name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
SpecialLinearGroup.centerEquivRootsOfUnity.eq_1 | Mathlib.LinearAlgebra.SpecialLinearGroup | [
"SpecialLinearGroup.centerEquivRootsOfUnity._proof_4",
"Nontrivial",
"LinearMap.id",
"SpecialLinearGroup.centerEquivRootsOfUnity._proof_6",
"LinearEquiv.det",
"SpecialLinearGroup.centerEquivRootsOfUnity_invFun",
"CommRing",
"instHSMul",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass... | true |
Equiv.traverse.eq_1 | Mathlib.Control.Traversable.Equiv | [
"Equiv.instEquivLike",
"Equiv.traverse",
"Equiv",
"Applicative",
"Traversable.traverse",
"Traversable",
"Applicative.toFunctor",
"Eq.refl",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"Functor.map",
"EquivLike.toFunLike"
] | true |
MvPolynomial.pderiv_X_of_ne | Mathlib.Algebra.MvPolynomial.PDeriv | [
"Derivation",
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semiring.toModule",
"eq_false",
"AddMonoidAlgebra.addAddCommMonoid",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"MvPolynomial.X",
"AddMonoidAlgebra.commSemiring",
"... | true |
RelSeries.head_append | Mathlib.Order.RelSeries | [
"instNeZeroNatHAdd_1",
"SetRel",
"RelSeries.last",
"Membership.mem",
"Fin.instOfNat",
"RelSeries.length",
"Prod.mk",
"instOfNatNat",
"RelSeries",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"RelSeries.append",
"RelSeries.append_apply_left",
"instAddNat",
"RelSeries.head",
... | true |
RestrictedProduct.instMonoidCoeOfSubmonoidClass._proof_4 | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"SetLike",
"Monoid",
"MulOne.toOne",
"Monoid.toMulOneClass",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"MulOneClass.toMulOne",
"RestrictedProduct.instOneCoeOfOneMemClass",
"SetLike.coe",
"One.toOfNat1",
"RestrictedProduct.instMonoidCoeOfSubmonoidClass._proof_2",
"SubmonoidClass",
... | false |
Subsingleton.measurable | Mathlib.MeasureTheory.MeasurableSpace.Basic | [
"Subsingleton.measurableSet",
"MeasurableSet",
"Measurable",
"MeasurableSpace",
"Set.preimage",
"Subsingleton",
"Set"
] | true |
_private.Mathlib.RingTheory.AdicCompletion.Exactness.0.AdicCompletion.mapPreimage._proof_2 | Mathlib.RingTheory.AdicCompletion.Exactness | [
"Exists.choose_spec",
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup",
"instOfNatNat",
"Ideal",
"LinearMap",
"CommRing.toCommSemiring",
"Nat",
"Exists.choose",
"AdicCompletion.IsAdicCauchy",
"_private.Mathlib.RingTheory.AdicCom... | false |
Ideal.isPrime_map_of_isLocalizationAtPrime | Mathlib.RingTheory.Localization.AtPrime.Basic | [
"Semiring.toModule",
"ChainCompletePartialOrder.instOfCompleteLattice",
"SetLike.coe_subset_coe._simp_1",
"compl_compl",
"Algebra.algebraMap",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"CommSemiring.toSemiring",
"Compl.compl",
"PartialOrder.toPreorder",
"Algebra",
"Preorde... | true |
TensorProduct.ext' | Mathlib.LinearAlgebra.TensorProduct.Basic | [
"Eq.mpr",
"LinearMap.map_add",
"SemilinearMapClass.distribMulActionSemiHomClass",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"AddZeroClass.toAddZero",
"map_zero",
"id",
"LinearMap.se... | true |
CategoryTheory.Limits.hasFiniteProducts_of_hasFiniteLimits | Mathlib.CategoryTheory.Limits.Shapes.FiniteProducts | [
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Limits.HasFiniteLimits",
"inferInstance",
"Fin.fintype",
"CategoryTheory.Limits.HasFiniteProducts.mk",
"CategoryTheory.discreteCategory",
"Nat",
"CategoryTheory.finCategoryDiscreteOfFintype",
"Fin",
"CategoryTheory.Limits.HasFiniteProducts"... | true |
_private.Mathlib.Topology.MetricSpace.Bounded.0.IsComplete.nonempty_iInter_of_nonempty_biInter._simp_1_1 | Mathlib.Topology.MetricSpace.Bounded | [
