name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Mathlib.Meta.Finset.ProveEmptyOrConsResult.empty.elim | Mathlib.Tactic.NormNum.BigOperators | [
"PULift.up",
"Lean.Expr.const",
"Mathlib.Meta.Finset.ProveEmptyOrConsResult.empty",
"Mathlib.Meta.Finset.ProveEmptyOrConsResult.ctorIdx",
"Mathlib.Meta.Finset.ProveEmptyOrConsResult.ctorElim",
"Lean.Expr.sort",
"Lean.Level",
"Mathlib.Meta.Finset.ProveEmptyOrConsResult",
"List.cons",
"Qq.Quoted",
... | false |
_private.Mathlib.LinearAlgebra.ExteriorAlgebra.Basic.0.ExteriorAlgebra.map_injective.match_1_1 | Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | [
"LinearMap.id",
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Exists",
"AddCommGroup",
"LinearMap",
"LinearMap.comp",
"CommRing.toCommSemiring",
"Exists.casesOn",
"Exists.intro",
"Module",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring",
"... | false |
_private.Lean.Meta.Coe.0.Lean.Meta.coerceSimple?.match_1 | Lean.Meta.Coe | [
"Unit.unit",
"Lean.LOption.undef",
"Lean.Expr",
"Prod.mk",
"Lean.LOption.some",
"Lean.LOption.none",
"List",
"Lean.LOption.casesOn",
"Unit",
"Lean.Name",
"Prod",
"Prod.casesOn",
"Lean.LOption"
] | false |
AddActionSemiHomClass.mk | Mathlib.GroupTheory.GroupAction.Hom | [
"outParam",
"AddActionSemiHomClass",
"VAdd",
"HVAdd.hVAdd",
"AddActionSemiHomClass.mk",
"instHVAdd",
"Eq",
"DFunLike.coe",
"FunLike"
] | true |
Filter.smul.instNeBot | Mathlib.Order.Filter.Pointwise | [
"instHSMul",
"Filter.NeBot",
"SMul",
"Filter.instSMul",
"Filter.NeBot.smul",
"HSMul.hSMul",
"Filter"
] | true |
_private.Mathlib.Geometry.Euclidean.Volume.Measure.0.MeasureTheory.Measure.euclideanHausdorffMeasure._proof_3 | Mathlib.Geometry.Euclidean.Volume.Measure | [
"WithLp",
"InnerProductSpace.toNormedSpace",
"Real",
"WithLp.instModuleFinite",
"Real.instRCLike",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Pi.module",
"FiniteDimensional.rclike_to_real",
"WithLp.instAddCommGroup",
"NormedField.toField",
"DivisionRing.toDivisionSemiring",
"Ad... | false |
Asymptotics.SuperpolynomialDecay.add | Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | [
"Distrib.leftDistribClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"nhds",
"Eq.mp",
"id",
"Distrib.toAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSemiring",
"Monoid.toPow",
"Co... | true |
Subgroup.quotientiInfSubgroupOfEmbedding._proof_1 | Mathlib.GroupTheory.Coset.Basic | [
"iInf",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Subgroup",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",
"Subgroup.instCompleteLattice",
"CompleteLattice.toCompleteSemilatticeSup",
"CompleteSemilatticeInf.toInfSet",
"CompleteSemilatticeSup.toPartialOrder",
"iInf_le"
] | false |
EMetric.ball_disjoint | Mathlib.Topology.EMetricSpace.Defs | [
"ENNReal.instAdd",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Disjoint",
"CompleteLattice.toConditionallyCompleteLattice",
"LE.le",
"Metric.eball",
"PseudoEMetricSpace",
"instHAdd",
"PseudoEMetricSpace.toEDist",
"HAdd.hAdd",
"ENNReal.instLE",
"Metric.eball_disjoint",
"ENNReal",
"C... | true |
_private.Init.Data.Order.Lemmas.0.Std.instAssociativeMaxOfIsLinearOrderOfLawfulOrderMax._simp_1 | Init.Data.Order.Lemmas | [
"Std.LawfulOrderSup",
"Max",
"Std.max_le_iff",
"LE.le",
"LE",
"And",
"Max.max",
"propext",
"Eq"
] | false |
LinearMap.BilinForm.baseChange_eq_zero_iff._simp_1 | Mathlib.LinearAlgebra.BilinearForm.TensorProduct | [
"LinearMap.BilinForm.baseChange",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"Algebra",
"Algebra.toSMul",
"Algebra.toModule",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"FaithfulSMul",
"CommSemiri... | false |
le_mul_of_one_le_left' | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"MulOne.toOne",
"Trans.trans",
"HMul.hMul",
"MulOne.toMul",
"MulRightMono",
"LE.le",
"LE",
"instTransEq",
"MulOneClass.toMulOne",
"mul_le_mul_left",
"One.toOfNat1",
"MulOneClass",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"one_mul",
