name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Setoid.liftEquiv._proof_2 | Mathlib.Data.Setoid.Basic | [
"Function.LeftInverse",
"Setoid.ker",
"Quotient.mk''",
"Function.comp",
"Subtype",
"Setoid",
"Setoid.liftEquiv._proof_1",
"LE.le",
"Subtype.mk",
"Setoid.instLE_mathlib",
"Quotient",
"Eq.refl",
"Quotient.lift",
"Subtype.val",
"Setoid.r",
"Subtype.property"
] | false |
CategoryTheory.BraidedCategory.curriedBraidingNatIso._proof_2 | Mathlib.CategoryTheory.Monoidal.Braided.Basic | [
"CategoryTheory.BraidedCategory.braiding_naturality_right",
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.map",
"CategoryTheo... | false |
Aesop.EqualUpToIds.MVarValue.ctorIdx | Aesop.Util.EqualUpToIds | [
"Lean.MVarId",
"Lean.Expr",
"Lean.DelayedMetavarAssignment",
"Nat",
"Aesop.EqualUpToIds.MVarValue.casesOn",
"Aesop.EqualUpToIds.MVarValue"
] | false |
MeasureTheory.eLpNorm'_zero' | Mathlib.MeasureTheory.Function.LpSeminorm.Basic | [
"Real.instIsOrderedRing",
"MeasureTheory.lintegral_const",
"GroupWithZero.toMonoidWithZero",
"False",
"Real.partialOrder",
"Real",
"DivInvMonoid.toInv",
"MeasureTheory.Measure",
"Preorder.toLT",
"instHDiv",
"IsOrderedRing.toPosMulMono",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"DivIn... | true |
Simps.ProjectionRule.add.inj | Mathlib.Tactic.Simps.Basic | [
"Simps.ProjectionRule.add",
"Lean.Syntax",
"Simps.ProjectionRule",
"And",
"Simps.ProjectionRule.add.noConfusion",
"And.intro",
"Lean.Name",
"Eq"
] | true |
CategoryTheory.instHasLimitsOfShapeOverOfWithTerminal | Mathlib.CategoryTheory.WithTerminal.Cone | [
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Over.hasLimit_of_hasLimit_liftFromOver",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.HasLimitsOfShape.mk",
"CategoryTheory.instCategoryOver",
"CategoryTheory.WithTerminal",
"Categ... | true |
CategoryTheory.AddMonObj.lift_comp_zero_right | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"Eq.mp",
"CategoryTheory.AddMonObj.add",
"CategoryTheory.CartesianMonoidalCategory.lift",
"CategoryTheory.SemiCartesianMonoida... | true |
CategoryTheory.Abelian.SpectralObject.opcyclesIsoH_hom_inv_id._auto_1 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Matrix.«_aux_Mathlib_LinearAlgebra_Matrix_ConjTranspose___macroRules_Matrix_term_ᴴ_1» | Mathlib.LinearAlgebra.Matrix.ConjTranspose | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad"... | false |
Set.Ioc_disjoint_Ioi | Mathlib.Order.Interval.Set.Disjoint | [
"Iff.mpr",
"Set.Ioc",
"Set.Ioi",
"Preorder.toLT",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Set.disjoint_left",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"Set.instDistribLattice"... | true |
CategoryTheory.ComposableArrows.homMk₄._proof_3 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.ComposableArrows.map'._proof_8",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._proof_363",
"instAddNat",
"instLTNat",
"OfNat.ofNat"
] | false |
Lean.Meta.Grind.Goal.hasSameRoot | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.Goal",
"Lean.Expr",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.hasSameRoot",
"Lean.Meta.Grind.GoalState.enodeMap",
"Lean.Meta.Grind.Goal.toGoalState",
"Bool"
] | true |
egauge_pi' | Mathlib.Analysis.Convex.EGauge | [
"ENNReal.instCanonicallyOrderedAdd",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"instDecidableNot",
"not_exists._simp_1",
"iSup₂_le",
"False",
"Real.instLE",
"Real",
"ENNReal.ofNNReal",
"instHSMul",
"Preorder.toLT",
"exists_enorm... | true |
CyclotomicRing.eq_adjoin_primitive_root | Mathlib.NumberTheory.Cyclotomic.Basic | [
"Subalgebra.instSetLike",
"Eq.mpr",
"False",
"Nat.instMulZeroClass",
"CommRing",
"eq_false",
"CyclotomicField.instAlgebra",
