fin",
"Eq",
"rfl",
"Set"
] | true |
MulEquiv.map_finprod_mem | Mathlib.Algebra.BigOperators.Finprod | [
"MulEquiv.instEquivLike",
"Monoid.toMulOneClass",
"Set.Finite",
"Membership.mem",
"MonoidHom.map_finprod_mem",
"MulOne.toMul",
"MulEquiv.toMonoidHom",
"MulOneClass.toMulOne",
"finprod",
"CommMonoid.toMonoid",
"MulEquiv",
"Eq",
"CommMonoid",
"Set.instMembership",
"DFunLike.coe",
"EquivL... | true |
_private.Mathlib.NumberTheory.FLT.Polynomial.0.fermatLastTheoremWith'_polynomial._simp_1_3 | Mathlib.NumberTheory.FLT.Polynomial | [
"UniqueFactorizationMonoid.normalizedFactors",
"Dvd.dvd",
"NormalizationMonoid",
"PartialOrder.toPreorder",
"semigroupDvd",
"Preorder.toLE",
"SemigroupWithZero.toSemigroup",
"Multiset",
"UniqueFactorizationMonoid",
"Ne",
"CommMonoidWithZero.toMonoidWithZero",
"LE.le",
"MonoidWithZero.toSemig... | false |
AlgebraicGeometry.ValuativeCriterion | Mathlib.AlgebraicGeometry.ValuativeCriterion | [
"AlgebraicGeometry.ValuativeCommSq.algebra",
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.ValuativeCommSq",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.ValuativeCommSq.field",
"Algebra.algebraMap",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Uniqu... | true |
Lean.AsyncConstantInfo.mk | Lean.Environment | [
"Task",
"Lean.ConstantVal",
"Lean.AsyncConstantInfo.mk",
"Lean.ConstantKind",
"Lean.Name",
"Lean.ConstantInfo",
"Lean.AsyncConstantInfo"
] | true |
SeminormedGroup.mem_closure_iff | Mathlib.Analysis.Normed.Group.Continuity | [
"Norm.norm",
"Real",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Real.instZero",
"Monoid.toMulOneClass",
"congrArg",
"SeminormedGroup",
"SeminormedGroup.toGroup",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"SeminormedGroup.toPseudoMetricSpace",
"Group.toDivisionMonoid",
"dist_eq... | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.Horn.0.SSet.horn.edge._simp_10 | Mathlib.AlgebraicTopology.SimplicialSet.Horn | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
_private.Mathlib.RingTheory.WittVector.DiscreteValuationRing.0.WittVector.inverseCoeff.match_1._arg_pusher | Mathlib.RingTheory.WittVector.DiscreteValuationRing | [
"Unit.unit",
"WittVector.inverseCoeff.match_1",
"_private.Mathlib.RingTheory.WittVector.DiscreteValuationRing.0.WittVector.inverseCoeff.match_1.splitter",
"id",
"instOfNatNat",
"Unit",
"Nat",
"Eq.ndrec",
"Eq.refl",
"OfNat.ofNat",
"Eq.symm",
"Nat.succ",
"Eq"
] | false |
SeminormedAddCommGroup.mk.noConfusion | Mathlib.Analysis.Normed.Group.Defs | [
"Norm.norm",
"Real",
"SeminormedAddCommGroup",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Norm",
"id",
"autoParam",
"SeminormedAddCommGroup.noConfusion",
"instHAdd",
"AddSemigroup.toAdd",
"PseudoMetricSpace",
"heq_of_eq",
"AddGroup.toSubNegMonoid",
"HAdd.hA... | false |
AlgCat.instBraidedModuleCatForget₂AlgHomCarrierLinearMapIdCarrier._proof_1 | Mathlib.Algebra.Category.AlgCat.Symmetric | [
"CommRing",
"CategoryTheory.Monoidal.InducingFunctorData.mk",
"AlgCat.instMonoidalCategory._proof_3",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"AlgCat.instCategory",
"AddCommGroup.toAddCommMonoid",
"AlgHom",
"AlgCat.instConcreteCategoryAlgHomCarrier",
"AlgHom.funLike"... | false |
List.IsZeckendorfRep.sum_fib_lt | Mathlib.Data.Nat.Fib.Zeckendorf | [
"List.head?",
"List.brecOn",