"instHMul"
] | true |
Std.LawfulEqOrd.compare_eq_iff_eq._simp_1 | Init.Data.Order.Ord | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"propext",
"Eq",
"Std.LawfulEqOrd",
"Std.LawfulEqOrd.compare_eq_iff_eq"
] | false |
Std.HashSet.Raw.WF.casesOn | Std.Data.HashSet.Raw | [
"Std.HashSet.Raw.inner",
"Std.HashSet.Raw.WF",
"Std.HashMap.Raw.WF",
"Unit",
"Std.HashSet.Raw.WF.mk",
"Hashable",
"BEq",
"Std.HashSet.Raw.WF.rec",
"Std.HashSet.Raw"
] | false |
_private.Mathlib.Tactic.Simproc.ExistsAndEq.0.ExistsAndEq.withNestedExistsElim.match_1 | Mathlib.Tactic.Simproc.ExistsAndEq | [
"Unit.unit",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"List",
"Unit",
"Qq.Quoted",
"List.casesOn",
"ExistsAndEq.VarQ",
"Sigma.mk",
"Sigma.casesOn",
"Sigma",
"List.nil"
] | false |
Configuration.HasPoints.lineCount_eq_pointCount | Mathlib.Combinatorics.Configuration | [
"Configuration.Dual",
"Configuration.lineCount",
"Membership.mem",
"Fintype.card",
"Membership",
"Fintype",
"Configuration.HasLines.lineCount_eq_pointCount",
"Nat",
"Configuration.Dual.hasLines",
"Configuration.pointCount",
"Configuration.HasPoints",
"Eq.symm",
"Eq",
"Not",
"Configuratio... | true |
Set.FiniteExhaustion._sizeOf_inst | Mathlib.Data.Set.FiniteExhaustion | [
"SizeOf.mk",
"Set.FiniteExhaustion",
"SizeOf",
"Set.FiniteExhaustion._sizeOf_1",
"Set"
] | false |
_private.Std.Data.TreeSet.Lemmas.0.Std.TreeSet.contains_toArray._simp_1_1 | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"Std.TreeSet.toList",
"Std.TreeSet.toArray_toList",
"Ordering",
"Std.TreeSet.toArray",
"List.toArray",
"Array",
"Eq.symm",
"Eq"
] | false |
IntermediateField.induction_on_adjoin | Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra | [
"Iff.mpr",
"IntermediateField.restrictScalars",
"IntermediateField.isScalarTower_mid'",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField.induction_on_adjoin_fg",
"CompleteLattice.toLattice",
"AddCommGro... | true |
Lean.Sym.UInt16.lt_eq_true | Init.Sym.Lemmas | [
"UInt16.decLt",
"congrArg",
"Eq.mp",
"id",
"Bool.true",
"UInt16",
"LT.lt",
"True",
"eq_self",
"eq_true",
"Bool",
"of_eq_true",
"instLTUInt16",
"congrFun'",
"decide_eq_true_eq",
"Decidable.decide",
"Eq",
"Eq.trans"
] | true |
Std.HashMap.Raw.getKey_eq | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.WF.out",
"LawfulBEq",
"Membership.mem",
"Std.HashMap.Raw.WF",
"Std.HashMap.Raw",
"Std.HashMap.Raw.inner",
"Std.HashMap.Raw.instMembershipOfBEqOfHashable",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap.Raw.getKey_eq",
"Std.HashMap.Raw.getKey"
] | true |
AlgebraicGeometry.Scheme.basicOpen_restrict | Mathlib.AlgebraicGeometry.Scheme | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Ope... | true |
String.eq_append_of_dropPrefix?_prop_eq_some | Init.Data.String.Lemmas.Pattern.TakeDrop.Pred | [
"String.toSlice",
"String.Slice.dropPrefix?",
"congrArg",
"String",
"Option.some",
"String.Slice",
"Exists",
"String.dropPrefix?",
"Eq.mp",
"String.dropPrefix?_eq_dropPrefix?_toSlice",
"String.Slice.copy",
"instAppendString",
"funext",
"instHAppendOfAppend",
"And",
"String.Slice.eq_app... | true |
CategoryTheory.Pretriangulated.instHasFiniteCoproducts | Mathlib.CategoryTheory.Triangulated.Pretriangulated | [
"CategoryTheory.Pretriangulated.instHasBinaryBiproducts",
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Limits.HasFiniteCoproducts",
"CategoryTheory.hasFiniteCoproducts_of_has_binary_and_initial",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Preadditive",
"Category... | true |
Std.DTreeMap.Const.getKey?_insertMany_list_of_mem | Std.Data.DTreeMap.Lemmas | [
"List.Pairwise",
"Std.DTreeMap",
"instForInOfForIn'",
"Std.DTreeMap.Internal.Impl.Const.getKey?_insertMany_list_of_mem",
"List.map",
"Ord.mk",
"Option.some",
"Membership.mem",
"Ordering",
"inferInstance",
"Ordering.eq",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Id",
"Std.DTreeMap.Const.inse... | true |
intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae_of_le | Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus | [
"MeasureTheory.ae",
"Set.Ioc",
"Real.instLE",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"CompleteSpace",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"intervalIntegral.FTCFilter.finiteAt_inner",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"Me... | true |
ProbabilityTheory.complexMGF_id_gaussianReal | Mathlib.Probability.Distributions.Gaussian.Real | [
"instInnerProductSpaceRealComplex",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"zero_le",
"NormedCommRing.toNormedRing",
"Mathlib.Tactic.RingNF.nnrat_rawCast",
"AddGroup.toSubtractionMonoid",
"Real.instIsOrderedRing",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Mathlib.Tactic.Ring.Common.neg_... | true |
CategoryTheory.LocalizerMorphism.inv_functor | Mathlib.CategoryTheory.Localization.LocalizerMorphism | [
"CategoryTheory.LocalizerMorphism.inv",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.LocalizerMorphism.IsInduced",
"CategoryTheory.LocalizerMorphism.functor",
"CategoryTheory.MorphismProperty.RespectsIso",
"Eq.refl",
"CategoryTheory.Functor.inv",
"CategoryTheory.Categ... | true |
TopCat.Presheaf.EtaleSpace.homeomorph._proof_5 | Mathlib.Topology.Sheaves.EtaleSpace | [
"Opposite",
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheory.ConcreteCategory.hom",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Membership.mem",
"TopCat.Presheaf",
"Preorder.smallCategory",
"TopCat.Presheaf.stalk",
"TopologicalSpace.Opens.instSetLike",
"TopCat.Presheaf.germ",... | false |
_private.Init.Data.String.Lemmas.Pattern.Char.0.String.Slice.Pattern.Model.Char.isValidRevSearchFrom_iff_isValidRevSearchFrom_beq._simp_1_3 | Init.Data.String.Lemmas.Pattern.Char | [
"String.instLEPos_1",
"String.Slice.Pattern.SearchStep",
"String.Slice",
"String.Slice.Pattern.Model.IsValidRevSearchFrom",
"String.Slice.Pattern.SearchStep.rejected",
"LE.le",
"List.cons",
"List",
"LT.lt",
"String.instLTPos_1",
"True",
"eq_true",
"String.Slice.Pattern.Model.PatternModel",
... | false |
Matroid.freeOn.eq_1 | Mathlib.Combinatorics.Matroid.Constructions | [
"Matroid.loopyOn",
"Matroid.dual",
"Eq.refl",
"Eq",
"Matroid",
"Matroid.freeOn",
"Set"
] | true |
Lean.Elab.Tactic.Do.SpecAttr.SpecTheorems.isErased | Lean.Elab.Tactic.Do.Attr | [
"Lean.Elab.Tactic.Do.SpecAttr.SpecTheorems",
"Lean.PersistentHashSet.contains",
"Lean.Elab.Tactic.Do.SpecAttr.instHashableSpecProof",
"Bool",
"Lean.Elab.Tactic.Do.SpecAttr.instBEqSpecProof",
"Lean.Elab.Tactic.Do.SpecAttr.SpecTheorems.erased",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof"
] | true |
Ring.instAddCommMonoidDirectLimit._aux_1 | Mathlib.Algebra.Colimit.Ring | [
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"FreeCommRing",
"Submodule.Quotient.addMonoid._aux_1",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"instCommRingFreeCommRing",
"Preorder.toLE",
"FreeCommRing.of",
"Exists"... | false |
PSigma.Lex.preorder._proof_4 | Mathlib.Data.PSigma.Order | [
"LE.le.lt_of_not_ge",
"PSigma.Lex",
"False",
"Preorder.toLT",
"lt_irrefl",
"PSigma.Lex.casesOn",
"PSigma.Lex.left",
"HEq.refl",
"Lex",
"PSigma.mk.noConfusion",
"le_of_lt",
"Preorder.toLE",
"PSigma.Lex.right",
"PSigma.Lex.le",
"LE.le",
"And.casesOn",
"PSigma.Lex.lt",
"And",
"Iff",... | false |
«command#long_names_» | Mathlib.Util.LongNames | [
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
OrderedFinpartition.eraseMiddle._proof_11 | Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | [
"Nat.sub_one_lt_of_lt",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"dite_cond_eq_true",
"Eq.mpr",
"of_eq_false",
"instNeZeroNatHAdd_1",
"False",
"_private.Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno.0.OrderedFinpartition.eraseMiddle._proof_10",
"Preorder.toLT",
"Nat.instIsOrderedAddM... | false |
Sub.noConfusion | Init.Prelude | [
"Sub.casesOn",