"IsCyclotomicExtension.adjoin_roots_cyclotomic_eq_adjoin_root_cyclotomic",
"congrArg",
"CommSemiring.toSemiring",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"Polyno... | true |
CategoryTheory.yonedaMon._proof_3 | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.Mon.instIsMonHomHom",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.IsMonHom",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.Mon",
"CategoryTheory.Mon.X",
"CategoryThe... | false |
Std.ExtDHashMap.filterMap_eq_map | Std.Data.ExtDHashMap.Lemmas | [
"Std.DHashMap.filterMap",
"Option.some",
"Std.ExtDHashMap.inductionOn",
"Std.DHashMap.filterMap_equiv_map",
"LawfulHashable",
"EquivBEq",
"Std.ExtDHashMap",
"Std.ExtDHashMap.map",
"Hashable",
"Std.DHashMap.map",
"Std.ExtDHashMap.sound",
"BEq",
"Eq",
"Std.ExtDHashMap.filterMap",
"Std.DHas... | true |
ISize.ofIntLE_eq_ofIntTruncate | Init.Data.SInt.Lemmas | [
"Eq.mpr",
"ISize.ofIntTruncate",
"ISize.minValue",
"ISize.maxValue",
"congrArg",
"Int.decLe",
"dif_pos",
"ISize.ofIntTruncate.eq_1",
"id",
"Int",
"LE.le",
"dite",
"Eq.refl",
"ISize.ofIntLE",
"ISize",
"Eq",
"Not",
"Int.instLEInt",
"ISize.toInt"
] | true |
CategoryTheory.NatTrans.naturality._autoParam | Mathlib.CategoryTheory.NatTrans | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.Limits.HasWidePushouts | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.WidePushoutShape.category",
"CategoryTheory.Limits.WidePushoutShape",
"CategoryTheory.Category"
] | true |
wbtw_self_iff._simp_1 | Mathlib.Analysis.Convex.Between | [
"IsOrderedRing",
"AddCommGroup.toAddCommMonoid",
"Wbtw",
"AddCommGroup.toAddGroup",
"PartialOrder",
"AddCommGroup",
"wbtw_self_iff",
"AddTorsor",
"propext",
"Module",
"Ring.toSemiring",
"Eq",
"Ring"
] | false |
Lean.Compiler.LCNF.Simp.DiscrM | Lean.Compiler.LCNF.Simp.DiscrM | [
"ReaderT",
"Lean.Compiler.LCNF.Simp.DiscrM.Context",
"Lean.Compiler.LCNF.CompilerM"
] | true |
Mathlib.Tactic.Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm.casesOn | Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Datatypes | [
"Mathlib.Tactic.Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm.rec",
"Mathlib.Tactic.Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm",
"Rat",
"Mathlib.Tactic.Linarith.SimplexAlgorithm.UsableInSimplexAlgorithm.mk",
"List",
"Nat",
"Prod"
] | false |
VertexOperator.ncoeff_apply | Mathlib.Algebra.Vertex.VertexOperator | [
"HahnModule.instBaseModule",
"Pi.Function.module",
"CommRing",
"VertexOperator.ncoeff",
"HVertexOperator",
"Pi.addCommMonoid",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"HVertexOperator.coeff",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLik... | true |
Lean.TrailingParserDescr | Init.Prelude | [
"Lean.ParserDescr"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.ChebyshevGauss.0.Polynomial.Chebyshev.sumZeroes_T_of_not_dvd._proof_1_9 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.ChebyshevGauss | [
"instIsCharPOfIsLeftCancelAddOfCharP",
"Lean.Grind.eq_false_of_not_eq_true",
"Int.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"of_eq_false",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.CommRing.Mon.mult",
"Dvd.dvd",
"Lean.Grind.CommRing.diseq_to_eq",
"instHDiv... | false |
Asymptotics.instTransForallIsBigOIsTheta | Mathlib.Analysis.Asymptotics.Theta | [
"SeminormedAddCommGroup",
"Asymptotics.IsBigO",
"Norm",
"Asymptotics.IsTheta",
"Trans",
"SeminormedAddCommGroup.toNorm",
"Trans.mk",
"Filter",
"Asymptotics.IsBigO.trans_isTheta"
] | true |
FreeGroup.Red.eq_1 | Mathlib.GroupTheory.FreeGroup.Basic | [
"FreeGroup.Red.Step",
"List",
"Bool",
"Eq.refl",
"Prod",
"Eq",
"FreeGroup.Red",
"Relation.ReflTransGen"
] | true |
String.utf8Len.eq_def | Batteries.Data.String.Lemmas | [
