name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
iteratedDerivWithin_fun_id | Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"UniqueDiffOn",
"AddGroupWithOne.toAddMonoidWithOne",
"iteratedDerivWithin",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"id",
"instOfNatNat",
"Nor... | true |
MeasurableSpace.CountablySeparated.rec | Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated | [
"MeasurableSet",
"Set.univ",
"MeasurableSpace.CountablySeparated.mk",
"MeasurableSpace",
"MeasurableSpace.CountablySeparated",
"HasCountableSeparatingOn"
] | false |
PresheafOfModules.colimitPresheafOfModules_map | Mathlib.Algebra.Category.ModuleCat.Presheaf.Colimits | [
"PresheafOfModules.map",
"PresheafOfModules.evaluation",
"CategoryTheory.Functor",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CategoryTheory.Functor.comp",
"PresheafOfModules.instCategory",
"CategoryTheory.Functor.whiskerLeft",
"ModuleC... | true |
CategoryTheory.ProjectiveResolution.extAddEquivCohomologyClass._proof_1 | Mathlib.CategoryTheory.Abelian.Projective.Ext | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"Equiv.instEquivLike",
"congrArg",
"CochainComplex.singleFunctor",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Abelian.Ext.instAddCommGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",... | false |
CategoryTheory.Functor.Elements.coconeπOpCompShrinkYonedaObj_pt | Mathlib.CategoryTheory.Limits.Presheaf | [
"CategoryTheory.Functor.op",
"CategoryTheory.categoryOfElements",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.LocallySmall",
"CategoryTheory.shrinkYoneda",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryOfEleme... | true |
_private.Std.Data.Iterators.Lemmas.Consumers.Monadic.Set.0.Std.IterM.toExtTreeSet_eq_ofList._simp_1_3 | Std.Data.Iterators.Lemmas.Consumers.Monadic.Set | [
"Std.ExtTreeSet.ofList_eq_foldl",
"Ordering",
"List.foldl",
"Std.TransCmp",
"Std.ExtTreeSet.ofList",
"List",
"Std.ExtTreeSet",
"Std.ExtTreeSet.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq.symm",
"Eq",
"Std.ExtTreeSet.insert"
] | false |
Lean.Meta.checkAssignment | Lean.Meta.ExprDefEq | [
"Pure.pure",
"_private.Lean.Meta.ExprDefEq.0.Lean.Meta.mkLambdaFVarsWithLetDeps.collectLetDepsAux.match_1",
"Lean.instantiateMVars",
"Unit.unit",
"_private.Lean.Meta.ExprDefEq.0.Lean.Meta.typeOccursCheck",
"Bool.not",
"instMonadReaderOfReaderTOfMonad",
"instForInOfForIn'",
"Lean.Meta.Context.lctx",
... | true |
GetElem.getElem.congr_simp | Init.GetElem | [
"GetElem",
"Eq.rec",
"GetElem.getElem",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
Aesop.Frontend.evalSaturate? | Aesop.Frontend.Saturate | [
"Lean.TSyntax",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.State",
"Aesop.Frontend.evalSaturateCore",
"Lean.Syntax.isOfKind",
"Option.some",
"Lean.Elab.Tactic.Context",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecida... | true |
Lean.Elab.CommandContextInfo.fileMap | Lean.Elab.InfoTree.Types | [
"Lean.Elab.CommandContextInfo",
"Lean.FileMap"
] | true |
zero_le_four | Mathlib.Algebra.Order.Monoid.NatCast | [
"Eq.mpr",
"zero_le_three",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"Nat.instAtLeastTwoHAddOfNat",
"AddLeftMono",
"Preorder.toLE",
"three_add_one_eq_four",
"AddZeroClass.toAddZero",
"id",
"ZeroLEOneClass",
"add_nonneg",
"AddMonoidWithOne.toNatCast",
"instOfNatN... | true |
Aesop.NormM.Context.mk | Aesop.Search.Expansion.Norm | [
"Aesop.NormM.Context.mk",
"Aesop.Options'",
"Aesop.LocalRuleSet",
"Aesop.NormM.Context",
"Aesop.NormSimpContext"
] | true |
_private.Mathlib.RingTheory.Localization.Module.0.IsLocalizedModule.linearIndependent_lift._simp_1_1 | Mathlib.RingTheory.Localization.Module | [
"instHSMul",
"SMul",
"Membership.mem",
"Subtype",
"Submonoid.smul",
"Submonoid.smul_def",
"HSMul.hSMul",
"Submonoid.instSetLike",
"MulOneClass",