"List.IsZeckendorfRep.sum_fib_lt._f",
"Nat.instMulZeroClass",
"Option.instMembership",
"List.map",
"List.sum",
"List.IsZeckendorfRep",
"Membership.mem",
"instOfNatNat",
"List.cons",
"instHAppendOfAppend",
"List",
"Nat.fib",
"Nat",
"LT.lt",
"instAddNat",
... | true |
supsSupHom_apply | Mathlib.Order.Hom.CompleteLattice | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"SemilatticeSup.toMax",
"supsSupHom",
"sSupHom.instFunLike",
"Prod.fst",
"Max.max",
"sSupHom",
"CompleteSemilatticeSup.toSupSet",
"CompleteLattice.toCompleteSemilatticeSup",
"Prod.supSet",
"Prod",
"CompleteLattice",
"Eq",
"Prod.snd... | true |
_private.Mathlib.Algebra.Order.Antidiag.Pi.0.Finset.map_sym_eq_piAntidiag._simp_1_1 | Mathlib.Algebra.Order.Antidiag.Pi | [
"Finset.mem_sym_iff",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"Nat",
"Sym",
"propext",
"Sym.instMembership",
"Finset.sym",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
HasStrictDerivAt.sinh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"RCLike.toNormedAlgebra",
"HMul.hMul",
"Real.hasStrictDerivAt_sinh",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.denselyNormedField",
"Real.instRCLike",
"IsTopologicalSemir... | true |
SemilatticeSup.mk'._proof_1 | Mathlib.Order.Lattice | [
"Eq.mpr",
"congrArg",
"Max",
"id",
"Max.max",
"Eq.refl",
"Eq.symm",
"Eq"
] | false |
Nat.sqrt.iter_sq_le | Mathlib.Data.Nat.Sqrt | [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"congrArg",
"InvImage",
"Decidable",
"WellFounded.Nat.fix",
"dif_pos",
"id",
"HDiv.hDiv",
"Nat.sqrt.iter.eq_def",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"dite",
"instHAdd",
"Nat.sqrt.iter",
"_private.Mathlib.Data.Nat.Sqrt.0.Nat.sqrt... | true |
Sublocale.mk_le_mk._simp_1 | Mathlib.Order.Sublocale | [
"Sublocale.instPartialOrder",
"Sublocale.mk",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"GeneralizedHeytingAlgebra.toHImp",
"HasSubset.Subset",
"LE.le",
"Order.Frame.toCompleteLattice",
"HeytingAlgebra.toGeneralizedHeytingAlge... | false |
USize.xor_assoc | Init.Data.UInt.Bitwise | [
"BitVec",
"USize.toBitVec_inj",
"System.Platform.numBits",
"USize.toBitVec",
"HXor.hXor",
"Iff.mp",
"BitVec.xor_assoc",
"Eq",
"instHXorOfXorOp",
"instXorOpUSize",
"USize"
] | true |
Aesop.GoalKind.preNorm | Aesop.Stats.Basic | [
"Aesop.GoalKind.preNorm",
"Aesop.GoalKind"
] | true |
InitialSeg.mk.noConfusion | Mathlib.Order.InitialSeg | [
"HEq.refl",
"Membership.mem",
"id",
"RelEmbedding",
"heq_of_eq",
"InitialSeg.noConfusion",
"InitialSeg",
"Eq.refl",
"HEq",
"InitialSeg.mk",
"Set.range",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"RelEmbedding.instFunLike",
"Set"
] | false |
_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic.0.IsProperLinearSet.floor_add_nsmul_self | Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | [
"Rat.addCommMonoid",
"Finsupp.instFunLike",
"Rat.instSub",
"Eq.mpr",
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"AddMonoidHom.instAddMonoidHomClass",
"Semiring.toModule",
"Pi.addCommMonoid",
"Finsupp.single_eq_same",
"Finsupp.module",
"Pi.addGroup",
"map_... | true |
_private.Std.Time.Notation.0.Std.Time.convertPlainTime | Std.Time.Notation | [
"Std.Time.PlainTime",
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"String",
"Lean.SourceInfo",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"ReaderT.instMonad",
