name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Aesop.Forward.State.0.Aesop.InstMap.insertMatch.match_1 | Aesop.Forward.State | [
"_private.Aesop.Forward.State.0.Aesop.InstMap.modify._sparseCasesOn_7",
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"Option"
] | false |
Finset.prod_Ioc_succ_top | Mathlib.Algebra.BigOperators.Intervals | [
"Eq.mpr",
"Nat.Ioc_succ_singleton",
"HMul.hMul",
"Finset.prod_singleton",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Nat.instLocallyFiniteOrder",
"id",
"MulOne.toMul",
"Nat.le_succ",
"instOfNatNat",
"LE.le",
"instLENat",
"Finset.prod",
"instHAdd",
"MulOneClass.toMulOne",
"HAdd.... | true |
Finset.biUnion_image_sup_left | Mathlib.Data.Finset.Sups | [
"Finset.biUnion_image_left",
"Finset.hasSups",
"Finset",
"SemilatticeSup.toMax",
"Finset.biUnion",
"Max.max",
"Eq",
"SemilatticeSup",
"Finset.image",
"HasSups.sups",
"DecidableEq"
] | true |
_private.Lean.Elab.DeclNameGen.0.PSum.casesOn._arg_pusher | Lean.Elab.DeclNameGen | [
"PSum.casesOn",
"PSum",
"PSum.inr",
"PSum.inl",
"Eq.refl",
"Eq"
] | false |
Real.tendsto_logb_atTop_of_base_lt_one | Mathlib.Analysis.SpecialFunctions.Log.Base | [
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.instPow",
"Real.partialOrder",
"Real.instLE",
"Real",
"Real.instArchimedean",
"Real.logb_le_iff_le_rpow_of_base_lt_one",
"Real.instZero",
"_private.Mathlib.Analysis.SpecialFunctions.Log.Base.0.Real.tendsto_logb_atTop_of_base_lt_one._simp_1_1",
"Real.inst... | true |
tensorKaehlerQuotKerSqEquiv._proof_3 | Mathlib.RingTheory.Smooth.Kaehler | [
"RingHom.instRingHomClass",
"CommRing",
"Algebra.to_smulCommClass",
"instSMulOfMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toSMul",
"Algebra.id",
"Ideal.instAlgebraQuotient",
"instOfNatNat",
"Ideal",
"retractionOfSectionOfKerSqZero._proof_1",
"in... | false |
Lean.Compiler.LCNF.JoinPointFinder.find | Lean.Compiler.LCNF.JoinPoints | [
"Pure.pure",
"Lean.instBEqFVarId",
"Lean.Compiler.LCNF.JoinPointFinder.FindState.mk",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"Lean.FVarIdMap",
"_private.Lean.Compiler.LCNF.JoinPoints.0.Lean.Compiler.LCNF.JoinPointFinder.find.match_1",
"instMonadLiftT",
"IO",
"Lean.i... | true |
Asymptotics.IsEquivalent | Mathlib.Analysis.Asymptotics.Defs | [
"SeminormedAddCommGroup",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"SubNegMonoid.toSub",
"SeminormedAddCommGroup.toNorm",
"instHSub",
"AddGroup.toSubNegMonoid",
"SeminormedAddCommGroup.toAddCommGroup",
"Asymptotics.IsLittleO",
"Pi.instSub",
"Filter"
] | true |
AffineSubspace.subtype_linear | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"Subtype",
"Submodule.module",
"AffineSubspace.toAddTorsor",
"LinearMap",
"AffineSubspace.instSetLike",
"AffineSubspace.subtype",
"Submodule.addCommGroup",
"Submodule.setLike",
"Affine... | true |
_private.Batteries.Data.List.Basic.0.List.next?.match_1.eq_2 | Batteries.Data.List.Basic | [
"List.next?.match_1",
"List.cons",
"List",
"Unit",
"Eq.refl",
"Eq",
"List.nil"
] | true |
Set.mulIndicator_eq_one_or_self | Mathlib.Algebra.Notation.Indicator | [
"One",
"Set.mulIndicator",
"Set.mulIndicator_of_notMem",
"Classical.propDecidable",
"Membership.mem",
"dite",
"One.toOfNat1",
"Or.inl",
"Or",
"OfNat.ofNat",
"Set.mulIndicator_of_mem",
"Eq",
"Set.instMembership",
"Not",
"Or.inr",
"Set"
] | true |
_private.Mathlib.Tactic.Linter.TextBased.0.Mathlib.Linter.TextBased.ErrorContext.recOn | Mathlib.Tactic.Linter.TextBased | [
"_private.Mathlib.Tactic.Linter.TextBased.0.Mathlib.Linter.TextBased.StyleError",
"_private.Mathlib.Tactic.Linter.TextBased.0.Mathlib.Linter.TextBased.ErrorContext.rec",
"_private.Mathlib.Tactic.Linter.TextBased.0.Mathlib.Linter.TextBased.ErrorContext",
"Nat",
"_private.Mathlib.Tactic.Linter.TextBased.0.Mat... | false |
_private.Init.Data.Nat.ToString.0.Nat.length_toDigits_le_iff._simp_1_4 | Init.Data.Nat.ToString | [
"Nat.pos_iff_ne_zero",
"Ne",
"instOfNatNat",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | false |
Lean.Elab.Tactic.RCases.instCoeIdentTSyntaxConsSyntaxNodeKindMkStr1Nil_lean | Lean.Elab.Tactic.RCases | [
"Pure.pure",
"Lean.TSyntax",
"Lean.Unhygienic.run",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Unhygienic",
"Lean.SourceInfo",
"Lean.Name.mkStr5",
"Lean.Syntax.Ident",
"Lean.TSyntax.mk",
"ReaderT.instMonad",
"Lean.MonadQuotation.toMonadRef",
"Coe.mk",
"Lean.TSyntax.raw",
"Id",
"Applicative.... | true |
ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"Norm.norm",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"SeminormedRing.toNorm",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"Finset.univ",