"List.brecOn",
"Eq.mpr",
"List.brecOn.go",
"List.brecOn.eq",
"congrArg",
"String.utf8Len",
"id",
"instOfNatNat",
"List.rec",
"List.cons",
"List",
"instHAdd",
"Unit",
"PProd",
"HAdd.hAdd",
"PUnit",
"Nat",
"Eq.ndrec",
"instAddNat",
"List.below",
"Eq.refl",
"Char",
"String.u... | true |
_private.Mathlib.Data.EReal.Operations.0.Mathlib.Meta.Positivity.evalERealAdd._proof_2 | Mathlib.Data.EReal.Operations | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"PLift",
"Lean.Expr.sort",
"Lean.Level",
"PLift.down",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Level.instOfNat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"List.nil"
] | false |
Std.Tactic.BVDecide.BVExpr.WithCache.ctorIdx | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Expr | [
"Std.Sat.AIG",
"Nat",
"Std.Tactic.BVDecide.BVExpr.WithCache",
"Std.Tactic.BVDecide.instDecidableEqBVBit",
"Std.Tactic.BVDecide.BVBit",
"Std.Tactic.BVDecide.instHashableBVBit"
] | false |
PrincipalSeg.ofElement_toFun | Mathlib.Order.InitialSeg | [
"PrincipalSeg.toRelEmbedding",
"Subtype",
"RelEmbedding.toEmbedding",
"Subrel",
"Eq.refl",
"Function.Embedding.toFun",
"PrincipalSeg.ofElement",
"Subtype.val",
"Eq"
] | true |
Equiv.Perm.Basis.rec | Mathlib.GroupTheory.Perm.Centralizer | [
"Equiv.Perm.support",
"Finset",
"Equiv.Perm.cycleFactorsFinset",
"Equiv.Perm.Basis.mk",
"Membership.mem",
"Subtype",
"Fintype",
"Finset.instSetLike",
"Equiv.Perm",
"Equiv.Perm.Basis",
"Subtype.val",
"SetLike.instMembership",
"DecidableEq"
] | false |
Nat.dfold_add._proof_16 | Init.Data.Nat.Fold | [
"LE.le",
"instLENat",
"_private.Init.Data.Nat.Fold.0.Nat.dfold_add._proof_15",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Decidable.byContradiction",
"instAddNat",
"Not",
"Nat.decLe"
] | false |
Lean.Grind.CommRing.Mon.revlexFuel.induct_unfolding | Init.Grind.Ring.CommSolver | [
"Nat.blt",
"cond",
"Lean.Grind.CommRing.Power",
"Ordering.gt",
"Eq.mpr",
"Lean.Grind.CommRing.Mon.revlexWF.match_1.congr_eq_3",
"Lean.Grind.CommRing.Mon.mult",
"Bool.cond_neg",
"congrArg",
"Lean.Grind.CommRing.Mon.revlexFuel.eq_def",
"Lean.Grind.CommRing.Mon.revlexWF",
"Lean.Grind.CommRing.Mon... | true |
_private.Std.Data.Iterators.Lemmas.Producers.Repeat.0.Nat.repeat.match_1.splitter | Std.Data.Iterators.Lemmas.Producers.Repeat | [
"instOfNatNat",
"Nat",
"Nat.repeat.match_1",
"OfNat.ofNat",
"Nat.succ"
] | true |
Ideal.span_range_eq_span_range_support | Mathlib.RingTheory.Ideal.Span | [
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"_private.Mathlib.RingTheory.Ideal.Span.0.Ideal.span_range_eq_span_range_support._proof_1_8",
"Function.support.eq_1",
"congrArg",
"_private.Mathlib.RingTheory.Ideal.Span.0.Ideal.span_range_eq_span_range_support._simp_1_1",
"setOf",
"Membership.mem",
"Exists",
"Id... | true |
MulActionHomClass.eq_1 | Mathlib.GroupTheory.GroupAction.Hom | [
"MulActionHomClass",
"SMul",
"MulActionSemiHomClass",
"id",
"Eq.refl",
"Eq",
"FunLike"
] | true |
Std.DHashMap.Raw.Equiv.constInsertMany_list | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"congrArg",
"instForInOfForIn'",
"Std.DHashMap.Raw",
"inferInstance",
"id",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"Id",
"Membership",
"LawfulHashable",
"Std.DHashMap.Internal.Raw₀.Const.insertMany_list_equiv_congr",
"Std.DHashMap.Raw.Equiv... | true |
CategoryTheory.Functor.isoWhiskerRight_left_assoc | Mathlib.CategoryTheory.Whiskering | [
"CategoryTheory.Functor",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.associator",
"Eq.mp",
"id",
"CategoryTheory.Iso",
"CategoryTheory.Iso.trans_assoc",
"CategoryTheory.Functor.isoWhiskerLeft",
"Mathlib.Tactic.Reassoc.Iso.eq_whisker",
... | true |