"Lean.TSyntax.raw",
"Lean.Macro.instMonadQuotationMacroM",
"instDecida... | true |
Prod.instIsOrderBornology | Mathlib.Topology.Order.Bornology | [
"Eq.mpr",
"Prod.instLE_mathlib",
"congrArg",
"Iff.rfl",
"bddAbove_prod",
"Preorder.toLE",
"id",
"bddBelow_prod",
"Bornology.IsBounded",
"IsOrderBornology.mk",
"Prod.fst",
"BddAbove",
"Bornology.isBounded_image_fst_and_snd",
"And",
"Iff",
"and_and_and_comm",
"Prod.instBornology",
"B... | true |
IsCompact.exists_mapClusterPt_of_frequently | Mathlib.Topology.Compactness.Compact | [
"Filter.map",
"Membership.mem",
"Exists",
"Filter.Frequently",
"TopologicalSpace",
"And",
"MapClusterPt",
"IsCompact.exists_clusterPt_of_frequently",
"Set.instMembership",
"Filter",
"IsCompact",
"Set"
] | true |
Lean.Meta.Sym.Internal.AlphaShareBuilderM | Lean.Meta.Sym.AlphaShareBuilder | [
"ReaderT",
"Bool",
"Lean.Meta.Sym.AlphaShareCommonM"
] | true |
_private.Mathlib.Geometry.Manifold.VectorField.LieBracket.0.Filter.EventuallyEq.mlieBracketWithin_vectorField_eq._proof_1_12 | Mathlib.Geometry.Manifold.VectorField.LieBracket | [
"Real.instLE",
"Real",
"extChartAt",
"chartedSpaceSelf",
"NormedSpace",
"NormedAddCommGroup.toMetricSpace",
"PseudoMetricSpace.toUniformSpace",
"PseudoMetricSpace.dist_triangle",
"LE.le",
"_private.Mathlib.Geometry.Manifold.VectorField.LieBracket.0.Filter.EventuallyEq.mlieBracketWithin_vectorField... | false |
CategoryTheory.Functor.leftDerivedZeroIsoSelf_inv_hom_id_app_assoc | Mathlib.CategoryTheory.Abelian.LeftDerived | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Functor.leftDerivedZeroIsoSelf",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryThe... | true |
Commute.symm | Mathlib.Algebra.Group.Commute.Defs | [
"HMul.hMul",
"Mul",
"Commute",
"Eq.symm",
"instHMul"
] | true |
_private.Mathlib.LinearAlgebra.Matrix.Circulant.0.Matrix.Fin.transpose_circulant.match_1_1 | Mathlib.LinearAlgebra.Matrix.Circulant | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
_private.Mathlib.Algebra.Homology.LocalCohomology.0.localCohomology.idealPowersToSelfLERadical._simp_1 | Mathlib.Algebra.Homology.LocalCohomology | [
"LE.le",
"OrderTop",
"LE",
"OrderTop.toTop",
"le_top",
"True",
"eq_true",
"Top.top",
"Eq"
] | false |
star_nnratCast | Mathlib.Algebra.Star.Rat | [
"RingEquiv.instEquivLike",
"MulOpposite",
"RingEquiv.instRingEquivClass",
"MulOpposite.unop_nnratCast",
"map_nnratCast",
"Distrib.toAdd",
"NNRat",
"StarAddMonoid.toInvolutiveStar",
"DivisionSemiring.toNNRatCast",
"congr_arg",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAddMono... | true |
CategoryTheory.Enriched.FunctorCategory.functorEnriched_id_comp_assoc | Mathlib.CategoryTheory.Enriched.FunctorCategory | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom",
"CategoryTheory.EnrichedOrdinaryCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.catego... | true |
Lean.Meta.Grind.SymbolPriorityEntry.mk._flat_ctor | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"Lean.Meta.Grind.SymbolPriorityEntry.mk",
"Lean.Meta.Grind.SymbolPriorityEntry",
"Nat",
"Lean.Name"
] | false |
GroupLike.toUnits._proof_1 | Mathlib.RingTheory.HopfAlgebra.GroupLike | [
"Units.val",
"MulOne.toOne",
"HopfAlgebraStruct.toBialgebra",
"Monoid.toMulOneClass",
"Bialgebra.toCoalgebra",
"CommSemiring.toSemiring",
"GroupLike.instMonoid",