"Eq.symm",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"Submonoid"
] | false |
ENNReal.hasSum_coe._simp_1 | Mathlib.Topology.Algebra.InfiniteSum.ENNReal | [
"NNReal.instTopologicalSpace",
"ENNReal.ofNNReal",
"ENNReal.instAddCommMonoid",
"NNReal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"HasSum",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"ENNReal",
"propext",
"NNReal.instSemiring",
"ENNReal.instTopologicalSpace",
"ENNReal.hasSum_coe",
... | false |
Std.Http.Status.match_on_same_ctor.het._@.Std.Internal.Http.Data.Status.2943301344._hygCtx._hyg.108 | Std.Internal.Http.Data.Status | [
"Std.Http.Status.preconditionRequired",
"Std.Http.Status.noContent.elim",
"Std.Http.Status.requestTimeout",
"Std.Http.Status.locked.elim",
"Std.Http.Status.rangeNotSatisfiable",
"Std.Http.Status.rangeNotSatisfiable.elim",
"Std.Http.Status.expectationFailed",
"Std.Http.Status.notFound",
"Std.Http.Sta... | false |
Nat.mod_pow_succ | Init.Data.Nat.Mod | [
"instPowNat",
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"Nat.mod_mul",
"congrArg",
"Nat.pow_succ",
"id",
"HDiv.hDiv",
"Nat.instMod",
"instHMod",
"instMulNat",
"instOfNatNat",
"instNatPowNat",
"instHAdd",
"HMod.hMod",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"Nat.instDiv",
"instAddNat",
"E... | true |
FractionalIdeal.map_div | Mathlib.RingTheory.FractionalIdeal.Operations | [
"Eq.mpr",
"Submodule",
"IsDomain",
"RingHomSurjective.ids",
"CommRing",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"FractionalIdeal.isFractional_div_of_ne_zero",
"CommRing.toNonUnitalCommRing",
"AlgEquiv.toAlgHom",
"congrArg",
"CommSemiring.toSemiring",
"IsFractionRing",
... | true |
Int8.ofInt_neg | Init.Data.SInt.Lemmas | [
"instPowNat",
"congrArg",
"Int8.instNeg",
"Int8",
"Int8.toInt_neg",
"Int8.toInt",
"Int.instNegInt",
"Int8.toInt_inj",
"instOfNatNat",
"Int",
"Int.bmod_neg_bmod",
"instNatPowNat",
"Int8.size",
"HPow.hPow",
"Int.bmod",
"Nat",
"congr",
"True",
"eq_self",
"Iff.mp",
"of_eq_true",
... | true |
ProbabilityTheory.integral_tilted_mul_eq_mgf | Mathlib.Probability.Moments.Tilted | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"instHDiv",
"HMul.hMul",
"NormedSpace",
"MeasureTheory.integral_tilted",
"Real.instRCLike",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Real.instDivInvMonoid",
"N... | true |
MeasureTheory.SimpleFunc.approxOn.congr_simp | Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | [
"Measurable",
"MeasureTheory.SimpleFunc",
"Membership.mem",
"Eq.rec",
"Set.Elem",
"PseudoEMetricSpace",
"MeasurableSpace",
"PseudoEMetricSpace.toUniformSpace",
"Nat",
"MeasureTheory.SimpleFunc.approxOn",
"OpensMeasurableSpace",
"Eq.ndrec",
"Eq.refl",
"instTopologicalSpaceSubtype",
"Unifo... | true |
LieSubmodule.restr_toSubmodule | Mathlib.Algebra.Lie.Submodule | [
"Submodule",
"CommRing",
"LieSubmodule.restr",
"LieSubalgebra.instSetLike",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieSubmodule.toSubmodule",
"LieSubmodule",
"Membership.mem",
"AddCommGroup",
"Subtype",
"LieSubalgebra.lieRing",
"LieRing",
"CommRing.toCommSemiring",
"... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.minKey?_alterKey_eq_self._simp_1_3 | Std.Data.Internal.List.Associative | [
"Option.isNone",
"Option.isNone_iff_eq_none",
"Bool.true",
"Option.none",
"propext",
"Bool",
"Eq",
"Option"
] | false |
Turing.PartrecToTM2.unrev | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.K'.rev",
"Turing.PartrecToTM2.Γ'",
"Turing.PartrecToTM2.Λ'",
"Turing.PartrecToTM2.Λ'.move",
"Turing.PartrecToTM2.K'.main",
"Bool.false"
] | true |
CategoryTheory.Limits.Sigma.isoColimit.eq_1 | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Sigma.isoColimit",
"CategoryTheory.Limits.colimit.isColimit",
"CategoryTheory.Iso",
"CategoryTheory.Limits.HasCoproduct",
"CategoryTheory.Limits.colimit",
"CategoryTheory.Discrete.mk",