HomologicalComplex.homologicalComplexToDGO | Mathlib.Algebra.Homology.DifferentialObject | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"instHSMul",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"HomologicalComplex.dgoToHomologicalComplex._proof_7",
"CategoryTh... | true |
Lean.Lsp.SymbolInformation.containerName? | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolInformation",
"String",
"Option"
] | true |
Fin.insertNthEquiv_last | Mathlib.Data.Fin.Tuple.Basic | [
"Equiv.instEquivLike",
"Fin.snocEquiv",
"congrArg",
"Fin.insertNth",
"Fin.snoc",
"Equiv",
"Equiv.ext",
"instOfNatNat",
"Prod.fst",
"funext",
"instHAdd",
"Fin.insertNth_last'",
"HAdd.hAdd",
"congrFun",
"Nat",
"Fin.last",
"True",
"eq_self",
"of_eq_true",
"instAddNat",
"congrFun... | true |
Int.inductionOn'_add_one | Mathlib.Data.Int.Init | [
"Int.inductionOn'._proof_1",
"Eq.mpr",
"Int.inductionOn'.match_1",
"Int.inductionOn'.neg",
"HSub.hSub",
"_private.Mathlib.Data.Int.Init.0.Int.inductionOn'_add_one._proof_1_11",
"cast",
"Eq.rec",
"id",
"Int.inductionOn'.pos",
"instOfNatNat",
"Int",
"LE.le",
"Nat.cast",
"Mathlib.Tactic.Dep... | true |
RatFunc.CompletionAtInfty.instValuedWithZeroMultiplicativeInt._proof_10 | Mathlib.FieldTheory.RatFunc.Valuation | [
"RatFunc.CompletionAtInfty",
"Int.instAddCommGroup",
"Multiplicative.linearOrder",
"Int.instLinearOrder",
"RatFunc.CompletionAtInfty.instValuedWithZeroMultiplicativeInt._proof_4",
"Field.toDivisionRing",
"WithZero.instLinearOrderedCommGroupWithZero",
"nhds",
"RatFunc.CompletionAtInfty.instValuedWith... | false |
ProbabilityTheory.Kernel.integral_deterministic' | Mathlib.Probability.Kernel.Integral | [
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"CompleteSpace",
"NormedSpace",
"congrArg",
"Measurable",
"PseudoMetricSpace.toUniformSpace",
"ProbabilityTheory.Kernel.deterministic_apply",
"ProbabilityTheory.Kernel.instFunLike",
"id",
"ProbabilityTheory.Kernel.deterministic",
"MeasureTheory.Meas... | true |
CategoryTheory.Limits.MonoFactorisation.e | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.MonoFactorisation.I",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.MonoFactorisation",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
List.min_singleton | Init.Data.List.MinMax | [
"List.min",
"Min",
"List.cons",
"List.cons_ne_nil",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Multiset.zero_product | Mathlib.Data.Multiset.Bind | [
"Multiset.instSProd",
"SProd.sprod",
"Multiset",
"Zero.toOfNat0",
"Prod",
"OfNat.ofNat",
"Eq",
"rfl",
"Multiset.instZero"
] | true |
ChevalleyThm.MvPolynomialC.degBound_casesOn_succ._mutual | Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Eq.mpr",
"_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.MvPolynomialC.degBound_casesOn_succ.match_1",
"PSum.casesOn",
"NonAssocSemiring.toAddCommMonoidWithOne",
"ChevalleyThm.MvPolynomialC.numBound_zero",
"Lean.Omega.Constraint.n... | false |
Directed.le_sequence | Mathlib.Logic.Encodable.Basic | [
"Directed.rel_sequence",
"Directed",
"Preorder.toLE",
"instOfNatNat",
"LE.le",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Directed.sequence",
"instAddNat",
"Inhabited",
"Encodable.encode",
"OfNat.ofNat",
"Encodable",
"Preorder"
] | true |
List.tailsTR.go.eq_def | Batteries.Data.List.Basic | [
"List.brecOn",
"Eq.mpr",
"List.tailsTR.go",
"List.brecOn.go",
"List.brecOn.eq",
"Array.push",
"congrArg",
"_private.Batteries.Data.List.Basic.0.List.next?.match_1.splitter",
"List.next?.match_1",
"List.tailsTR.go._f",
"id",
"List.rec",
"List.cons",
"Array",
"List",
"Unit",
"PProd",
... | true |
_private.Mathlib.Data.Finsupp.Indicator.0.Finsupp.indicator_indicator._proof_1_2 | Mathlib.Data.Finsupp.Indicator | [
"Finsupp.instFunLike",