"LinearMap.instFunLike",
"Units",
"Algebra.toModule",
"HopfAlgebra",
"Units.ext",
"LinearMap",
"CommSemiring",
"NonUnitalNonAs... | false |
Lean.Grind.CommRing.Expr.below | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Expr",
"Int",
"Lean.Grind.CommRing.Var",
"PProd",
"PUnit",
"Nat",
"Lean.Grind.CommRing.Expr.rec"
] | false |
_private.Init.Data.List.Monadic.0.List.allM.eq_1 | Init.Data.List.Monadic | [
"Pure.pure",
"List.allM",
"Monad.toApplicative",
"Applicative.toPure",
"Bool.true",
"Bool",
"Eq.refl",
"Monad",
"Eq",
"List.nil"
] | true |
_private.Lean.Environment.0.Lean.instReprConstantKind.repr.match_1 | Lean.Environment | [
"Unit.unit",
"Lean.ConstantKind.ctor",
"Lean.ConstantKind.opaque",
"Lean.ConstantKind.quot",
"Lean.ConstantKind.casesOn",
"Lean.ConstantKind.recursor",
"Unit",
"Lean.ConstantKind",
"Lean.ConstantKind.thm",
"Lean.ConstantKind.induct",
"Lean.ConstantKind.axiom",
"Lean.ConstantKind.defn"
] | false |
ProfiniteGrp.ContinuousMulEquiv.toProfiniteGrpIso._proof_1._to_additive_1 | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"ProfiniteAddGrp",
"TotallyDisconnectedSpace",
"CompactSpace",
"TopCat.str",
"CompHausLike.is_compact",
"TopCat.carrier",
"TopCat",
"CompHausLike.toTop",
"ProfiniteAddGrp.toProfinite"
] | false |
_private.Mathlib.Data.Nat.Totient.0.ZMod.card_units_eq_totient._simp_1_2 | Mathlib.Data.Nat.Totient | [
"Finset.univ",
"Fin.sum_univ_eq_sum_range",
"Fin.val",
"AddCommMonoid",
"Fin.fintype",
"Finset.range",
"Nat",
"Eq.symm",
"Fin",
"Eq",
"Finset.sum"
] | false |
NormedAddGroupHom.ext_iff | Mathlib.Analysis.Normed.Group.Hom | [
"NormedAddGroupHom.ext",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"HEq.refl",
"Eq.casesOn",
"NormedAddGroupHom.funLike",
"Iff",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"DFunLike.coe"
] | true |
USize.lt_or_le | Init.Data.UInt.Lemmas | [
"Eq.mpr",
"congrArg",
"instLEUSize",
"_private.Init.Data.UInt.Lemmas.0.USize.lt_or_le._simp_1_1",
"_private.Init.Data.UInt.Lemmas.0.USize.lt_or_le._proof_1_3",
"id",
"LE.le",
"instLENat",
"_private.Init.Data.UInt.Lemmas.0.USize.lt_or_le._simp_1_2",
"USize.toNat",
"Nat",
"congr",
"LT.lt",
"... | true |
CategoryTheory.Pretriangulated.id_hom₃ | Mathlib.CategoryTheory.Triangulated.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pretriangulated.Triangle.obj₃",
"CategoryTheory.CategoryStruct.id",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Triangle",
"CategoryTheory.Pretriangulated.triangleCategory",
"CategoryTheory.Category.toCategoryStr... | true |
CategoryTheory.Monoidal.commMonFunctorCategoryEquivalence_counitIso | Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | [
"CategoryTheory.CommMon.instCategory",
"CategoryTheory.Functor",
"CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso",
"CategoryTheor... | true |
RatFunc.toFractionRingAlgEquiv._proof_1 | Mathlib.FieldTheory.RatFunc.Basic | [
"Eq.mpr",
"IsDomain",
"Polynomial.instOne",
"RingEquiv.toEquiv",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"OreLocalization.instAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"FractionRing",
"Al... | false |
Set.indicator_comp_of_zero | Mathlib.Algebra.Notation.Indicator | [
"Eq.mpr",
"False",
"eq_false",
"congrArg",
"Set.indicator",
"Classical.propDecidable",
"Function.comp",
"Membership.mem",