"Sub.noConfusionType",
"HEq.refl",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq",
"Sub"
] | false |
BooleanAlgebra.recOn | Mathlib.Order.BooleanAlgebra.Defs | [
"BooleanAlgebra",
"Lattice.toSemilatticeSup",
"Compl.compl",
"HImp",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"Bot.bot",
"Bot",
"SemilatticeInf.toMin",
"LE.le",
"SemilatticeInf.mk",
"SDiff.sdiff",
"DistribLattice",
"Max.max",
"Bo... | false |
RingHom.liftOfRightInverse_comp | Mathlib.RingTheory.Ideal.Maps | [
"RingHom.instRingHomClass",
"Semiring.toModule",
"Equiv.instEquivLike",
"PartialOrder.toPreorder",
"RingHom.liftOfRightInverse",
"Preorder.toLE",
"RingHom",
"Equiv",
"Subtype",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"RingHom.liftOfRightInverse_comp_apply",
"RingHom.ext",
"NonUni... | true |
LinearMap.extendScalarsOfIsLocalizationEquiv._proof_8 | Mathlib.RingTheory.Localization.Module | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.IsScalarTower.compatibleSMul",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"Semiri... | false |
Int.Linear.Poly.insert | Init.Data.Int.Linear | [
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.brecOn",
"Int.Linear.Poly.insert._f",
"Int.Linear.Poly"
] | true |
_private.Mathlib.Topology.Category.CompHaus.EffectiveEpi.0.CompHaus.effectiveEpiFamily_tfae.match_1_1 | Mathlib.Topology.Category.CompHaus.EffectiveEpi | [
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finite",
"CompHaus.instHasPropTrue",
"instTopologicalSpaceSigma",
"CompHausLike.instHasCoproduct",
"TopCat.str",
"TopCat.carrier",
"True",
"CompHausLike.category",
"CategoryTheory.Category.toCategoryStruct",
"TopC... | false |
_private.Mathlib.Combinatorics.Matroid.Constructions.0.Matroid.empty_isBase_iff._simp_1_2 | Mathlib.Combinatorics.Matroid.Constructions | [
"Matroid.Indep",
"Matroid.empty_indep",
"True",
"eq_true",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Matroid",
"Set"
] | false |
CategoryTheory.shrinkYonedaMonObjObjEquiv._proof_1 | Mathlib.CategoryTheory.Monoidal.Cartesian.ShrinkYoneda | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.LocallySmall",
"CategoryTheory.Functor.category",
"MonCat",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"MonCat.instCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.instSmallCarrierObjOppositeMonCatMon... | false |
_private.Mathlib.AlgebraicTopology.DoldKan.Degeneracies.0.AlgebraicTopology.DoldKan.σ_comp_P_eq_zero._simp_1_5 | Mathlib.AlgebraicTopology.DoldKan.Degeneracies | [
"Finset.mem_univ",
"Finset.univ",
"Finset",
"Membership.mem",
"Fintype",
"Finset.instSetLike",
"True",
"eq_true",
"Eq",
"SetLike.instMembership"
] | false |
Tactic.NormNum.int_lcm_helper | Mathlib.Tactic.NormNum.GCD | [
"Nat.lcm",
"Eq.mpr",
"Int.lcm",
"congrArg",
"id",
"Int",
"Int.lcm_def",
"Nat",
"Int.natAbs",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
IsZGroup.isCyclic_commutator | Mathlib.GroupTheory.SpecificGroups.ZGroup | [
"Subgroup.instFiniteSubtypeMem",
"Iff.mpr",
"isCyclic_of_surjective",
"Eq.mpr",
"instNormalCommutator",
"SetLike.mem_coe._simp_1",
"IsSolvable.commutator_lt_of_ne_bot",
"Semigroup.toMul",
"MulEquiv.instEquivLike",
"Subgroup.subgroupOf",
"Preorder.toLT",
"Subgroup.instSubgroupClass",
"MonoidH... | true |
CategoryTheory.Limits.limit.isLimit | Mathlib.CategoryTheory.Limits.HasLimits | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasLimit",
"CategoryTheory.Limits.limit.cone",
"CategoryTheory.Limits.getLimitCone",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Limits.LimitCone.isLimit",
"CategoryTheory.Category"
] | true |
LinearMap.compMultilinearMap_add | Mathlib.LinearAlgebra.Multilinear.Basic | [
"MultilinearMap.instAdd",
"LinearMap.instFunLike",
"map_add",
"LinearMap.semilinearMapClass",
"LinearMap",
"MultilinearMap",
"AddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"MultilinearMap.instFunLikeForall",
"MultilinearMap.ext",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCo... | true |