"CategoryTheory.Limits.coproductIsCoproduct'",
"CategoryTheory.dis... | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction.0.SSet.Truncated.liftOfStrictSegal_app_1._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | [
"False",
"Classical.byContradiction",
"eq_false_of_decide",
"Nat.not_le_eq",
"False.casesOn",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Bool",
"Lean.Grind.intro_with_eq",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Not",
"Nat.decLe",
"Eq.... | false |
CategoryTheory.Abelian.LeftResolution.chainComplexMap_f_succ_succ._proof_1 | Mathlib.Algebra.Homology.LeftResolution.Basic | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"CategoryTheory.Abelian... | false |
WeierstrassCurve.Projective.Point.toAffine | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Point | [
"WeierstrassCurve.Projective.neg._proof_1",
"instDecidableNot",
"WeierstrassCurve.Projective.toAffine",
"instHDiv",
"WeierstrassCurve.Projective.Nonsingular",
"WeierstrassCurve.Affine.Point.instZero",
"WeierstrassCurve.Projective.Point.toAffine._proof_1",
"Classical.propDecidable",
"Field.toDivision... | true |
_private.Mathlib.SetTheory.Ordinal.Notation.0.ONote.nf_repr_split'._simp_1_3 | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.NF",
"ONote.instZero",
"True",
"eq_true",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"ONote",
"ONote.NF.zero"
] | false |
MeasureTheory.exists_lt_lowerSemicontinuous_lintegral_ge | Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | [
"NNReal.instTopologicalSpace",
"Eq.mpr",
"add_lt_add_right",
"NonAssocSemiring.toAddCommMonoidWithOne",
"ENNReal.instAdd",
"le_refl",
"ENNReal.ofNNReal",
"Trans.trans",
"MeasureTheory.Measure",
"Preorder.toLT",
"instHDiv",
"NNReal.instSecondCountableTopology",
"AddMonoid.toAddSemigroup",
"... | true |
Continuous.cfcₙ_fun._auto_3 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Topology.IsLocallyConstructible.isConstructible_of_subset_of_isCompact | Mathlib.Topology.Constructible | [
"Filter.instMembership",
"Eq.mpr",
"IsOpen.isOpenEmbedding_subtypeVal",
"Set.iUnion₂_subset",
"congrArg",
"HEq.refl",
"Finset",
"Set.subset_inter_iff",
"IsRetrocompact",
"Subtype.image_preimage_coe",
"setOf",
"Topology.IsConstructible.preimage_of_isOpenEmbedding",
"Membership.mem",
"Exists... | true |
List.splitLengths_nil | Mathlib.Data.List.SplitLengths | [
"List",
"Nat",
"Eq",
"rfl",
"List.splitLengths",
"List.nil"
] | true |
Ultrafilter.mk.inj | Mathlib.Order.Filter.Ultrafilter.Defs | [
"Filter.NeBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"Ultrafilter.mk.noConfusion",
"Ultrafilter.mk",
"eq_of_heq",
"HEq",
"Ultrafilter",
"Eq",
"Filter",
"Filter.instPartialOrder"
] | true |
Valued.toUniformSpace | Mathlib.Topology.Algebra.Valued.ValuationTopology | [
"UniformSpace",
"outParam",
"LinearOrderedCommGroupWithZero",
"Valued",
"Ring"
] | true |
Nat.Partition.UniquePartitionZero._proof_2 | Mathlib.Combinatorics.Enumerative.Partition.Basic | [
"Nat.Partition.instInhabited",
"Inhabited.default",
"Nat.Partition.UniquePartitionZero._proof_1",
"instOfNatNat",
"Nat.Partition.ext",
"Nat.Partition",
"Nat",
"OfNat.ofNat",
"Eq"
] | false |
Set.notMem_Ioc_of_le | Mathlib.Order.Interval.Set.Basic | [
"Set.Ioc",
"Preorder.toLT",
"lt_irrefl",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"And.left",
"LT.lt.trans_le",
"LT.lt",
"Set.instMembership",
"Not",
"Preorder",
"Set"
] | true |
Order.Coframe.recOn | Mathlib.Order.CompleteBooleanAlgebra | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"Order.Coframe.mk",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"CompleteLattice.toBoundedOrder",
"LE.le",
"HNot.hnot",
"SDiff.sdiff",
"Iff",
"OrderTop.toTop",
"Order.Coframe",
"HNot",
"Max.max",
"BoundedO... | false |
CategoryTheory.SingleObj.inv_as_inv | Mathlib.CategoryTheory.SingleObj | [