"Classical.decPred",
"id",
"if_pos",
"dite",
"funext",
"Set.indicator_of_mem",
"True",
"eq_self",
"of_eq_true",
"Zero.toOfNat0",
"congrFun'",
"Set.indicator... | true |
Tactic.ComputeAsymptotics.UnitMonomial.FirstNonzeroIsPos.eq_1 | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates | [
"Tactic.ComputeAsymptotics.UnitMonomial.Sign.pos",
"Tactic.ComputeAsymptotics.UnitMonomial.FirstNonzeroIsPos",
"Tactic.ComputeAsymptotics.UnitMonomial",
"Eq.refl",
"Tactic.ComputeAsymptotics.UnitMonomial.sign",
"Tactic.ComputeAsymptotics.UnitMonomial.Sign",
"Eq"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.size_diff_add_size_inter_eq_size_left._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof.bound.noConfusion | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof.noConfusion",
"Lean.Expr",
"id",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof.bound",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof"
] | false |
_private.Init.Data.UInt.Bitwise.0.UInt16.toUInt32_shiftLeft._simp_1_1 | Init.Data.UInt.Bitwise | [
"instModUInt32",
"instHMod",
"UInt32.toUInt16",
"HMod.hMod",
"UInt16",
"UInt16.toUInt32_eq_mod_65536_iff",
"propext",
"UInt32",
"OfNat.ofNat",
"Eq",
"UInt32.instOfNat",
"UInt16.toUInt32"
] | false |
Submonoid.centralizer_eq_top_iff_subset | Mathlib.GroupTheory.Submonoid.Centralizer | [
"Monoid",
"Submonoid.centralizer",
"Monoid.toMulOneClass",
"Set.centralizer_eq_top_iff_subset",
"HasSubset.Subset",
"Submonoid.instTop",
"Iff",
"SetLike.coe",
"Monoid.toSemigroup",
"SetLike.ext'_iff",
"Iff.trans",
"Submonoid.instSetLike",
"Top.top",
"Eq",
"Submonoid.center",
"Submonoid... | true |
TrivSqZeroExt.nonAssocSemiring._proof_7 | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"add_mul",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"TrivSqZeroExt",
"HMul.hMul",
"TrivSqZeroExt.ext",
"AddMonoid.toAddSemigroup",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"Distrib.rightDistribClass",
"AddZeroClass.toAddZero",
"TrivSqZeroExt... | false |
NumberField.hermiteTheorem.rankOfDiscrBdd | Mathlib.NumberTheory.NumberField.Discriminant.Basic | [
"NumberField.hermiteTheorem.rankOfDiscrBdd._proof_2",
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"instHDiv",
"Real.pi",
"HMul.hMul",
"FloorRing.toFloorSemiring",
"Real.instDivInvMonoid",
"Real.semiring",
"HDiv.hDiv",
"Real.instFloorRing",
"Real.instRing",
"instOfNatNat",
"Nat... | true |
RingSubgroupsBasis.mk | Mathlib.Topology.Algebra.Nonarchimedean.Bases | [
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"Exists",
"RingSubgroupsBasis.mk",
"HasSubset.Subset",
"LE.le",
"instDistribOfSemiring",
"AddSubgroup",
"SetLike.coe",
"Set.preimage",
"Distrib.toMul",
"AddSubgroup.inst... | true |
inTangentCoordinates_eq_mfderiv_comp | Mathlib.Geometry.Manifold.MFDeriv.Tangent | [
"ContinuousLinearMap.comp",
"Eq.mpr",
"mfderiv",
"extChartAt",
"instAddMonoidWithOneENat",
"chartedSpaceSelf",
"inTangentCoordinates",
"NormedSpace",
"chartAt",
"achart",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"PartialEquiv",
"instAddCommGroupTangentSpace",
"CompTriple.instId_comp",... | true |
nilradical_eq_bot_iff | Mathlib.RingTheory.Nilpotent.Lemmas | [
"Eq.mpr",
"Submodule",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"OrderBot.toBot",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"Submodule.instPartialOrder",