_private.Mathlib.Order.Interval.Set.Basic.0.Set.instNoMinOrderElemIio.match_1 | Mathlib.Order.Interval.Set.Basic | [
"Preorder.toLT",
"Membership.mem",
"Exists",
"Set.Elem",
"Exists.casesOn",
"LT.lt",
"Exists.intro",
"Subtype.val",
"Set.Iio",
"Set.instMembership",
"Preorder",
"Set"
] | false |
BitVec.ushiftRight_and_distrib | Init.Data.BitVec.Lemmas | [
"BitVec.instAndOp",
"BitVec.instHShiftRightNat",
"congrArg",
"BitVec.getElem_and",
"BitVec",
"BitVec.getLsbD",
"Bool.and",
"BitVec.getLsbD_and",
"GetElem.getElem",
"instHAdd",
"HAdd.hAdd",
"HShiftRight.hShiftRight",
"Nat",
"congr",
"LT.lt",
"True",
"eq_self",
"Bool",
"of_eq_true"... | true |
ENNReal.toReal_eq_toReal_iff' | Mathlib.Data.ENNReal.Basic | [
"Real",
"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.toReal_eq_toReal_iff'._simp_1_2",
"congrArg",
"ENNReal.toNNReal_eq_toNNReal_iff'",
"NNReal",
"Ne",
"ENNReal.toNNReal",
"iff_self",
"Iff",
"ENNReal.toReal",
"True",
"ENNReal",
"propext",
"of_eq_true",
"ENNReal.instTop",
"congrFun'",... | true |
List.zipWithM.loop | Init.Data.List.Control | [
"List.brecOn",
"List.zipWithM.loop._f",
"Array",
"List",
"Monad"
] | true |
_private.Mathlib.MeasureTheory.Integral.CircleIntegral.0.circleIntegrable_sub_inv_iff._simp_1_1 | Mathlib.MeasureTheory.Integral.CircleIntegral | [
"DivInvMonoid.toInv",
"zpow_neg_one",
"DivInvMonoid.toZPow",
"Int.instNegInt",
"Int",
"DivInvMonoid",
"Inv.inv",
"HPow.hPow",
"instOfNat",
"instHPow",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Neg.neg"
] | false |
GradedRing.projZeroRingHom'_surjective | Mathlib.RingTheory.GradedAlgebra.Basic | [
"GradedRing.toGradedMonoid",
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"GradedRing.projZeroRingHom'_apply_coe",
"Preorder.toLE",
"RingHom",
"Membership.mem",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
"PartialOrder",
"Sub... | true |
factorPowSucc.isUnit_of_isUnit_image | Mathlib.RingTheory.Ideal.Quotient.PowTransition | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Ideal.mem_image_of_mem_map_of_surjective",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Ideal.Quotient.commSemiring",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"isUnit_iff_exists",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"... | true |
Filter.tendstoIxxClass_principal | Mathlib.Order.Filter.Interval | [
"Set.instSProd",
"Filter.smallSets",
"SProd.sprod",
"congrArg",
"Filter.TendstoIxxClass.tendsto_Ixx",
"Set.powerset",
"Membership.mem",
"Filter.prod_principal_principal",
"_private.Mathlib.Order.Filter.Interval.0.Filter.tendstoIxxClass_principal._simp_1_1",
"Prod.mk",
"HasSubset.Subset",
"Filt... | true |
optParam | Init.Prelude | [] | true |
Std.Slice.Internal.SubarrayData.stop_le_array_size | Init.Data.Array.Subarray | [
"LE.le",
"instLENat",
"Std.Slice.Internal.SubarrayData",
"Nat",
"Std.Slice.Internal.SubarrayData.array",
"Array.size",
"Std.Slice.Internal.SubarrayData.stop"
] | true |
CategoryTheory.GrothendieckTopology.W_eq_inverseImage_isomorphisms | Mathlib.CategoryTheory.Sites.Localization | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.MorphismProperty.inverseImage",
"CategoryTheory.Functor.category",
"CategoryTheory.presheafToSheaf",
"CategoryTheory.MorphismProperty.isomorphisms",
"CategoryTheory.GrothendieckTopology.W",
"CategoryTheory.sheaf... | true |
OrthogonalIdempotents.mul_sum_of_mem | Mathlib.RingTheory.Idempotents | [
"Finset.mul_sum",
"HMul.hMul",
"congrArg",
"OrthogonalIdempotents",
"Finset",
"AddMonoid.toAddZeroClass",
"Classical.propDecidable",
"Membership.mem",
"AddZeroClass.toAddZero",
"ite_cond_eq_true",
"instDistribOfSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"Fins... | true |
CategoryTheory.Enriched.HasConicalLimitsOfSize.hasConicalLimitsOfShape._autoParam | Mathlib.CategoryTheory.Enriched.Limits.HasConicalLimits | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_80 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_73",