"CategoryTheory.IsIso.inv_eq_of_hom_inv_id",
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"CategoryTheory.SingleObj.id_as_one",
"inv_mul_cancel",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Monoid.toMulOneClass",
"congrArg",
"Quiv... | true |
iSupIndep.subtype_ne_bot_le_finrank | Mathlib.LinearAlgebra.Dimension.Finite | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"IsDomain",
"IsOrderedRing.toZeroLEOneClass",
"Cardinal",
"iSupIndep",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"Cardinal.commSemiring",
"Module.IsTorsionFree",
"Cardinal.mk",
... | true |
LieDerivation.SMulBracketCommClass.rec | Mathlib.Algebra.Lie.Derivation.Basic | [
"instHSMul",
"LieDerivation.SMulBracketCommClass.mk",
"SMul",
"Bracket.bracket",
"AddCommGroup",
"LieRingModule.toBracket",
"LieRing",
"LieRingModule",
"HSMul.hSMul",
"LieDerivation.SMulBracketCommClass",
"Eq"
] | false |
Lean.Grind.IntModule.OfNatModule.instLTQOfOrderedAdd | Init.Grind.Module.Envelope | [
"LT.mk",
"LE.le",
"LE",
"Lean.Grind.IntModule.OfNatModule.Q",
"instHAdd",
"And",
"Std.IsPreorder",
"Lean.Grind.AddCommMonoid.toAdd",
"Lean.Grind.IntModule.OfNatModule.instLEQOfOrderedAdd",
"Lean.Grind.NatModule",
"Lean.Grind.OrderedAdd",
"Not",
"LT",
"Lean.Grind.NatModule.toAddCommMonoid"
... | true |
_private.Mathlib.FieldTheory.Extension.0.IntermediateField.Lifts.nonempty_algHom_of_exist_lifts_finset._simp_1_5 | Mathlib.FieldTheory.Extension | [
"Preorder.toLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"left_lt_sup",
"LE.le",
"Max.max",
"LT.lt",
"propext",
"SemilatticeSup.toPartialOrder",
"Eq",
"SemilatticeSup",
"Not"
] | false |
HahnSeries.instDistribMulAction._proof_4 | Mathlib.RingTheory.HahnSeries.Addition | [
"Monoid",
"instHSMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"HahnSeries.ext",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"AddZero.toZero",
"funext",
"instHAdd",
"AddSemigroup.toAdd",
"HahnSerie... | false |
PerfectClosure.instCommRing._proof_8 | Mathlib.FieldTheory.PerfectClosure | [
"Semigroup.toMul",
"CommRing",
"Nat.Prime",
"HMul.hMul",
"AddGroupWithOne.toAddMonoidWithOne",
"Fact",
"inferInstance",
"PerfectClosure.instCommMonoid",
"CommMonoid.toMonoid",
"Monoid.one_mul",
"Nat",
"Monoid.toSemigroup",
"One.toOfNat1",
"CharP",
"Monoid.toOne",
"PerfectClosure",
"C... | false |
CategoryTheory.ShortComplex.RightHomologyData.ofHasKernel_p | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.HasKernel",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.Sho... | true |
_private.Mathlib.RingTheory.Smooth.Kaehler.0.derivationOfSectionOfKerSqZero._simp_6 | Mathlib.RingTheory.Smooth.Kaehler | [
"Submodule",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"AddCommMonoid",
"Subtype.mk",
"AddZero.toZero",
"Submodule.setLike",
"propext",
"Semiring",
"Zero.toOfNat0",
"Submodule.zero",
"AddCommMonoid.toAddMonoid",
"Module",
"OfNat.ofNat",
"Eq",
... | false |
_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.ExprWithHoles.mk.inj | Lean.Elab.MutualDef | [
"_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.ExprWithHoles.mk",
"Lean.Syntax",
"Lean.Expr",
"And",
"And.intro",
"_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.ExprWithHoles",
"_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.ExprWithHoles.mk.noConfusion",
"Eq"
] | true |
CategoryTheory.ObjectProperty.IsClosedUnderQuotients.mk | Mathlib.CategoryTheory.ObjectProperty.EpiMono | [
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ObjectProperty.IsClosedUnderQuotients.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty",
"CategoryTheory.ObjectProperty.IsClosedUnderQuotients",
"CategoryTheory.Category"
] | true |
SimpleGraph.Subgraph.symm | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"Symmetric",
"SimpleGraph.Subgraph",
"SimpleGraph",
"SimpleGraph.Subgraph.Adj"