"Finsupp.indicator",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Finset.mem_of_mem_inter_left",
"Lean.Grind.nestedProof",
"Finsupp.ext",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"HEq.refl",
"Finset",
"Classical.byContradiction",
"_private.Mathlib.Data.Finsupp... | false |
BialgCat.mk | Mathlib.Algebra.Category.BialgCat.Basic | [
"CommRing",
"BialgCat",
"BialgCat.mk",
"CommRing.toCommSemiring",
"Bialgebra",
"Ring.toSemiring",
"Ring"
] | true |
Std.TreeSet.Raw.le_maxD_of_contains | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.contains",
"Std.TreeSet.Raw.WF.out",
"Std.TreeMap.Raw.le_maxKeyD_of_contains",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.TreeSet.Raw",
"Unit",
"Bool",
"Ordering.isLE",
"Std.TreeSet.Raw.maxD",
"Std.TreeSet.Raw.inner",
"Eq",
"Std.TreeSet.Raw.WF"
] | true |
AffineSubspace.SOppSide.trans_wSameSide | Mathlib.Analysis.Convex.Side | [
"AffineSubspace.SOppSide.symm",
"AffineSubspace.WOppSide.symm",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"IsStrictOrderedRing",
"AddCommGroup.toAddGroup",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"AffineSubspace.WSameSide.symm",
... | true |
SupBotHom.dual_comp | Mathlib.Order.Hom.BoundedLattice | [
"OrderDual.instMinOfMax",
"SupBotHom.comp",
"Equiv.instEquivLike",
"Max",
"Equiv",
"Bot",
"SupBotHom",
"SupBotHom.dual",
"InfTopHom.comp",
"InfTopHom",
"OrderDual",
"Eq",
"DFunLike.coe",
"OrderDual.instTopOfBot",
"rfl",
"EquivLike.toFunLike"
] | true |
UInt16.le_refl._simp_1 | Init.Data.UInt.Lemmas | [
"instLEUInt16",
"LE.le",
"UInt16",
"UInt16.le_refl",
"True",
"eq_true",
"Eq"
] | false |
AlexDisc.recOn | Mathlib.Topology.Order.Category.AlexDisc | [
"AlexDisc.mk",
"AlexDisc.rec",
"AlexDisc",
"TopCat.str",
"AlexandrovDiscrete",
"TopCat.carrier",
"TopCat"
] | false |
_private.Mathlib.Data.Fintype.Prod.0.Finset.product_eq_univ._simp_1_1 | Mathlib.Data.Fintype.Prod | [
"Finset.eq_univ_iff_forall",
"Finset.univ",
"Finset",
"Membership.mem",
"Fintype",
"Finset.instSetLike",
"propext",
"Eq",
"SetLike.instMembership"
] | false |
PowerSeries.exp_pow_eq_rescale_exp | Mathlib.RingTheory.PowerSeries.Exp | [
"Eq.mpr",
"RingHom.instRingHomClass",
"MulOne.toOne",
"CommRing",
"Nat.recAux",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"pow_succ",
"AddMonoid.toAddZeroClass",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra",
"Power... | true |
ContinuousMulEquiv.eq_symm_comp | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"Equiv.eq_symm_comp",
"ContinuousMulEquiv.instEquivLike",
"Mul",
"Function.comp",
"MulEquiv.toEquiv",
"TopologicalSpace",
"Iff",
"ContinuousMulEquiv.symm",
"ContinuousMulEquiv",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"ContinuousMulEquiv.toMulEquiv"
] | true |
QuotientGroup.preimage_image_mk | Mathlib.GroupTheory.Coset.Defs | [
"Set.ext",
"Eq.mpr",
"DivInvMonoid.toInv",
"Subgroup.instSubgroupClass",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Iff.of_eq",
"Monoid.toMulOneClass",
"congrArg",
"QuotientGroup.mk",
"_private.Mathlib.GroupTheory.Coset.Defs.0.QuotientGroup.preimage_image_mk._simp_1_3",
"Group",
"Group.t... | true |
ZFSet.singleton_inj._simp_1 | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"ZFSet.instSingleton",
"propext",
"ZFSet.singleton_inj",
"Singleton.singleton",
"Eq"
] | false |
CategoryTheory.Limits.WalkingMultispan.instSubsingletonHomLeft | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"False",
"CategoryTheory.Limits.WalkingMultispan.instUniqueHom",
"CategoryTheory.Limits.WalkingMultispan",
"CategoryTheory.Limits.MultispanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HEq.refl",
"CategoryTheory.Limits.MultispanShape",
"False.elim",
"CategoryTheo... | true |