"Set.iInter",
"Membership.mem",
"Set.mem_iInter",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
ModularForm.const_apply | Mathlib.NumberTheory.ModularForms.Basic | [
"ModularForm",
"ModularForm.const",
"Real",
"Subgroup.HasDetOne",
"Matrix",
"instDecidableEqFin",
"Real.semiring",
"Subgroup",
"instOfNatNat",
"Int",
"Units.instGroup",
"Real.commRing",
"Fin.fintype",
"instOfNat",
"UpperHalfPlane",
"Nat",
"Semiring.toMonoid",
"Matrix.GeneralLinearG... | true |
LieIdeal.map_sup_ker_eq_map' | Mathlib.Algebra.Lie.Ideal | [
"LieHom",
"LieAlgebra.toModule",
"Eq.mpr",
"CommRing",
"Lattice.toSemilatticeSup",
"LieRing.toAddCommGroup",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"LieIdeal.map",
"Eq.mp",
"id",
"LE.le",
"LieRing",
"LieHom.ker",
"Max... | true |
Set.vadd_empty | Mathlib.Algebra.Group.Pointwise.Set.Scalar | [
"VAdd",
"HVAdd.hVAdd",
"Set.image2_empty_right",
"instHVAdd",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Set.vadd",
"Eq",
"Set"
] | true |
ProofWidgets.CheckRequestResponse.ctorElimType | ProofWidgets.Cancellable | [
"cond",
"Lean.Json",
"ProofWidgets.CheckRequestResponse",
"Nat.ble",
"ProofWidgets.CheckRequestResponse.done",
"PULift",
"Nat",
"ProofWidgets.CheckRequestResponse.running",
"ProofWidgets.LazyEncodable"
] | false |
CategoryTheory.MorphismProperty.HasQuotient.iff_of_eqvGen | Mathlib.CategoryTheory.MorphismProperty.Quotient | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Iff.rfl",
"HomRel",
"CategoryTheory.MorphismProperty.HasQuotient",
"CategoryTheory.HomRel.IsStableUnderPostcomp",
"Iff",
"CategoryTheory.MorphismProperty.HasQuotient.iff",
"Iff.trans",
"CategoryTheory.Cat... | true |
Lean.Lsp.instFromJsonDiagnosticCode.match_1 | Lean.Data.Lsp.Diagnostics | [
"Lean.Json",
"String",
"Lean.Json.ctorIdx",
"Lean.JsonNumber",
"Nat.hasNotBit",
"Lean.JsonNumber.mk",
"instOfNatNat",
"Int",
"dite",
"Lean.JsonNumber.casesOn",
"Nat",
"Lean.Lsp.instFromJsonDiagnosticCode._sparseCasesOn_1",
"Eq.ndrec_symm",
"instDecidableEqNat",
"OfNat.ofNat",
"Lean.Jso... | false |
Std.ExtTreeSet.contains_max? | Std.Data.ExtTreeSet.Lemmas | [
"Option.some",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Bool.true",
"Unit",
"Std.ExtTreeSet",
"Bool",
"Std.ExtTreeSet.contains",
"Std.ExtTreeSet.max?",
"Eq",
"Std.ExtTreeMap.contains_maxKey?",
"Option"
] | true |
CategoryTheory.Functor.mapTriangleInvRotateIso_inv_app_hom₃ | Mathlib.CategoryTheory.Triangulated.Functor | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Pretriangulated.Triangle.obj₃",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.mapTriangleInvRotateIso",
"CategoryTheory.Functor.comp",
"CategoryTheory.Cat... | true |
instDecidableEqDihedralGroup.decEq._proof_1 | Mathlib.GroupTheory.SpecificGroups.Dihedral | [
"ZMod",
"DihedralGroup.r",
"Nat",
"DihedralGroup",
"Eq",
"rfl"
] | false |
_private.Mathlib.Topology.MetricSpace.HausdorffDimension.0.hausdorffMeasure_of_lt_dimH._simp_1_1 | Mathlib.Topology.MetricSpace.HausdorffDimension | [
"Preorder.toLT",
"iSup",
"PartialOrder.toPreorder",
"Exists",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"LT.lt",
"propext",
"CompleteSemilatticeSup.toSupSet",
"CompleteLinearOrder",
"CompleteLattice.toCompleteSemilatticeSup",
"Eq",
"CompleteLinearOr... | false |
Int16.toInt_div_of_ne_left | Init.Data.SInt.Lemmas | [
"Eq.mpr",
"instHDiv",
"Int16",
"congrArg",
"Int16.instOfNat",
"Int16.toBitVec_ofNat",
"BitVec",
"Eq.mp",
"id",
"HDiv.hDiv",
"BitVec.toInt_sdiv_of_ne_or_ne",
"Ne",
"instOfNatNat",
"Int",
"BitVec.ofNat",
"BitVec.instNeg",
"Int16.toBitVec_neg",
"BitVec.sdiv",