] | true |
Complex.instNormedField._proof_1 | Mathlib.Analysis.Complex.Basic | [
"Real",
"Complex.instNormedAddCommGroup",
"NormedAddCommGroup.toMetricSpace",
"MetricSpace.toPseudoMetricSpace",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Complex",
"Eq",
"rfl"
] | false |
Dyadic.instHShiftRightInt | Init.Data.Dyadic.Basic | [
"HShiftRight.mk",
"HShiftRight",
"Dyadic",
"Int",
"Dyadic.shiftRight"
] | true |
Mathlib.Tactic.Choose.choose1WithInfo | Mathlib.Tactic.Choose | [
"Pure.pure",
"Mathlib.Tactic.Choose.ChooseArg.expectedType?",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.MVarId.withContext",
"Lean.instMonadExceptOfExceptionCoreM",
"_private.Mathlib.Tactic.Choose.0.Mathlib.Tactic.Choose.choose1WithInfo.match_1",
"Lean.Elab.Term.instAddErrorMessageContextTermEla... | true |
Std.DHashMap.containsThenInsertIfNew | Std.Data.DHashMap.Basic | [
"Std.DHashMap.Raw",
"Prod.mk",
"instOfNatNat",
"Prod.fst",
"Std.DHashMap.Internal.Raw₀.containsThenInsertIfNew",
"_private.Std.Data.DHashMap.Basic.0.Std.DHashMap.containsThenInsertIfNew._proof_1",
"Subtype.mk",
"Std.DHashMap.inner",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.mk"... | true |
Complex.sin_add_int_mul_two_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Int.cast",
"Function.Periodic.int_mul",
"Real.pi",
"HMul.hMul",
"Complex.commRing",
"Complex.sin",
"Nat.instAtLeastTwoHAddOfNat",
"Complex.instMul",
"instOfNatNat",
"Int",
"Complex.instNatCast",
"Complex.instIntCast",
"CommRing.toNonAssocCommRing",
"Complex.ofReal",
"instHAdd",
"Compl... | true |
Option.forM_some | Init.Data.Option.Monadic | [
"Option.instForMOfMonad",
"ForM.forM",
"Option.some",
"PUnit",
"Monad",
"Eq",
"rfl",
"Option"
] | true |
_private.Init.Data.String.Lemmas.Pattern.Find.String.0.String.Slice.isInfix_toList_iff | Init.Data.String.Lemmas.Pattern.Find.String | [
"String.toList_ofList",
"String.toList_inj",
"List.append_assoc",
"congrArg",
"String",
"Exists",
"List.IsInfix",
"instAppendString",
"instHAppendOfAppend",
"List",
"Iff",
"Exists.casesOn",
"String.toList",
"congr",
"True",
"Iff.intro",
"eq_self",
"Exists.intro",
"Iff.mp",
"of_... | true |
PartialEquiv.symm_image_target_eq_source | Mathlib.Logic.Equiv.PartialEquiv | [
"PartialEquiv.target",
"PartialEquiv",
"PartialEquiv.image_source_eq_target",
"PartialEquiv.symm",
"PartialEquiv.source",
"Set.image",
"PartialEquiv.toFun",
"Eq",
"Set"
] | true |
Lean.Elab.Tactic.Do.BVarUses.rec | Lean.Elab.Tactic.Do.LetElim | [
"Lean.Elab.Tactic.Do.BVarUses",
"Vector",
"Lean.Elab.Tactic.Do.Uses",
"Lean.Elab.Tactic.Do.BVarUses.none",
"Lean.Elab.Tactic.Do.BVarUses.some",
"Nat"
] | false |
Std.TreeMap.mem_union_iff | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Iff",
"Std.TreeMap.instMembership",
"Std.DTreeMap.mem_union_iff",
"Or",
"Union.union",
"Std.TreeMap.instUnion",
"Std.TreeMap"
] | true |
_private.Mathlib.Topology.AlexandrovDiscrete.0.alexandrovDiscrete_iff_nhds._simp_1_2 | Mathlib.Topology.AlexandrovDiscrete | [
"Membership.mem",
"IsClosed",
"TopologicalSpace",
"ClusterPt",
"isClosed_iff_clusterPt",
"propext",
"Filter.principal",
"Eq",
"Set.instMembership",
"Set"
] | false |
Std.Do.PredTrans.throw | Std.Do.PredTrans | [
"Std.Do.PostShape.except",
"Std.Do.PostCond",
"Std.Do.Assertion",
"Std.Do.PostShape",
"Prod.fst",
"Std.Do.PredTrans.mk",
"Std.Do.PredTrans",
"Std.Do.PredTrans.throw._proof_1",
"Prod.snd",
"Std.Do.ExceptConds"
] | true |
CategoryTheory.Functor.mapSquare_obj | Mathlib.CategoryTheory.Square | [
"CategoryTheory.Functor",
"CategoryTheory.Square.category",
"CategoryTheory.Square",
"CategoryTheory.Square.map",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Functor.mapSquare",
"CategoryTheory.Category"
] | true |
RCLike.add_conj | Mathlib.Analysis.RCLike.Basic | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RCLike.re_add_im",
"Real",