ENNReal.isConjExponent_iff_eq_conjExponent | Mathlib.Data.Real.ConjExponents | [
"ENNReal.instAdd",
"HSub.hSub",
"LE.le",
"ENNReal.HolderConjugate.conj_eq",
"instHAdd",
"Iff",
"ENNReal.HolderConjugate.conjExponent",
"instHSub",
"Inv.inv",
"HAdd.hAdd",
"ENNReal.HolderConjugate",
"ENNReal.instLE",
"Iff.intro",
"ENNReal",
"ENNReal.instSub",
"Eq.ndrec",
"One.toOfNat1... | true |
_private.Mathlib.Algebra.Category.Ring.Basic.0.CommSemiRingCat.Hom.ext.match_1 | Mathlib.Algebra.Category.Ring.Basic | [
"CommSemiring.toSemiring",
"CommSemiRingCat.carrier",
"RingHom",
"_private.Mathlib.Algebra.Category.Ring.Basic.0.CommSemiRingCat.Hom.mk",
"CommSemiRingCat.Hom.casesOn",
"CommSemiRingCat",
"CommSemiRingCat.commSemiring",
"Semiring.toNonAssocSemiring",
"CommSemiRingCat.Hom"
] | false |
CategoryTheory.MorphismProperty.rlp_isStableUnderProductsOfShape | Mathlib.CategoryTheory.MorphismProperty.LiftingProperty | [
"CategoryTheory.HasLiftingProperty",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Limits.HasProduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"inferInstance",
"CategoryTheory.MorphismProperty.rlp",
"CategoryTheory.Limits.piObj",
"CategoryTheory.MorphismProperty.IsStableUnderPro... | true |
Aesop.GoalData.mvars | Aesop.Tree.Data | [
"Aesop.GoalData",
"Lean.instBEqMVarId",
"Lean.MVarId",
"Aesop.UnorderedArraySet"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.foldl_eq_foldl_toList._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
UInt64.toUInt32_toUSize | Init.Data.UInt.Lemmas | [
"instPowNat",
"UInt32.size",
"UInt32.toNat",
"UInt64.toUSize",
"congrArg",
"UInt64",
"UInt64.toNat_toUInt32",
"Nat.instMod",
"instHMod",
"mod_usizeSize_uInt32Size",
"instOfNatNat",
"UInt64.toNat",
"UInt32.toNat.inj",
"instNatPowNat",
"System.Platform.numBits",
"UInt64.toNat_toUSize",
... | true |
CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp_eq_id | Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant | [
"Eq.mpr",
"CategoryTheory.Functor.IsEventuallyConstantFrom.coconeιApp",
"CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"id",
"Nonempty.intro",
"... | true |
Std.Rcc.Sliceable.recOn | Init.Data.Slice.Notation | [
"Std.Rcc.Sliceable.rec",
"Std.Rcc.Sliceable.mk",
"Std.Rcc.Sliceable",
"Std.Rcc"
] | false |
String.Pos.prev! | Init.Data.String.FindPos | [
"String.toSlice",
"String",
"String.Pos.toSlice",
"String.Pos.ofToSlice",
"String.Pos",
"String.Slice.Pos.prev!"
] | true |
CategoryTheory.Sum.swapCompInl | Mathlib.CategoryTheory.Sums.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.sum",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.inlCompSum'",
"Sum",
"CategoryTheory.Iso",
"CategoryTheory.Sum.inr_",
"CategoryTheory.Sum.inl_",
"CategoryTheory.Sum.swap",
"CategoryTheory.Category"
] | true |
Cardinal.power_mul | Mathlib.SetTheory.Cardinal.Order | [
"Eq.mpr",
"HMul.hMul",
"Cardinal.instPowCardinal",
"Cardinal",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"Cardinal.commSemiring",
"Cardinal.instMul",
"id",
"CommMagma.toMul",
"NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring",
"HPow.hPow",
"NonUnitalNonAssocCommSemiring.toComm... | true |
Batteries.BinomialHeap.Imp.FindMin.mk | Batteries.Data.BinomialHeap.Basic | [
"Batteries.BinomialHeap.Imp.Heap",
"Batteries.BinomialHeap.Imp.HeapNode",
"Batteries.BinomialHeap.Imp.FindMin.mk",
"Batteries.BinomialHeap.Imp.FindMin"
] | true |
Matrix.SpecialLinearGroup.map_intCast_injective | Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | [
"Int.cast",
"Eq.mpr",
"CommRing",
"Matrix.SpecialLinearGroup",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Matrix",
"AddGroupWithOne.toAddMonoidWithOne",