"Int.tdiv",
"Int16.to... | true |
Filter.TendstoCofinite.mk | Mathlib.Order.Filter.TendstoCofinite | [
"Filter.Tendsto",
"Filter.cofinite",
"Filter.TendstoCofinite.mk",
"Filter.TendstoCofinite"
] | true |
CategoryTheory.SimplicialObject.σ₀Iter_δ'._auto_5 | Mathlib.AlgebraicTopology.SimplicialObject.DeltaZeroIter | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.MonoidalCategory.InducedLawfulDayConvolutionMonoidalCategoryStructCore.ofHasDayConvolutions._proof_1 | Mathlib.CategoryTheory.Monoidal.DayConvolution | [
"CategoryTheory.MonoidalCategory.DayConvolution.convolution",
"CategoryTheory.Functor",
"CategoryTheory.Functor.pointwiseLeftKanExtensionUnit",
"CategoryTheory.Functor.essImage.getIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.c... | false |
Std.Tactic.BVDecide.BVLogicalExpr.bitblast.go.match_3 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Substructure | [
"Unit.unit",
"Std.Tactic.BVDecide.Gate.xor",
"Std.Tactic.BVDecide.Gate.or",
"Std.Tactic.BVDecide.Gate.casesOn",
"Std.Tactic.BVDecide.Gate.and",
"Unit",
"Std.Tactic.BVDecide.Gate",
"Std.Tactic.BVDecide.Gate.beq"
] | false |
CategoryTheory.Functor.LaxLeftLinear.μₗ | Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction.toMonoidalLeftActionStruct",
"CategoryTheory.MonoidalCategory.Mon... | true |
Function.Injective.groupWithZero | Mathlib.Algebra.GroupWithZero.InjSurj | [
"Nontrivial",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",
"DivInvMonoid.toInv",
"instHDiv",
"Function.Injective.groupWithZero._proof_3",
"One",
"Inv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"Pow",
"Function.Injective.monoidWithZero",
"GroupWithZero",
"Di... | true |
ENat.floor_le_self | Mathlib.Algebra.Order.Floor.Extended | [
"le_rfl",
"ENat.le_floor",
"instPreorderENat",
"ENat.toENNReal",
"LE.le",
"instLEENat",
"ENat.floor",
"ENat",
"ENNReal.instLE",
"ENNReal",
"Iff.mp"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Extremal.Turan.0.SimpleGraph.sum_ne_add_mod_eq_sub_one | Mathlib.Combinatorics.SimpleGraph.Extremal.Turan | [
"Nat.mul_add_mod_self_left",
"Eq.mpr",
"instDecidableNot",
"Nat.instCanonicallyOrderedAdd",
"Nat.mod_zero",
"MulOne.toOne",
"Nat.instOrderedSub",
"HMul.hMul",
"Nat.instDecidableModEq",
"congrArg",
"Finset",
"add_assoc",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HSub.hSub",
... | true |
MLList.filterMap | Batteries.Data.MLList.Basic | [
"Pure.pure",
"Monad.toApplicative",
"Applicative.toPure",
"MLList.filterMapM",
"Monad",
"MLList",
"Option"
] | true |
Std.Http.Method.uncheckout.sizeOf_spec | Std.Internal.Http.Data.Method | [
"Std.Http.Method",
"instOfNatNat",
"Std.Http.Method.uncheckout",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"Std.Http.Method._sizeOf_inst",
"OfNat.ofNat",
"Eq"
] | true |
CFC.log_one | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"IsSelfAdjoint",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"cfc_apply_one",
"NormedRing.toRing",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"... | true |
_private.Init.Data.Range.Polymorphic.SInt.0.Int32.instUpwardEnumerable._proof_1 | Init.Data.Range.Polymorphic.SInt | [
"Int32.minValue",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
... | false |
FirstOrder.Language.HomClass.mk._flat_ctor | Mathlib.ModelTheory.Basic | [
"outParam",
"Function.comp",
"FirstOrder.Language.Structure.RelMap",
"FirstOrder.Language.Structure",
"FirstOrder.Language.HomClass",
"FirstOrder.Language.HomClass.mk",
"Nat",
"FirstOrder.Language.Relations",
"FirstOrder.Language.Functions",
"FirstOrder.Language",
"FirstOrder.Language.Structure.... | false |