"Trans.trans",
"NormedRing.toRing",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Real.instAddMonoid",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid... | true |
ModuleCat.shortComplexOfConj_exact | Mathlib.Algebra.Homology.ShortComplex.ModuleCat | [
"Function.Exact",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"LinearMap",
"_private.Mathlib.Algebra.Homology.ShortComplex.ModuleCat.0.e... | true |
Lean.Meta.Simp.Arith.Nat.toLinearExpr | Lean.Meta.Tactic.Simp.Arith.Nat.Basic | [
"Pure.pure",
"Lean.Meta.Simp.Arith.Nat.LinearExpr",
"Nat.Linear.Expr.applyPerm",
"Lean.Meta.State",
"Lean.Perm",
"Nat.Linear.Expr",
"Lean.Meta.Simp.Arith.Nat.ToLinear.toLinearExpr",
"Lean.sortExprs",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"Prod.mk",
"instOfN... | true |
IsLocalization.adjoin_inv | Mathlib.RingTheory.Localization.Away.AdjoinRoot | [
"Polynomial.C",
"Polynomial.instOne",
"CommRing",
"HMul.hMul",
"AdjoinRoot",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"Localization.awayEquivAdjoin",
"HSub.hSub",
"IsLocalization.Away",
"Localization.Away",
"RingHom",
"Algebra.id",
"Polynomial",
"AdjoinRoot.instAlgebra",... | true |
WeierstrassCurve.Projective.baseChange_polynomialY | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Basic | [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instMulZeroClass",
"CommRing",
"AlgHom.algHomClass",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"WeierstrassCurve.Projective.polynomialY",
"AlgHom.funLike",
"AddMonoid.toAddZeroClass",
"Algebra",
"Nat.instAddMonoid",
"Ring... | true |
Lean.Linter.MissingDocs.lintNamed | Lean.Linter.MissingDocs | [
"Lean.Syntax.getId",
"String",
"Lean.Syntax",
"ToString.toString",
"instAppendString",
"instHAppendOfAppend",
"Unit",
"Lean.Linter.MissingDocs.lint",
"Lean.Name.instToString",
"Lean.Name",
"Lean.Elab.Command.CommandElabM",
"HAppend.hAppend",
"instToStringString"
] | true |
_private.Lean.Elab.Tactic.Omega.Frontend.0.Lean.Elab.Tactic.Omega.asLinearComboImpl.handleNatCast.match_1 | Lean.Elab.Tactic.Omega.Frontend | [
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"_private.Lean.Elab.Tactic.Omega.Frontend.0.Lean.Elab.Tactic.Omega.asLinearComboImpl.handleNatCast._sparseCasesOn_1",
"Option"
] | false |
_private.Lean.Compiler.LCNF.ToDecl.0.Lean.Compiler.LCNF.macroInline._sparseCasesOn_1 | Lean.Compiler.LCNF.ToDecl | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
isExtrFilter_dual_iff | Mathlib.Order.Filter.Extr | [
"OrderDual.toDual",
"Equiv.instEquivLike",
"IsMinFilter",
"Function.comp",
"Equiv",
"Iff",
"IsExtrFilter",
"OrderDual",
"or_comm",
"OrderDual.instPreorder",
"DFunLike.coe",
"Filter",
"Preorder",
"EquivLike.toFunLike",
"IsMaxFilter"
] | true |
BddLat.hasForgetToBddOrd._proof_1 | Mathlib.Order.Category.BddLat | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"BoundedLatticeHom.toBoundedOrderHom",
"BddLat.toLat",
"Lat.carrier",
"SemilatticeInf.toPartialOrder",
"CategoryTheory.CategoryStruct.id",
"id",
"BddOrd",
"BddLat.instLargeCategory",
"BddOrd.of",
"BddOrd.ofHom",
"BddLat",
"BddLat.Hom.... | false |
AddHom.instAdd.eq_1 | Mathlib.Algebra.Group.Hom.Basic | [
"AddHom.instAdd",
"AddHom",
"AddHom.instAdd._proof_1",
"Add.mk",
"AddHom.funLike",
"instHAdd",
"HAdd.hAdd",
"Eq.refl",
"AddCommSemigroup.toAddCommMagma",
"AddHom.mk",
"AddCommSemigroup",
"Eq",
"DFunLike.coe",
"Add",
"AddCommMagma.toAdd"
] | true |
CoalgCat.mk.noConfusion | Mathlib.Algebra.Category.CoalgCat.Basic | [
"CommRing",
"CoalgCat",
"Coalgebra",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"id",
"CoalgCat.noConfusion",
"CoalgCat.mk",
"heq_of_eq",
"CommRing.toCommSemiring",
"ModuleCat.isAddCommGroup",
"ModuleCat.carrier",
"Eq.refl",
"HEq",
"CommRing.toRing",
"Eq",
"ModuleCat.... | false |
Prod.seminormedRing._proof_12 | Mathlib.Analysis.Normed.Ring.Basic | [
"Semiring.toNatCast",