"Bot.bot",
"LE.le",
"Ideal",
"_... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Copy.0.SimpleGraph.killCopies_eq_left._simp_1_5 | Mathlib.Combinatorics.SimpleGraph.Copy | [
"Exists",
"not_exists",
"propext",
"Eq",
"Not"
] | false |
CategoryTheory.ULiftHom.objUp | Mathlib.CategoryTheory.Category.ULift | [
"CategoryTheory.ULiftHom"
] | true |
minpoly.ofSubring | Mathlib.FieldTheory.Minpoly.IsIntegrallyClosed | [
"Subalgebra.instSetLike",
"Iff.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Subring.instSetLike",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"Field.toDivisionRing",
"Field.instIs... | true |
Std.Time.Database.TZdb.ctorIdx | Std.Time.Zoned.Database.TZdb | [
"Std.Time.Database.TZdb",
"Nat"
] | false |
essSup_map_measure._auto_7 | Mathlib.MeasureTheory.Function.EssSup | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Lean.Server.Watchdog.0.Lean.Server.Watchdog.handleRequest.match_1 | Lean.Server.Watchdog | [
"Unit.unit",
"Option.ctorIdx",
"Lean.Server.Watchdog.FileWorker",
"Nat.hasNotBit",
"Option.none",
"Unit",
"_private.Lean.Server.Watchdog.0.Lean.Server.Watchdog.handleRequest._sparseCasesOn_1",
"Option"
] | false |
Subgroup.exists_finsupp_of_mem_closure_range | Mathlib.Algebra.Group.Subgroup.Finsupp | [
"Int.instAddCommGroup",
"Finsupp.instFunLike",
"Eq.mpr",
"NegZeroClass.toNeg",
"MulOne.toOne",
"zpow_add",
"InvOneClass.toOne",
"HMul.hMul",
"Subgroup.closure",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Finsupp.prod_add_index",
"Finset.instUnion",
"Monoid.toM... | true |
PreTilt.instCommRing._proof_10 | Mathlib.RingTheory.Perfection | [
"CommRing",
"Perfection.instCommSemiring._proof_10",
"Nat.Prime",
"CommSemiring.toSemiring",
"ModP",
"AddGroupWithOne.toAddMonoidWithOne",
"AddMonoid.nsmul_zero._autoParam",
"IsUnit",
"Fact",
"Set.instSingletonSet",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"Nat.cast",
"autoParam",
"... | false |
PiNat.mem_cylinder_iff._simp_1 | Mathlib.Topology.MetricSpace.PiNat | [
"PiNat.cylinder",
"Membership.mem",
"Nat",
"LT.lt",
"PiNat.mem_cylinder_iff",
"propext",
"instLTNat",
"Eq",
"Set.instMembership",
"Set"
] | false |
PowerBasis.ofAdjoinEqTop | Mathlib.RingTheory.Adjoin.PowerBasis | [
"Subalgebra.instSetLike",
"PowerBasis",
"CommRing",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"Subalgebra.equivOfEq",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"Algebra.adjoin",
"Membership.mem",
... | true |
ZeroAtInftyContinuousMap.instSeminormedAddCommGroup._proof_4 | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"ZeroAtInftyContinuousMap.toBCF",
"SeminormedAddCommGroup",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"ZeroAtInftyContinuousMap.instAddZeroClass",
"ZeroAtInftyContinuousMap.instSeminormedAddCommGroup._proof_2",
"SubtractionMo... | false |
SimpleGraph.isVertexCover_image_iso | Mathlib.Combinatorics.SimpleGraph.VertexCover | [
"SimpleGraph.isVertexCover_preimage_iso._simp_1",
"SimpleGraph.Iso",
"congrArg",
"SimpleGraph.Adj",
"RelIso.symm",
"SimpleGraph",
"iff_self",
"RelIso",
"Iff",
"SimpleGraph.IsVertexCover",
"Set.preimage",
"RelIso.instFunLike",
"True",
"RelIso.image_eq_preimage_symm",
"of_eq_true",
"Set.... | true |
CategoryTheory.Limits.HasFiniteWidePullbacks.out | Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits | [
"CategoryTheory.Limits.HasFiniteWidePullbacks",
"CategoryTheory.Limits.HasLimitsOfShape",
"Finite",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Category"
] | true |
CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.ctorIdx | Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalClosed",
"Nat",
"CategoryTheory.MonoidalCategory.DayConvolutionInternalHom",
"CategoryTheory.Category"
] | false |
CategoryTheory.Limits.BinaryBiproductData.casesOn | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.BinaryBiproductData.rec",
"CategoryTheory.Limits.BinaryBicone",
"CategoryTheory.Limits.BinaryBiproductData",
"CategoryTheory.Limits.BinaryBicone.IsBilimit",
"CategoryTheory.Limits.BinaryBiproductData.mk",
"CategoryTheory.Category"
] | false |
Turing.FinTM2.step.eq_1 | Mathlib.Computability.TuringMachine.Computable | [
"Turing.FinTM2.Λ",
"Turing.FinTM2.K",
"Turing.FinTM2.decidableEqK",
"Turing.FinTM2.step",
"Turing.TM2.step",
"Turing.FinTM2",
"Turing.FinTM2.σ",
"Turing.FinTM2.Γ",
"Eq.refl",
"Turing.FinTM2.m",
"Turing.FinTM2.Cfg",
"Eq",
"Option"
] | true |
Lean.Elab.Term.Do.Code.matchExpr.sizeOf_spec | Lean.Elab.Do.Legacy | [
"Lean.Elab.Term.Do.AltExpr._sizeOf_inst",
"congrArg",
"Lean.Elab.Term.Do.Code._sizeOf_inst",
"Lean.Syntax._sizeOf_inst",
"Lean.Elab.Term.Do.Code._sizeOf_3",
"Lean.Syntax",
"Lean.Elab.Term.Do.Code._sizeOf_3_eq",
"instOfNatNat",
"Array._sizeOf_inst",
"Array",
"Lean.Elab.Term.Do.Code.matchExpr",
... | true |
NormedCommGroup.mk | Mathlib.Analysis.Normed.Group.Defs | [
"Norm.norm",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"HMul.hMul",
"Norm",
"DivInvMonoid.toMonoid",
"CommGroup",
"autoParam",
"NormedCommGroup",
"Group.toDivInvMonoid",
"Inv.inv",
"MetricSpace",
"NormedCommGroup.dist_eq._autoParam",
"NormedCommGroup.mk",
"Monoid.toSemigroup",
... | true |
Mathlib.Tactic.ComputeDegree.initFn._@.Mathlib.Tactic.ComputeDegree.1830119225._hygCtx._hyg.2 | Mathlib.Tactic.ComputeDegree | [
"Lean.Name.mkNum",
"IO",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.registerTraceClass",
"Lean.Name.anonymous",
"Unit",
"Nat",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Bool.false"
] | false |
_private.Mathlib.Analysis.Analytic.Within.0.hasFPowerSeriesWithinAt_iff_exists_hasFPowerSeriesAt._simp_1_5 | Mathlib.Analysis.Analytic.Within | [
"nhdsWithin",
"Filter.Eventually",
"Membership.mem",
"nhds",
"Filter.EventuallyEq",
"eventuallyEq_nhdsWithin_iff",
"TopologicalSpace",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
BitVec.lt_asymm | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"congrArg",
"BitVec",
"id",
"BitVec.toNat",
"implies_congr",
"instLTBitVec",
"Nat",
"LT.lt",
"BitVec.lt_def._simp_1",
"instLTNat",
"Nat.lt_asymm",
"Eq",
"Not"
] | true |
FirstOrder.Language.DirectLimit.dom_partialEquivLimit | Mathlib.ModelTheory.PartialEquiv | [
"iSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"FirstOrder.Language.PartialEquiv.dom",
"CompleteLattice.toConditionallyCompleteLattice",
"FirstOrder.Language.Substructure",
"FirstOrder.Language.PartialEquiv.instPartialOrder",
"FirstOrder.Language.DirectLimit.partialEquivLimit",
"OrderHom.instFu... | true |
Nat.minSqFacAux_has_prop._unary | Mathlib.Data.Nat.Squarefree | [
"dite_cond_eq_true",
"Iff.mpr",
"Distrib.leftDistribClass",