TendstoLocallyUniformlyOn.tendsto_at | Mathlib.Topology.UniformSpace.LocallyUniformConvergence | [
"Pure.pure",
"UniformSpace",
"Eq.mpr",
"TendstoLocallyUniformlyOn",
"congrArg",
"nhdsWithin",
"PartialOrder.toPreorder",
"TendstoUniformlyOnFilter.tendsto_at",
"Preorder.toLE",
"TendstoUniformlyOnFilter",
"Membership.mem",
"nhds",
"Set.instSingletonSet",
"id",
"LE.le",
"TopologicalSpac... | true |
CategoryTheory.StrictlyUnitaryLaxFunctor.mk.injEq | Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.StrictlyUnitaryLaxFunctor.map_id._autoParam",
"Eq.propIntro",
"CategoryTheory.eqToHom",
"CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_eq_eqToHom._autoParam",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.toCateg... | true |
padicValInt | Mathlib.NumberTheory.Padics.PadicVal.Basic | [
"padicValNat",
"Int",
"Nat",
"Int.natAbs"
] | true |
Int.Linear.instBEqPoly.beq_spec | Init.Data.Int.Linear | [
"Int.Linear.instBEqPoly.beq.eq_def",
"Int.Linear.instBEqPoly.beq.match_1",
"Int.instDecidableEq",
"Eq.mp",
"Bool.and",
"Int",
"Int.Linear.Var",
"instBEqOfDecidableEq",
"Int.Linear.instBEqPoly.beq",
"Int.Linear.instBEqPoly",
"BEq.beq",
"Bool",
"Eq.refl",
"instDecidableEqNat",
"Bool.false"... | true |
Partition.mem_removeBot | Mathlib.Order.Partition.Basic | [
"sSupIndep",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"OrderBot.toBot",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"Ne",
"Bot.bot",
"And",
"Partition",
"Iff",... | true |
_private.Lean.Elab.Tactic.Do.ProofMode.Frame.0.Lean.Elab.Tactic.Do.ProofMode.transferHypNames.label.match_5 | Lean.Elab.Tactic.Do.ProofMode.Frame | [
"_private.Lean.Elab.Tactic.Do.ProofMode.Frame.0.Lean.Elab.Tactic.Do.ProofMode.transferHypNames.label._sparseCasesOn_5",
"Nat.hasNotBit",
"List.cons",
"List",
"Lean.Elab.Tactic.Do.ProofMode.Hyp",
"List.ctorIdx"
] | false |
Std.ExtDHashMap.getD_ofList_of_contains_eq_false | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.getD",
"List.map",
"List.contains",
"LawfulBEq",
"Sigma.fst",
"List",
"Std.DHashMap.getD_ofList_of_contains_eq_false",
"Bool",
"Hashable",
"Bool.false",
"BEq",
"Eq",
"Sigma",
"Std.ExtDHashMap.ofList"
] | true |
Std.ExtDTreeMap.get_getKey? | Std.Data.ExtDTreeMap.Lemmas | [
"Iff.mpr",
"Std.ExtDTreeMap.mk",
"Std.ExtDTreeMap.mem_iff_isSome_getKey?",
"Std.ExtDTreeMap.getKey?",
"Std.DTreeMap",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Option.get",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Bool",
"Std.DTreeMap.get_getKey?",
"Option.isS... | true |
MeasureTheory.Measure.singularPart_eq_zero | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | [
"Eq.mpr",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure",
"congrArg",
"MeasureTheory.Measure.haveLebesgueDecomposition_add",
"AddMonoid.toAddZeroClass",
"MeasureTheory.Measure.rnDeriv",
"AddZeroClass.toAddZero",
"MeasureTheory.Measure.AbsolutelyContinuous",
"Eq.mp",
"id",
"Measur... | true |
CliffordAlgebra.ofBaseChangeAux._proof_5 | Mathlib.LinearAlgebra.CliffordAlgebra.BaseChange | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomCompTriple",
"CommRing.toCommSemiring",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
_private.Mathlib.Analysis.Analytic.Order.0.AnalyticAt.analyticOrderAt_deriv_add_one._simp_1_2 | Mathlib.Analysis.Analytic.Order | [
"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 |
LinearMap.coe_equivOfIsUnitDet | Mathlib.LinearAlgebra.Determinant | [
"CommRing",
"MonoidHom.instFunLike",
"MonoidHom",
"LinearMap.ext",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Module.End.instSemiring",
"IsUnit",
"LinearMap.equivOfIsUnitDet",
"AddCommGroup",
"LinearMap.det",