"AddMonoid.toAddSemigroup",
"Semiring.natCast_succ",
"SeminormedRing.toRing",
"instOfNatNat",
"NatCast.natCast",
"Prod.instRing",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"Semiring.toMonoid",
"One.toOfNat1",
"instAddNat",
"Monoid.toOne",
"AddCommMonoi... | false |
Nat.div_ne_zero_iff_of_dvd | Init.Data.Nat.Lemmas | [
"False",
"Dvd.dvd",
"instHDiv",
"eq_false",
"and_true",
"congrArg",
"not_true_eq_false",
"HDiv.hDiv",
"Ne",
"instOfNatNat",
"false_or",
"LE.le",
"instLENat",
"Or.casesOn",
"iff_self",
"Nat.div_zero",
"Nat.not_lt._simp_1",
"And",
"Iff",
"Nat.instDvd",
"Decidable.em",
"Nat",
... | true |
Lean.Widget.instEmptyCollectionInteractiveGoals | Lean.Widget.InteractiveGoal | [
"Lean.Widget.InteractiveGoals",
"EmptyCollection.mk",
"Lean.Widget.InteractiveGoals.mk",
"List.toArray",
"EmptyCollection",
"Lean.Widget.InteractiveGoal",
"List.nil"
] | true |
CategoryTheory.Functor.Faithful.div_comp | Mathlib.CategoryTheory.Functor.FullyFaithful | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.Faithful.div",
"CategoryTheory.Functor.casesOn",
"CategoryTheory.Functor.comp",
"heq_eq_eq",
"Function.comp",
"CategoryTheory.Functor.comp._proof_2",
"CategoryTh... | true |
ModuleCat.Hom._sizeOf_1 | Mathlib.Algebra.Category.ModuleCat.Basic | [
"ModuleCat.Hom",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"instSizeOfDefault",
"instOfNatNat",
"ModuleCat.Hom.rec",
"LinearMap",
"instHAdd",
"ModuleCat.isAddCommGroup",
"HAdd.hAdd",
"Nat",
"ModuleCat.carrier",
"SizeOf.sizeOf",
"instAddNat",
"LinearMap._sizeOf_inst",
"SizeOf",
"Of... | false |
PseudoEpimorphismClass.recOn | Mathlib.Topology.Order.Hom.Esakia | [
"Preorder.toLE",
"PseudoEpimorphismClass.rec",
"Exists",
"LE.le",
"PseudoEpimorphismClass",
"And",
"RelHomClass",
"Eq",
"DFunLike.coe",
"PseudoEpimorphismClass.mk",
"Preorder",
"FunLike"
] | false |
CategoryTheory.Subgroupoid.obj_surjective_of_im_eq_top | Mathlib.CategoryTheory.Groupoid.Subgroupoid | [
"Eq.mpr",
"CategoryTheory.Functor",
"congrArg",
"CategoryTheory.Subgroupoid.im",
"CategoryTheory.Subgroupoid.instTop",
"Membership.mem",
"Exists",
"CategoryTheory.Groupoid",
"id",
"CategoryTheory.Subgroupoid",
"propext",
"CategoryTheory.Subgroupoid.mem_top_objs",
"Function.Injective",
"Cat... | true |
NNRat.coe_pow._simp_1 | Mathlib.Data.NNRat.Defs | [
"CommSemiring.toSemiring",
"Rat",
"Rat.instPowNat",
"NNRat",
"Monoid.toPow",
"instCommSemiringNNRat",
"HPow.hPow",
"Nat",
"Rat.instNNRatCast",
"Semiring.toMonoid",
"instHPow",
"NNRat.coe_pow",
"Eq.symm",
"NNRat.cast",
"Eq"
] | false |
_private.Mathlib.LinearAlgebra.Matrix.ToLin.0.LinearMap.toMatrix_basis_equiv._simp_1_1 | Mathlib.LinearAlgebra.Matrix.ToLin | [
"eq_comm",
"propext",
"Eq"
] | false |
List.IsChain.backwards_cons_induction | Mathlib.Data.List.Chain | [
"List.getLast",
"Membership.mem",
"Eq.rec",
"List.IsChain",
"List.IsChain.backwards_induction",
"Ne",
"List.cons",
"List",
"List.instMembership",
"List.cons_ne_nil",
"Eq.symm",
"Eq",
"List.nil"
] | true |
NonUnitalAlgHom.Lmul._proof_4 | Mathlib.Analysis.Normed.Operator.Mul | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalSeminormedRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.toUniformContinuousConstSMul",
"... | false |
CategoryTheory.Pretopology.trivial._proof_2 | Mathlib.CategoryTheory.Sites.Pretopology | [
"Eq.mpr",
"CategoryTheory.IsIso",
"CategoryTheory.Presieve.singleton.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"congrArg",
"HEq.refl",
"setOf",
"Membership.mem",
"Exists",
"inferInstance",
"Eq.mp",
"id",
"CategoryTheory.Presieve.bind",
"Cat... | false |
_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.Methods.toMethodsRef.unsafe_impl_2 | Lean.Meta.Tactic.Grind.Types | [
"Classical.ofNonempty",
"Lean.Meta.Grind.instNonemptyMethodsRef",
"Lean.Meta.Grind.Methods",
"Lean.Meta.Grind.MethodsRef",