"Lean.Grind.nestedProof",
"HSub.hSub",
"SimpleGraph.Walk.support",
"List.length_dropLast",
"SimpleGraph.Walk",
"Eq.rec",
"instSubNat",
"List.dropLast",
"instOfNatNat",
"SimpleGr... | false |
Mathlib.Tactic.BicategoryLike.NormalExpr.nodesAux | Mathlib.Tactic.Widget.StringDiagram | [
"Mathlib.Tactic.BicategoryLike.NormalExpr",
"Mathlib.Tactic.BicategoryLike.MonadMor₁",
"List",
"Mathlib.Tactic.BicategoryLike.NormalExpr.nodesAux._f",
"Nat",
"Mathlib.Tactic.BicategoryLike.NormalExpr.brecOn",
"Mathlib.Tactic.BicategoryLike.CoherenceM",
"Mathlib.Tactic.Widget.StringDiagram.Node"
] | true |
Mathlib.Tactic.GCongr.GCongrKey.recOn | Mathlib.Tactic.GCongr.Core | [
"Mathlib.Tactic.GCongr.GCongrKey.rec",
"Mathlib.Tactic.GCongr.GCongrKey.mk",
"Nat",
"Lean.Name",
"Mathlib.Tactic.GCongr.GCongrKey"
] | false |
_private.Lean.Meta.RecursorInfo.0.Lean.Meta.getNumParams | Lean.Meta.RecursorInfo | [
"Inhabited.default",
"Lean.Expr",
"Array",
"Nat",
"Inhabited",
"Inhabited.mk"
] | true |
CategoryTheory.Arrow.equivSigma | Mathlib.CategoryTheory.Comma.Arrow | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.equivSigma._proof_1",
"Equiv.mk",
"CategoryTheory.Arrow.left",
"Equiv",
"CategoryTheory.Arrow.hom",
"Sigma.fst",
"CategoryTheory.Arrow.equivSigma._proof_2",
"CategoryTheory.Category.toCategoryStruct",
"Sigma.mk",
"Ca... | true |
AlgebraNorm.mk.inj | Mathlib.Analysis.Normed.Unbundled.AlgebraNorm | [
"AlgebraNorm.mk.noConfusion",
"Norm.norm",
"SeminormedRing.toNorm",
"Real",
"instHSMul",
"HMul.hMul",
"SeminormedCommRing",
"Ring.toNonAssocRing",
"SeminormedCommRing.toCommRing",
"NonUnitalNonAssocRing.toAddCommGroup",
"Algebra",
"AddCommGroup.toAddGroup",
"Algebra.toSMul",
"RingNorm.toRi... | true |
ContinuousAlternatingMap.curryLeft_add | Mathlib.Analysis.Normed.Module.Alternating.Curry | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousAlternatingMap.curryLeft",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Nor... | true |
cantorToTernary | Mathlib.Topology.Instances.CantorSet | [
"cond",
"Real",
"Fin.instOfNat",
"instOfNatNat",
"cantorToBinary",
"Stream'",
"Stream'.map",
"Nat",
"Bool",
"cantorToTernary._proof_1",
"OfNat.ofNat",
"Fin"
] | true |
Vector.extract_eq_pop | Init.Data.Vector.Extract | [
"Vector.cast_mk._proof_1",
"Vector",
"congrArg",
"HSub.hSub",
"Vector.pop_mk._proof_1",
"Vector.extract",
"Vector.casesOn",
"Array.extract_eq_pop",
"Eq.rec",
"Vector.pop",
"instSubNat",
"instOfNatNat",
"Array.pop",
"Array.extract",
"Array",
"instHSub",
"Vector.mk",
"Nat",
"True",... | true |
TensorPower.gmonoid._proof_2 | Mathlib.LinearAlgebra.TensorPower.Basic | [
"Nat.instMulZeroClass",
"instHSMul",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"GradedMonoid.GMul.mk",
"CommSemiring.toSemiring",
"GradedMonoid.GMonoid.gnpowRec",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"GradedMonoid.GMul.mul",
"TensorPo... | false |
_private.Lean.Elab.App.0.Lean.Elab.Term.mergeFailures.match_1 | Lean.Elab.App | [
"EStateM.Result.ctorIdx",
"Lean.Elab.Term.TermElabResult",
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Elab.Term.SavedState",
"EStateM.Result.error",
"_private.Lean.Elab.App.0.Lean.Elab.Term.mergeFailures._sparseCasesOn_1",
"Lean.Exception"
] | false |
Lean.Meta.Grind.Arith.Cutsat.DiseqCnstr.h | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstr",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof"
] | true |
TensorProduct.tmul_neg | Mathlib.LinearAlgebra.TensorProduct.Basic | [
"NegZeroClass.toNeg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"TensorProduct.addCommMonoid",
"LinearMap.instFunLike",
"TensorProduct.addCommGroup",
"LinearMap.map_neg",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"LinearMap.module... | true |
Stream'.WSeq.seq_destruct_think | Mathlib.Data.WSeq.Basic | [
"Option.some",
"Prod.mk",
"Option.none",
"Stream'.WSeq.think",
"Stream'.WSeq",
"Stream'.Seq.destruct_cons",