"LinearMap",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneCla... | true |
Std.Http.URI.Query.instEmptyCollection | Std.Internal.Http.Data.URI.Basic | [
"Std.Http.URI.Query.empty",
"EmptyCollection.mk",
"Std.Http.URI.Query",
"EmptyCollection"
] | true |
_private.Lean.Meta.Sym.Simp.Have.0.Lean.Meta.Sym.Simp.GetUnivsResult.casesOn | Lean.Meta.Sym.Simp.Have | [
"_private.Lean.Meta.Sym.Simp.Have.0.Lean.Meta.Sym.Simp.GetUnivsResult.rec",
"Lean.Level",
"Array",
"_private.Lean.Meta.Sym.Simp.Have.0.Lean.Meta.Sym.Simp.GetUnivsResult.mk",
"_private.Lean.Meta.Sym.Simp.Have.0.Lean.Meta.Sym.Simp.GetUnivsResult"
] | false |
_private.Mathlib.MeasureTheory.SetSemiring.0.MeasureTheory.IsSetSemiring.exists_disjoint_finset_diff_eq._simp_1_7 | Mathlib.MeasureTheory.SetSemiring | [
"Exists",
"propext",
"Eq",
"exists₂_imp"
] | false |
Function.Surjective.comp_left | Mathlib.Logic.Function.Basic | [
"Function.comp",
"Function.Surjective.piMap",
"Function.Surjective"
] | true |
Lean.Widget.instInhabitedStrictOrLazy | Lean.Widget.InteractiveDiagnostic | [
"Lean.Widget.StrictOrLazy",
"Lean.Widget.instInhabitedStrictOrLazy.default",
"Inhabited",
"Inhabited.mk"
] | true |
List.headD.eq_2 | Init.Data.List.Lemmas | [
"List.cons",
"List.headD",
"List",
"Eq.refl",
"Eq"
] | true |
Set.biUnion_union | Mathlib.Data.Set.Lattice | [
"Membership.mem",
"Set.instUnion",
"CompleteBooleanAlgebra.toCompleteLattice",
"Union.union",
"Eq",
"Set.instMembership",
"Set.iUnion",
"iSup_union",
"CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra",
"Set.instCompleteAtomicBooleanAlgebra",
"Set"
] | true |
_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.State.mk | Lean.Meta.LetToHave | [
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.State.mk",
"Std.HashMap",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.Result",
"_private.Lean.Meta.LetToHave.0.Lean.Meta.LetToHave.State",
"Nat",
"Lean.ExprStructEq.instHashable",
"Lean.ExprStructEq.instBEq",
"Lean.ExprStructEq"
] | true |
MaximalSpectrum.recOn | Mathlib.RingTheory.Spectrum.Maximal.Defs | [
"CommSemiring.toSemiring",
"MaximalSpectrum.mk",
"MaximalSpectrum",
"Ideal",
"MaximalSpectrum.rec",
"CommSemiring",
"Ideal.IsMaximal"
] | false |
CategoryTheory.PreGaloisCategory.PointedGaloisObject.incl.match_1 | Mathlib.CategoryTheory.Galois.Prorepresentability | [
"CategoryTheory.PreGaloisCategory.PointedGaloisObject.pt",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.PreGaloisCategory.PointedGaloisObject.instCategory",
"Finite",
"FintypeCat",
"TypeCat.instFunLikeFun",
... | false |
Lean.DeclNameGenerator.mk.inj | Lean.CoreM | [
"Lean.DeclNameGenerator.mk.noConfusion",
"List",
"Lean.DeclNameGenerator",
"And",
"Nat",
"And.intro",
"Lean.Name",
"Eq",
"Lean.DeclNameGenerator.mk"
] | true |
SSet.horn₂₀.ι₀₂._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | [
"SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat._proof_1",
"False",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"Nat.instCharZero",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"Nat.instAddMonoidWithOne",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"SimplexCategory.mk",
"Nat",
"Tr... | false |
ProperCone.toPointedCone_bot | Mathlib.Analysis.Convex.Cone.Basic | [
"ProperCone._proof_1",
"IsOrderedRing.toPosMulMono",
"IsOrderedRing.toZeroLEOneClass",
"IsOrderedRing",
"Nonneg.semiring",
"ProperCone",
"OrderBot.toBot",
"ClosedSubmodule.instPartialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"PointedCone",
"Subtype",
"Bot.bot",
... | true |
Equiv.decidableEq | Mathlib.Logic.Equiv.Defs | [
"Equiv.instEquivLike",
"Equiv",
"Equiv.injective",