"Pi.instNonempty"
] | true |
Module.Relations.solutionFinsupp._proof_1 | Mathlib.Algebra.Module.Presentation.Free | [
"Semiring.toModule",
"Finsupp.module",
"Ring.toNonAssocRing",
"AddCommGroup.toAddCommMonoid",
"False.elim",
"AddGroupWithOne.toAddMonoidWithOne",
"LinearMap.instFunLike",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Module.Relations.relation",
"SubtractionMonoid.toSubNegZeroMonoid",
"Is... | false |
CategoryTheory.MorphismProperty.epimorphisms.iff._simp_1 | Mathlib.CategoryTheory.MorphismProperty.Basic | [
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.epimorphisms.iff",
"CategoryTheory.MorphismProperty.epimorphisms",
"propext",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
OrderRingHom.apply_eq_self | Mathlib.Algebra.Order.Archimedean.Hom | [
"Eq.mpr",
"OrderRingHom.eq_id",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"OrderRingHom.instFunLike",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"NonUni... | true |
SheafOfModules.evaluationPreservesLimitsOfSize | Mathlib.Algebra.Category.ModuleCat.Sheaf.Limits | [
"CategoryTheory.Functor",
"Opposite",
"ModuleCat",
"SheafOfModules.evaluationPreservesLimitsOfShape",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.PreservesLimitsOfSize.mk",
"inferInstance",
"UnivLE.small",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"RingCat",
"UnivLE.self... | true |
RelIso.emptySumLex_apply | Mathlib.Order.RelIso.Basic | [
"Sum.swap",
"Equiv.instEquivLike",
"Sum",
"Equiv",
"IsEmpty",
"RelIso",
"RelIso.instFunLike",
"Eq.refl",
"RelIso.emptySumLex",
"Eq",
"DFunLike.coe",
"Sum.Lex",
"EquivLike.toFunLike",
"Equiv.sumEmpty"
] | true |
_private.Mathlib.Probability.Moments.Variance.0.ProbabilityTheory.evariance_eq_zero_iff._simp_1_2 | Mathlib.Probability.Moments.Variance | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
cfcₙ_smul._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
NonUnitalCommCStarAlgebra.recOn | Mathlib.Analysis.CStarAlgebra.Classes | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"instSMulOfMul",
"NormedSpace",
"NonUnitalNonAssocRing.toMul",
"NonUnitalCommCStarAlgebra",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"NormedSpace.toModule",
"NonUnitalNonAssocRing.toAddCommGroup",
"Complex.instNormedField"... | false |
IsDedekindDomain.HeightOneSpectrum.adicAbv._proof_1 | Mathlib.RingTheory.DedekindDomain.AdicValuation | [
"Real.instLE",
"Real",
"CommRing",
"Preorder.toLT",
"Real.instZero",
"IsFractionRing",
"IsDedekindDomain.HeightOneSpectrum.adicAbvDef",
"PartialOrder.toPreorder",
"IsDedekindDomain.HeightOneSpectrum",
"Algebra",
"NNReal",
"LE.le",
"Field.toSemifield",
"NNReal.instPartialOrder",
"CommRing... | false |
Nat.dvd_of_mem_primeFactorsList | Mathlib.Data.Nat.Factors | [
"Nat.mem_primeFactorsList_iff_dvd",
"Eq.mpr",
"dvd_zero",
"Dvd.dvd",
"Nat.prime_of_mem_primeFactorsList",
"Nat.instSemigroupWithZero",
"congrArg",
"Membership.mem",
"id",
"instOfNatNat",
"Or.casesOn",
"LT.lt.ne'",
"GT.gt",
"List",
"Nat.instDvd",
"List.instMembership",
"Nat.instPreord... | true |
_private.Mathlib.LinearAlgebra.Finsupp.Span.0.Finsupp.iInf_ker_lapply_le_bot._simp_1_2 | Mathlib.LinearAlgebra.Finsupp.Span | [
"Submodule",
"iInf",
"Submodule.mem_iInf",
"Membership.mem",
"AddCommMonoid",
"Submodule.setLike",
"propext",
"Semiring",
"Module",
"Eq",
"SetLike.instMembership",
"Submodule.instInfSet"
] | false |
Std.LinearPreorderPackage.le_total | Init.Data.Order.PackageFactories | [
"Std.LinearPreorderPackage.toPreorderPackage",
"LE.le",
"Or",
"Std.LinearPreorderPackage",
"Std.PreorderPackage.toLE"
] | true |
_private.Mathlib.Algebra.Lie.Semisimple.Basic.0.LieAlgebra.IsSemisimple.isSimple_of_isAtom._simp_1_15 | Mathlib.Algebra.Lie.Semisimple.Basic | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
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