"Stream'.Seq1",
"Stream'.Seq.destruct",
"Prod",
"Eq",
"Option"
] | true |
Polynomial.trinomial | Mathlib.Algebra.Polynomial.UnitTrinomial | [
"Polynomial.C",
"HMul.hMul",
"RingHom",
"Polynomial.instAdd",
"Polynomial",
"Monoid.toPow",
"instHAdd",
"RingHom.instFunLike",
"HPow.hPow",
"HAdd.hAdd",
"Polynomial.semiring",
"Nat",
"Semiring.toMonoid",
"Semiring",
"Polynomial.instMul",
"instHPow",
"Polynomial.X",
"Semiring.toNonA... | true |
MeasureTheory.setLAverage_congr_fun | Mathlib.MeasureTheory.Integral.Average | [
"MeasureTheory.Measure",
"instHDiv",
"MeasurableSet",
"MeasureTheory.laverage",
"congrArg",
"Set.univ",
"MeasureTheory.laverage_eq",
"MeasureTheory.setLIntegral_congr_fun",
"MeasureTheory.Measure.restrict",
"HDiv.hDiv",
"Set.EqOn",
"MeasurableSpace",
"congr",
"True",
"eq_self",
"ENNRea... | true |
TopCat.instCategory._proof_2 | Mathlib.Topology.Category.TopCat.Basic | [
"TopCat.Hom",
"ContinuousMap.comp",
"id",
"TopCat.Hom.hom'",
"TopCat.str",
"ContinuousMap.id",
"TopCat.carrier",
"_private.Mathlib.Topology.Category.TopCat.Basic.0.TopCat.Hom.mk",
"Eq.refl",
"TopCat",
"Eq"
] | false |
List.sym2_eq_nil_iff | Mathlib.Data.List.Sym | [
"False",
"Sym2.mk",
"congrArg",
"List.map",
"False.elim",
"noConfusion_of_Nat",
"List.cons",
"iff_self",
"instHAppendOfAppend",
"List",
"Iff",
"List.sym2",
"congr",
"True",
"List.casesOn",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"List.instAppend",
"Eq.symm",
"eq_fal... | true |
Fix.mk._flat_ctor | Mathlib.Control.Fix | [
"Fix",
"Fix.mk"
] | false |
_private.Std.Data.DHashMap.Internal.WF.0.Std.DHashMap.Internal.Raw₀.diff.eq_1 | Std.Data.DHashMap.Internal.WF | [
"Bool.not",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Raw",
"instOfNatNat",
"LE.le",
"Std.DHashMap.Internal.Raw₀.filter",
"instLENat",
"Id",
"Std.DHashMap.Raw.instForInSigmaOfMonad",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Eq.refl",
"Std.DHashMap.Internal.Raw₀.diff",
"Std... | true |
Primrec.list_head? | Mathlib.Computability.Primrec.List | [
"List.head?",
"Iff.mpr",
"Primrec.of_eq",
"Primrec.snd",
"Primrec.list_casesOn",
"Option.some",
"Primrec.fst",
"id",
"Prod.mk",
"Primrec.const",
"Prod.fst",
"List.cons",
"Primcodable.prod",
"Primrec",
"Option.none",
"List",
"List.casesOn",
"Primrec.comp",
"Primrec.option_some_iff... | true |
Std.TreeMap.getElem!_modify_self | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Option.get!",
"Std.TransCmp",
"Option.map",
"Std.TreeMap.instMembership",
"Std.TreeMap.instGetElem?Mem",
"Inhabited",
"Std.TreeMap.modify",
"Std.DTreeMap.Const.get!_modify_self",
"GetElem?.getElem?",
"Eq",
"GetElem?.getElem!",
"Std.Tree... | true |
Polynomial.le_trailingDegree_C | Mathlib.Algebra.Polynomial.Degree.TrailingDegree | [
"Polynomial.C",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Polynomial.le_trailingDegree_monomial",
"RingHom",
"AddZeroClass.toAddZero",
"LE.le",
"Nat.instAddMonoidWithOne",
"Polynomial",
"instLEENat",
"AddZero.toZero",
"RingHom.instFunLike",
"Polynomial.semiring",
"Nat",
"EN... | true |
RootPairing.finrank_rootSpan_map_polarization_eq_finrank_corootSpan | Mathlib.LinearAlgebra.RootSystem.Finite.Nondegenerate | [
"Eq.mpr",
"Submodule",
"IsDomain",
"RingHomSurjective.ids",
"CommRing",
"Semiring.toModule",
"RootPairing.finrank_range_polarization_eq_finrank_span_coroot",
"Module.Free.instFaithfulSMulOfNontrivial",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMon... | true |
Nat.forM | Init.Data.Nat.Control | [
"Unit",
"Nat",
"LT.lt",
"_private.Init.Data.Nat.Control.0.Nat.forM.loop",
"instLTNat",
"Monad",
"_private.Init.Data.Nat.Control.0.Nat.forM._proof_2"
] | true |
IsPGroup.of_surjective | Mathlib.GroupTheory.PGroup | [
"Eq.mpr",
"MulOne.toOne",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instMonoid",
"IsPGroup",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Exists",
"id",
"DivInvMonoid.t... | true |
Std.TreeMap.forIn_eq_forIn_keys | Std.Data.TreeMap.Lemmas | [