"DFunLike.coe",
"Function.Injective.decidableEq",
"EquivLike.toFunLike",
"DecidableEq"
] | true |
MulOpposite.instNonUnitalCommCStarAlgebra._proof_2 | Mathlib.Analysis.CStarAlgebra.Classes | [
"NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"NonUnitalCStarAlgebra.toCStarRing",
"NonUnitalCommCStarAlgebra",
"MulOpposite",
"MulOpposite.instNonUnitalCStarAlgebra",
"CStarRing",
"NonUnitalCStarAlgebra.toStarRing"
] | false |
Lean.Parser.Command.namespace.parenthesizer | Lean.Parser.Command | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.checkColGt.parenthesizer",
"Lean.Parser.ident.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyP... | true |
RelIso.apply_eq_iff_eq | Mathlib.Order.RelIso.Basic | [
"EquivLike.apply_eq_iff_eq",
"RelIso.instEquivLike",
"RelIso",
"Iff",
"RelIso.instFunLike",
"Eq",
"DFunLike.coe"
] | true |
MonoidAlgebra.instCoalgebra | Mathlib.RingTheory.Coalgebra.MonoidAlgebra | [
"MonoidAlgebra.addCommMonoid",
"Coalgebra",
"CommSemiring.toSemiring",
"MonoidAlgebra.instCoalgebra._aux_1",
"Coalgebra.mk",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"MonoidAlgebra.instCoalgebra._proof_6",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"MonoidAlgebra",
"Mono... | true |
RCLike.instPosMulReflectLE | Mathlib.Analysis.RCLike.Basic | [
"RCLike.pos_iff_exists_ofReal",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Real",
"Eq.ge",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedRing.toRing",
"HMul.hMul",
"Or.rec",
"mul_sub",
"MulZeroClass.toMul",
"Real.instZe... | true |
IsOpen.exists_eq_add_of_deriv_eq | Mathlib.Analysis.Calculus.MeanValue | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"RCLike.toNormedAlgebra",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"deriv",
"NormedSpace.... | true |
_private.Batteries.Data.List.Lemmas.0.List.take_succ_drop._proof_1 | Batteries.Data.List.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Om... | false |
AlgebraicGeometry.Scheme.Modules.pseudofunctor._proof_7 | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"AlgebraicGeometry.Scheme.Modules.pullback",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme.Modules.pushforward",
"AlgebraicGeometry.Scheme",
"Opposite",
"Equiv.instEquivLike",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.Category... | false |
instCircularOrderZMod._proof_8 | Mathlib.Order.Circular.ZMod | [
"Int.instLinearOrder",
"Preorder.toCircularPreorder._proof_4",
"PartialOrder.toPreorder",
"SBtw.sbtw",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"instOfNatNat",
"instCircularOrderZMod._aux_3",
"Int",
"ZMod",
"SBtw.mk",
"Nat",
"OfNat.ofNat",
"instDistribLatticeOfLinearOrd... | false |
_private.Mathlib.Algebra.Category.Ring.Basic.0.RingCat.Hom.mk | Mathlib.Algebra.Category.Ring.Basic | [
"RingCat.ring",
"RingHom",
"RingCat",
"_private.Mathlib.Algebra.Category.Ring.Basic.0.RingCat.Hom.mk",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"RingCat.carrier",
"RingCat.Hom"
] | true |
NonUnitalSubsemiring.map_equiv_eq_comap_symm | Mathlib.RingTheory.NonUnitalSubsemiring.Basic | [
"RingEquiv.toEquiv",
"RingEquivClass.toNonUnitalRingHomClass",
"RingEquiv.instEquivLike",
"NonUnitalSubsemiring.comap",
"RingEquiv.instRingEquivClass",
"Distrib.toAdd",
"SetLike.coe_injective",
"NonUnitalRingHom.instFunLike",
"NonUnitalRingHom.instNonUnitalRingHomClass",
"Equiv.image_eq_preimage_s... | true |
Polynomial.trailingDegree_eq_iff_natTrailingDegree_eq_of_pos | Mathlib.Algebra.Polynomial.Degree.TrailingDegree | [
"Eq.mpr",
"ENat.instNatCast",
"congrArg",
"Iff.rfl",
"ENat.toNat_eq_iff",
"id",
"Ne",
"instOfNatNat",
"Nat.cast",
"Polynomial",