"Eq.mpr",
"of_eq_false",
"lt_of_le_of_lt",
"False",
"Semigroup.toMul",
"Nat.Prime",
"Preorder.toLT",
"Dvd.dvd",
"instHDiv",
"HMul.hMul",
"of_decide_eq_true",
"eq_false",
"dvd_of_mul_right_dvd",
"Nat.minFac_lemma",
"congrAr... | false |
Order.pred_lt | Mathlib.Order.SuccPred.Basic | [
"not_isMin",
"Preorder.toLT",
"NoMinOrder",
"Order.pred",
"LT.lt",
"PredOrder",
"Preorder",
"Order.pred_lt_of_not_isMin"
] | true |
UInt8.xor_comm | Init.Data.UInt.Bitwise | [
"BitVec",
"instOfNatNat",
"UInt8.toBitVec",
"BitVec.xor_comm",
"Nat",
"HXor.hXor",
"Iff.mp",
"UInt8.toBitVec_inj",
"instXorOpUInt8",
"OfNat.ofNat",
"UInt8",
"Eq",
"instHXorOfXorOp"
] | true |
TopologicalSpace.Compacts.ext | Mathlib.Topology.Sets.Compacts | [
"SetLike.ext'",
"TopologicalSpace",
"SetLike.coe",
"TopologicalSpace.Compacts.instSetLike",
"Eq",
"TopologicalSpace.Compacts",
"Set"
] | true |
CategoryTheory.Limits.reflectsFiniteLimits_of_leftOp | Mathlib.CategoryTheory.Limits.Preserves.Opposites | [
"CategoryTheory.Functor",
"CategoryTheory.finCategoryOpposite",
"Opposite",
"CategoryTheory.Limits.ReflectsFiniteLimits",
"CategoryTheory.SmallCategory",
"CategoryTheory.Limits.ReflectsFiniteColimits.reflects",
"CategoryTheory.Limits.reflectsLimitsOfShape_of_leftOp",
"CategoryTheory.Limits.ReflectsFin... | true |
CategoryTheory.Functor.IsCartesian | Mathlib.CategoryTheory.FiberedCategory.Cartesian | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.IsCartesian.mk",
"CategoryTheory.Category"
] | true |
Mathlib.Meta.NormNum.minFacHelper_2 | Mathlib.Tactic.NormNum.Prime | [
"Nat.Prime",
"congrArg",
"Eq.mp",
"Nat.minFac",
"instOfNatNat",
"Mathlib.Meta.NormNum.MinFacHelper",
"Mathlib.Meta.NormNum.minFacHelper_1",
"LT.lt.ne'",
"instHAdd",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Not",
"Nat.minFac_prime",
"M... | true |
Equiv.smulZeroClass._proof_1 | Mathlib.Algebra.GroupWithZero.Action.TransferInstance | [
"Equiv.apply_symm_apply",
"instHSMul",
"Equiv.instEquivLike",
"SMulZeroClass",
"congrArg",
"smul_zero",
"Equiv",
"True",
"eq_self",
"of_eq_true",
"Zero.toOfNat0",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"Equiv.zero",
"congrFun'",
"implies_true",
"Equiv.symm",
"OfNat.ofNat",
"Eq",
... | false |
Std.TreeMap.Raw.filter | Std.Data.TreeMap.Raw.Basic | [
"Std.TreeMap.Raw.mk",
"Ordering",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Bool",
"Std.DTreeMap.Raw.filter"
] | true |
finprod_cond_eq_right | Mathlib.Algebra.BigOperators.Finprod | [
"congrArg",
"eq_comm",
"funext",
"finprod",
"finprod_cond_eq_left",
"finprod_congr_Prop",
"True",
"eq_self",
"propext",
"of_eq_true",
"Eq.refl",
"congrFun'",
"Eq",
"CommMonoid",
"Eq.trans"
] | true |
CategoryTheory.ShortComplex.quasiIso_unopMap | Mathlib.Algebra.Homology.ShortComplex.QuasiIso | [
"CategoryTheory.ShortComplex.QuasiIso",
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory.ShortComplex.instCategory",
"infer... | true |
Set.Ioc_disjoint_Ioi._simp_1 | Mathlib.Order.Interval.Set.Disjoint | [
"Set.Ioc",
"Set.Ioi",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Preorder.toLE",
"Disjoint",
"LE.le",
"Set.Ioc_disjoint_Ioi",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"True",
"CompleteDistribLattice.toFrame",
"eq_true",
"CompleteBooleanAlg... | false |
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