"_private.Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup.0.Matrix.SpecialLinearGroup.map_intCas... | true |
MvPowerSeries.coeff_mul_left_one_sub_of_lt_weightedOrder | Mathlib.RingTheory.MvPowerSeries.Order | [
"AddGroup.toSubtractionMonoid",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"Semiring.toModule",
"HMul.hMul",
"map_sub",
"SemilinearMapClass.distribMulActionSemiHomClass",
"Ring.toNonAssocRing",
"mul_sub",
"MvPowerSeries.le_weightedO... | true |
DirichletCharacter.LSeries_ne_zero_of_one_lt_re | Mathlib.NumberTheory.LSeries.Dirichlet | [
"Int.cast",
"False",
"Real",
"HMul.hMul",
"ArithmeticFunction.instFunLikeNat",
"ZMod.commRing",
"congrArg",
"NeZero.charZero_one",
"False.elim",
"MulZeroClass.zero_mul",
"AddGroupWithOne.toAddMonoidWithOne",
"Complex.instZero",
"Real.instLT",
"Complex.instMul",
"Complex.addGroupWithOne",... | true |
ContinuousAffineMap.instSub._proof_1 | Mathlib.Topology.Algebra.ContinuousAffineMap | [
"Continuous",
"AffineMap.instFunLike",
"AddCommGroup.toAddCommMonoid",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"IsTopologicalAddGroup.to_continuousSub",
"AddCommGroup",
"ContinuousAffineMap",
"addGroupIsAddTorsor",
"AffineMap",
"SubNegMonoid.toSub",
"TopologicalSpace",
"instHSub",
"AddGrou... | false |
Equiv.apply_swap_eq_self | Mathlib.Logic.Equiv.Basic | [
"Equiv.instEquivLike",
"Equiv.swap",
"Equiv.Perm",
"Eq",
"DFunLike.coe",
"_private.Mathlib.Logic.Equiv.Basic.0.Equiv.apply_swap_eq_self._proof_1_1",
"EquivLike.toFunLike",
"DecidableEq"
] | true |
Std.Rio.pairwise_toList_upwardEnumerableLt | Init.Data.Range.Polymorphic.Lemmas | [
"Eq.mpr",
"Decidable.casesOn",
"List.Pairwise.cons",
"Std.PRange.UpwardEnumerable",
"List.Pairwise",
"Std.Roo.upper",
"congrArg",
"Std.PRange.LawfulUpwardEnumerableLT",
"Std.PRange.UpwardEnumerable.LT",
"Decidable",
"_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Rio.pairwise_toList_upwardEnu... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.get?_empty._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
_private.Aesop.Util.EqualUpToIds.0.Aesop.EqualUpToIds.Unsafe.exprsEqualUpToIdsCore₃.match_5 | Aesop.Util.EqualUpToIds | [
"_private.Aesop.Util.EqualUpToIds.0.Aesop.EqualUpToIds.Unsafe.exprsEqualUpToIdsCore₃._sparseCasesOn_14",
"_private.Aesop.Util.EqualUpToIds.0.Aesop.EqualUpToIds.Unsafe.exprsEqualUpToIdsCore₃._sparseCasesOn_6",
"Lean.Expr.const",
"_private.Aesop.Util.EqualUpToIds.0.Aesop.EqualUpToIds.Unsafe.exprsEqualUpToIdsCor... | false |
Std.TreeMap.isEmpty_emptyc | Std.Data.TreeMap.Lemmas | [
"Ordering",
"Std.TreeMap.isEmpty",
"Bool.true",
"Bool",
"Std.TreeMap.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Std.DTreeMap.isEmpty_emptyc",
"Eq",
"Std.TreeMap"
] | true |
_private.Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions.0.hasMFDerivAt_inr._simp_1_1 | Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | [
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"Set.univ",
"NormedField.toField",
"HasMFDerivAt",
"instModuleTangentSpace",
"Field.toSemifield",
"instTopologicalSpaceTangentSpace",
"ContinuousLinearMap",
"TopologicalSpace",
"ModelWithCorners",
"hasMFDerivWithi... | false |
Int.neg_modEq_neg._simp_1 | Mathlib.Data.Int.ModEq | [
"Int.neg_modEq_neg",
"Int.instNegInt",
"Int",
"Int.ModEq",
"propext",
"Eq",
"Neg.neg"
] | false |
SimpleGraph.Walk.isSubwalk_nil_iff_mem_support._simp_1 | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Membership.mem",
"SimpleGraph.Walk.isSubwalk_nil_iff_mem_support",
"SimpleGraph",
"List",
"SimpleGraph.Walk.IsSubwalk",
"List.instMembership",
"SimpleGraph.Walk.nil",
"propext",
"Eq"
] | false |
CliffordAlgebra.changeFormEquiv._proof_2 | Mathlib.LinearAlgebra.CliffordAlgebra.Contraction | [
"Eq.mpr",
"add_neg_cancel",