"Iff",
"Nat",
"ENat",
"Polynomial.trailingDegree",
"propext",
"ENat.toNat",
"Semiring",
"Polynomial.natTrailingDegree",
"OfNat.ofNat",
"Polynomial.nat... | true |
ContinuousLinearMap.IsPositive.inner_nonneg_right | Mathlib.Analysis.InnerProductSpace.Positive | [
"InnerProductSpace.toNormedSpace",
"ContinuousLinearMap.IsPositive.toLinearMap",
"Inner.inner",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"ContinuousLinearMap.IsPositive",
"PseudoMetricSpace.toUniformSpace",
"Preorder.toLE",
... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Basic.0.Equiv.Perm.IsCycle.of_pow._simp_1_1 | Mathlib.GroupTheory.Perm.Cycle.Basic | [
"Equiv.Perm.support",
"Equiv.instEquivLike",
"Finset",
"Equiv.Perm.mem_support",
"Membership.mem",
"Ne",
"Fintype",
"Finset.instSetLike",
"Equiv.Perm",
"propext",
"Eq.symm",
"Eq",
"DFunLike.coe",
"SetLike.instMembership",
"EquivLike.toFunLike",
"DecidableEq"
] | false |
_private.Mathlib.Data.Set.Finite.Basic.0.Set.finite_of_forall_not_lt_lt._simp_1_1 | Mathlib.Data.Set.Finite.Basic | [
"Membership.mem",
"Set.Elem",
"propext",
"Subtype.val",
"Eq",
"Set.instMembership",
"SetCoe.forall'",
"Subtype.property",
"Set"
] | false |
Batteries.Tactic.Lint.SimpTheoremInfo.rec | Batteries.Tactic.Lint.Simp | [
"Lean.Expr",
"Batteries.Tactic.Lint.SimpTheoremInfo",
"Array",
"Batteries.Tactic.Lint.SimpTheoremInfo.mk"
] | false |
Equiv.sigmaCongrRight_trans | Mathlib.Logic.Equiv.Defs | [
"Equiv.trans",
"Equiv",
"Equiv.sigmaCongrRight",
"Eq",
"Sigma",
"rfl"
] | true |
instReprVector | Init.Data.Vector.Basic | [
"Vector",
"Repr.mk",
"Nat",
"instReprVector.repr",
"Repr"
] | true |
Std.TreeMap.getElem!_diff_of_mem_right | Std.Data.TreeMap.Lemmas | [
"Inhabited.default",
"Std.DTreeMap.Const.get!_diff_of_mem_right",
"Std.TreeMap.instSDiff",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"SDiff.sdiff",
"Std.TreeMap.instMembership",
"Std.TreeMap.instGetElem?Mem",
"Inhabited",
"Eq",
"GetElem?.getElem!",
"Std.TreeMap"
] | true |
_private.Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan.0.MeasureTheory.SignedMeasure.of_diff_eq_zero_of_symmDiff_eq_zero_negative._simp_1_1 | Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan | [
"NegZeroClass.toNeg",
"neg_eq_zero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq",
"Neg.neg"
] | false |
Lean.Grind.CommSemiring.casesOn | Init.Grind.Ring.Basic | [
"HMul.hMul",
"Lean.Grind.Semiring.toMul",
"Lean.Grind.CommSemiring.mk",
"Lean.Grind.CommSemiring.rec",
"Lean.Grind.Semiring",
"Lean.Grind.CommSemiring",
"Eq",
"instHMul"
] | false |
pointedToBipointedSndBipointedToPointedSndAdjunction | Mathlib.CategoryTheory.Category.Bipointed | [
"pointedToBipointedSndBipointedToPointedSndAdjunction._proof_2",
"pointedToBipointedSndBipointedToPointedSndAdjunction._proof_4",
"CategoryTheory.CategoryStruct.toQuiver",
"pointedToBipointedSndBipointedToPointedSndAdjunction._proof_1",
"Quiver.Hom",
"Pointed.Hom.mk",
"Bipointed.toProd",
"Pointed",
... | true |
RatFunc.instDiv | Mathlib.FieldTheory.RatFunc.Basic | [
"IsDomain",
"CommRing",
"CommSemiring.toSemiring",
"Div",
"Div.mk",
"CommRing.toCommSemiring",
"RatFunc",
"RatFunc.div"
] | true |
_private.Mathlib.Data.List.Basic.0.List.dropLast_append_getLast.match_1_1 | Mathlib.Data.List.Basic | [
"Ne",
"List.cons",
"List",
"List.casesOn",
"List.nil"
] | false |
HomotopicalAlgebra.cofibration_iff | Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.Cofibration",
"Iff",
"Iff.intro",
"HomotopicalAlgebra.cofibrations",
"CategoryTheory.Category.toCategoryStruct",
"HomotopicalAlgebra.CategoryWithCofibrations",
"HomotopicalAlgebra.Cofibration.mk",
"HomotopicalAlgebra.Cofib... | true |