"instForInOfForIn'",
"Std.TreeMap.inner",
"Std.TreeMap.keys",
"Ordering",
"inferInstance",
"LawfulMonad",
"ForIn.forIn",
"Membership",
"ForInStep",
"Prod.fst",
"List",
"List.instMembership",
"Std.TreeMap.instForInProdOfMonad",
"Prod",
"Monad",
"Std.DTreeMap.forIn_eq_forIn_keys",
"Eq"... | true |
Std.Http.Status.paymentRequired.elim | Std.Internal.Http.Data.Status | [
"PULift.up",
"Std.Http.Status.ctorIdx",
"Std.Http.Status",
"Std.Http.Status.ctorElim",
"Std.Http.Status.paymentRequired",
"Nat",
"Eq.symm",
"Eq"
] | false |
Asymptotics.isTheta_const_const_iff | Mathlib.Analysis.Asymptotics.Theta | [
"_private.Mathlib.Analysis.Asymptotics.Theta.0.Asymptotics.isTheta_const_const_iff._simp_1_2",
"Eq.mpr",
"congrArg",
"Filter.NeBot",
"Asymptotics.IsBigO",
"id",
"Asymptotics.IsTheta",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMon... | true |
Vector.mem_attach | Init.Data.Vector.Attach | [
"Vector.instMembership",
"Eq.mpr",
"Vector.attach",
"Vector",
"_private.Init.Data.Vector.Attach.0.Vector.mem_attach.match_1_1",
"congrArg",
"Subtype.casesOn",
"Vector.mem_map",
"Membership.mem",
"Exists",
"id",
"Subtype",
"Vector.map",
"Vector.attach_map_subtype_val",
"Subtype.mk",
"An... | true |
Lean.Elab.Tactic.iterateExactly' | Mathlib.Tactic.Core | [
"Lean.Elab.Tactic.iterateExactly'._f",
"Nat.brecOn",
"Unit",
"Nat",
"Monad"
] | true |
BoundedLatticeHom.dual._proof_2 | Mathlib.Order.Hom.BoundedLattice | [
"Lattice",
"Equiv.instEquivLike",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Equiv",
"BoundedLatticeHom.map_top'",
"LatticeHom",
"OrderDual.instLattice",
"LatticeHom.dual",
"BoundedLatticeHom.map_bot'",
"BoundedLatticeHom",
"Function.RightInverse",
"Eq.re... | false |
Std.DTreeMap.head?_keys | Std.Data.DTreeMap.Lemmas | [
"List.head?",
"Std.DTreeMap",
"Std.LawfulOrderMin",
"Std.LawfulOrderLeftLeaningMin",
"Ord.mk",
"Ordering",
"Std.DTreeMap.Internal.Impl.head?_keys",
"Std.DTreeMap.inner",
"Std.TransCmp",
"LE",
"Min",
"Std.LawfulEqCmp",
"Std.DTreeMap.wf",
"Std.DTreeMap.minKey?",
"Std.LawfulOrderCmp",
"St... | true |
Set.encard_pos | Mathlib.Data.Set.Card | [
"Eq.mpr",
"Set.encard_ne_zero",
"Set.encard",
"Preorder.toLT",
"instAddMonoidWithOneENat",
"instLinearOrderENat",
"congrArg",
"CommSemiring.toSemiring",
"instIsBotZeroClass",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",... | true |
_private.Mathlib.Geometry.Convex.Cone.Basic.0.ConvexCone.Flat.mono.match_1_1 | Mathlib.Geometry.Convex.Cone.Basic | [
"NegZeroClass.toNeg",
"AddCommGroup.toAddCommMonoid",
"SMul",
"ConvexCone.instSetLike",
"Membership.mem",
"PartialOrder",
"AddCommGroup",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"And.casesOn",
"And",
"Exi... | false |
Lean.Grind.Linarith.eq_eq_subst | Init.Grind.Ordered.Linarith | [
"Lean.Grind.Linarith.Poly.denote",
"Eq.mpr",
"instHSMul",
"Lean.Grind.Linarith.Poly.denote_mul",
"Lean.Grind.Linarith.Poly.combine",
"congrArg",
"Lean.Grind.Linarith.Context",
"Lean.Grind.Linarith.Poly.denote'",
"Lean.Grind.IntModule.toNatModule",
"Lean.Grind.IntModule.zsmul",
"id",
"Lean.Grin... | true |
AddCommMonCat.addCommMonoidObj._aux_4 | Mathlib.Algebra.Category.MonCat.Limits | [
"CategoryTheory.Functor",
"AddCommMonCat.instCategory",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"CategoryTheory.Functor.comp",
"AddCommMonCat",
"AddZeroClass.toAddZero",
"AddCommMonCat.instConcreteCategoryAddMonoidHomCarrier",
"AddCommMonCat.str",
"CategoryTheory.types",
"CategoryTheory.... | false |
SSet.PtSimplex.relStructCastSuccEquivMulStruct._proof_6 | Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | [
"Fin.succ_lt_succ_iff._simp_1",
"SSet.Subcomplex.toSSet",
"SSet.PtSimplex.RelStruct.map",
"SSet.Subcomplex.ofSimplex",
"SSet.const",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Fin.succ",
"instReflLe",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.ca... | false |
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