"CommRing",
"Semiring.toModule",
"Ring.toNonAssocRing",
"CliffordAlgebra.changeForm_self_apply",
"LinearMap.BilinForm",
"congrArg",
"CliffordAlgebra.changeForm.add_proof",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"LinearMap.add... | false |
Std.DTreeMap.Raw.WF.casesOn | Std.Data.DTreeMap.Raw.Basic | [
"Ord.mk",
"Ordering",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.WF.mk",
"Std.DTreeMap.Raw.WF.rec",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] | false |
_private.Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo.0.Matrix.isParabolic_iff_exists._simp_1_3 | Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | [
"map_sub",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"SubtractionMonoid.toSubNegMonoid",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"SubtractionMonoid",
"SubNegMonoid.toAddMonoid",
"Eq.symm",
"Eq",
"DFunLike.coe"... | false |
Part.getOrElse_of_not_dom | Mathlib.Data.Part | [
"Part",
"Decidable",
"Part.get",
"dif_neg",
"Part.Dom",
"Part.getOrElse",
"Eq",
"Not"
] | true |
CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex_left | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.Functor.PreOneHypercoverDenseData",
"Opposite.op",
"CategoryTheory.Category.opposite",
"Eq.refl",
"Eq",
"CategoryTheory.Functor.Pre... | true |
_private.Mathlib.MeasureTheory.OuterMeasure.AE.0.MeasureTheory.diff_ae_eq_self._simp_1_1 | Mathlib.MeasureTheory.OuterMeasure.AE | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Filter.eventuallyLE_antisymm_iff",
"PartialOrder",
"Filter.EventuallyEq",
"And",
"propext",
"Filter.EventuallyLE",
"Eq",
"Filter"
] | false |
Mathlib.TacticAnalysis.TacticNode.ctxI | Mathlib.Tactic.TacticAnalysis | [
"Lean.Elab.ContextInfo",
"Mathlib.TacticAnalysis.TacticNode"
] | true |
Set.Ico_subset_Icc_union_Ico | Mathlib.Order.Interval.Set.LinearOrder | [
"Set.Subset.trans",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"Set.instUnion",
"Set.union_subset_union_right",
"DistribLattice.toLattice",
"HasSubset.Subset",
"Set.Ico",
"Set.Ioo_subset_Ico_self",
"Set.Icc",
"Set.Ico_subset_Icc_union_Ioo",
"Union.union",
"S... | true |
_private.Init.Data.String.Decode.0.String.utf8EncodeChar_eq_utf8EncodeCharFast._proof_1_12 | Init.Data.String.Decode | [
"instPowNat",
"instDecidableNot",
"Nat.lt_of_not_le",
"Int.instDiv",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"UInt32.toNat",
"instHDiv",
"HMul.hMul",
"of_decide_eq_true",
"le_of_le_of_eq",
"Int.natCast_ediv",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat... | false |
Equiv.group.eq_1 | Mathlib.Algebra.Group.TransferInstance | [
"Function.Injective.group",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Equiv.instEquivLike",
"Monoid.toMulOneClass",
"DivInvMonoid.toZPow",
"Group",
"Equiv.group._proof_3",
"Equiv",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Int",
"Monoid.toPow",
"Group.toDivInvMonoid",
"Equiv.Inv",
"MulOne... | true |
Submonoid.orderOf_le_card | Mathlib.GroupTheory.OrderOfElement | [
"Iff.mpr",
"Eq.mpr",
"Monoid.toMulOneClass",
"congrArg",
"CancelMonoid.toLeftCancelMonoid",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Set.Finite",
"Membership.mem",
"id",
"Subtype",
"LeftCancelMonoid.toMonoid",
"Nat.card",
"DivInvMonoid.toMonoid",
"Nat.card_submonoidPowers"... | true |
_private.Mathlib.Data.Fintype.Quotient.0.Quotient.list_ind.match_1_1 | Mathlib.Data.Fintype.Quotient | [
"False",
"HEq.refl",
"List.Mem.tail",
"False.elim",
"noConfusion_of_Nat",
"Membership.mem",
"List.cons",
"List",
"List.instMembership",
"List.Mem.head",
"Eq.refl",
"HEq",
"List.Mem",
"Eq",
"List.ctorIdx",
"List.Mem.casesOn",
"List.nil"
] | false |
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