Function.mulSupport_fun_curry | Mathlib.Algebra.Notation.Support | [
"One",
"Prod.mk",
"Prod.fst",
"Pi.instOne",
"Function.mulSupport",
"Set.image",
"Function.mulSupport_curry",
"Prod",
"Eq",
"Set"
] | true |
Lean.MonadRecDepth.getRecDepth | Lean.Exception | [
"Nat",
"Lean.MonadRecDepth"
] | true |
List.le_sum_of_subadditive_on_pred | Mathlib.Algebra.Order.BigOperators.Group.List | [
"Eq.mpr",
"le_refl",
"List.map_cons",
"congrArg",
"List.map",
"AddMonoid.toAddZeroClass",
"List.sum",
"List.mem_cons_of_mem",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"add_le_add_right",
"List.rec",
"LE.le",
"AddCommMonoid",
"List.cons",
"AddZero.toZero",
"le_im... | true |
Units.ofPow._proof_1 | Mathlib.Algebra.Group.Commute.Units | [
"Monoid",
"Units.val",
"Eq.mpr",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Nat.succ_le_of_lt",
"HSub.hSub",
"Units",
"id",
"MulOne.toMul",
"instSubNat",
"Ne",
"instOfNatNat",
"Monoid.toPow",
"instHAdd",
"MulOneClass.toMulOne",
"Nat.pos_of_ne_zero",
"instHSub",
"Nat.sub_... | false |
Array.exists_mem_empty | Init.Data.Array.Lemmas | [
"False",
"Array.instMembership",
"Membership.mem",
"Exists",
"List.toArray",
"Array",
"_private.Init.Data.Array.Lemmas.0.Array.exists_mem_empty.match_1_1",
"Not",
"List.nil"
] | true |
Function.Injective.unique | Mathlib.Logic.Unique | [
"Function.Injective.subsingleton",
"Unique",
"Inhabited",
"Subsingleton",
"Function.Injective",
"Unique.mk'"
] | true |
InnerProductSpace.Core.inner_smul_left | Mathlib.Analysis.InnerProductSpace.Defs | [
"instHSMul",
"HMul.hMul",
"PreInnerProductSpace.Core.smul_left",
"Inner.inner",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"RingHom",
"NormedField.toField",
"AddZeroClass.toAddZero",
"Add... | true |
_private.Mathlib.RingTheory.PrincipalIdealDomain.0.Ideal.nonPrincipals_eq_empty_iff._simp_1_1 | Mathlib.RingTheory.PrincipalIdealDomain | [
"Membership.mem",
"Set.eq_empty_iff_forall_notMem",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instMembership",
"Not",
"Set"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Complex.LogBounds.0.Complex.norm_log_sub_logTaylor_le._simp_1_8 | Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | [
"False",
"HMul.hMul",
"eq_false",
"Mul",
"Ne",
"NoZeroDivisors",
"Zero.toOfNat0",
"mul_ne_zero",
"OfNat.ofNat",
"Eq",
"instHMul",
"Zero"
] | false |
Lean.Lsp.DeclInfo.mk | Lean.Data.Lsp.Internal | [
"Lean.Lsp.DeclInfo",
"Nat",
"Lean.Lsp.DeclInfo.mk"
] | true |
AddSubgroup.le_normalClosure | Mathlib.Algebra.Group.Subgroup.Basic | [
"AddSubgroup.normalClosure",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"AddSubgroup",
"AddGroup",
"SetLike.coe",
"AddSubgroup.instSetLike",
"AddSubgroup.subset_normalClosure",
"SetLike.instMembership"
] | true |
AddCommute.op | Mathlib.Algebra.Group.Opposite | [
"AddOpposite",
"AddOpposite.instAdd",
"AddCommute",
"AddSemiconjBy.op",
"AddOpposite.op",
"Add"
] | true |
MeasureTheory.Lp.instModule._proof_5 | Mathlib.MeasureTheory.Function.LpSpace.Basic | [
"MeasureTheory.Lp.instModule._proof_4",
"Submodule",
"Submodule.module._proof_1",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"NormedRing.toRing",
"MeasureTheory.Lp.LpSubmodule",
"UniformContinuousConstSMul.to_continuousConstSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAdd... | false |
CategoryTheory.Limits.Cone.fromStructuredArrow._proof_2 | Mathlib.CategoryTheory.Limits.ConeCategory | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.StructuredArrow.hom",
"CategoryTheory.Functor.map",
"CategoryTheory.discreteCategory",
"PU... | false |
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