"ContinuousMultilinearMap.mkPiAlgebraFin",
"Ring.toNonAssocR... | true |
FirstOrder.Ring.genericPolyMap.eq_1 | Mathlib.RingTheory.MvPolynomial.FreeCommRing | [
"Nat.instMulZeroClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"FreeCommRing",
"CommSemiring.toSemiring",
"Finset",
"instCommRingFreeCommRing",
"FreeCommRing.of",
"Membership.mem",
"Sum",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonA... | true |
_private.Mathlib.Algebra.Order.Ring.WithTop.0.WithTop.pow_right_strictMono.match_1_1 | Mathlib.Algebra.Order.Ring.WithTop | [
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.zero",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Sylow.normal_of_normalizerCondition | Mathlib.GroupTheory.Sylow | [
"Sylow.toSubgroup",
"Sylow.normalizer_normalizer",
"Nat.Prime",
"Sylow",
"Finite",
"Group",
"Fact",
"Subgroup",
"Subgroup.normalizer",
"NormalizerCondition",
"normalizerCondition_iff_only_full_group_self_normalizing",
"SetLike.coe",
"Nat",
"Subgroup.normalizer_eq_top_iff",
"Iff.mp",
"S... | true |
ContinuousAddMonoidHom.instAddCommMonoid._proof_1 | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"AddMonoid.toAddSemigroup",
"Zero.zero",
"ContinuousAddMonoidHom",
"add_assoc",
"Add.mk",
"AddMonoid.toAddZeroClass",
"instTopologicalSpaceProd",
"AddZeroClass.toAddZero",
"ContinuousAddMonoidHom.instZero",
"instOfNatNat",
"ContinuousAddMonoidHom.add",
"ContinuousAddMonoidHom.instFunLike",
"... | false |
CategoryTheory.CommRingObjCat.instCategory._proof_2 | Mathlib.CategoryTheory.Monoidal.Ring | [
"CategoryTheory.CommRingObjCat.X",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.BraidedCategory",
"CategoryTheory.CommRingObjCat",
"CategoryTheory.CommRingObjCat.commRingObj",
"CategoryTheory.CommRingObj.toRingObj",
"Cat... | false |
NNReal.coe_real_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Real",
"Real.pi",
"NNReal.pi",
"Eq",
"NNReal.toReal",
"rfl"
] | true |
FiniteDimensional.RCLike.properSpace_submodule | Mathlib.Analysis.RCLike.Lemmas | [
"NormedCommRing.toNormedRing",
"Submodule",
"FiniteDimensional.proper_rclike",
"instSMulOfMul",
"NormedRing.toRing",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedDivisionRing.toDivisionRing",
"Membership.mem",
"NormedField.toField",
"Submodule.normedSpace",
"... | true |
IsPrimitiveRoot.neZero' | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Eq.mpr",
"RingHom.instRingHomClass",
"IsDomain",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"CommRing",
"NeZero.mk",
"IsDomain.to_noZeroDivisors",
"Nat.Prime",
"Dvd.dvd",
"HMul.hMul",
"IsPrimitiveRoot.pow_ne_one_of_pos_of_lt",
"IsStrictOrderedRing.toMulPosStrictMono",
"Nat.Prime.o... | true |
MeasureTheory.setIntegral_indicatorConstLp | Mathlib.MeasureTheory.Integral.Bochner.Set | [
"MeasureTheory.ae",
"Eq.mpr",
"Real",
"instHSMul",
"Trans.trans",
"MeasureTheory.Measure",
"CompleteSpace",
"MeasurableSet",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Set.indicator",
"MeasureTheory.indicatorConstLp",
"MeasureTheory.AEEq... | true |
Polynomial.degree_map_le | Mathlib.Algebra.Polynomial.Eval.Degree | [
"Iff.mpr",
"WithBot.instPreorder",
"RingHom.instRingHomClass",
"WithBot",
"Preorder.toLT",
"Polynomial.coeff_map",
"le_rfl",
"congrArg",
"Preorder.toLE",
"RingHom",
"map_zero",
"Eq.mp",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMulZeroOneClass",
"Polynomial.degree",
... | true |
LinearMap.flip._proof_5 | Mathlib.LinearAlgebra.BilinearMap | [
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"RingHom.instFunLike",
"LinearMap.addCommMonoid",
"Sem... | false |
AddSemiconjBy.map._simp_1 | Mathlib.Algebra.Group.Commute.Hom | [
"AddSemiconjBy",
"AddSemiconjBy.map",
"True",
"AddHomClass",
"eq_true",
"Eq",
"DFunLike.coe",
"Add",
"FunLike"
] | false |
_private.Mathlib.Tactic.Ring.Basic.0.Mathlib.Tactic.Ring.RingCompute.pow._proof_1 | Mathlib.Tactic.Ring.Basic | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"Qq.Quoted",
"Lean.Level.zero",
"Qq.Quoted.unsafeMk",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Qq.QuotedDefEq.unsafeIntro",
"List.nil"
] | false |
_private.Mathlib.Data.List.Cycle.0.List.prev_eq_getElem?_idxOf_pred_of_ne_head._proof_1_14 | Mathlib.Data.List.Cycle | [
"Membership.mem",
"List.ne_nil_of_mem",
"Ne",
"List.cons",
"List",
"List.instMembership",
"List.nil"
] | false |
_private.Lean.Meta.Tactic.Replace.0.Lean.MVarId.withReverted.match_1 | Lean.Meta.Tactic.Replace | [
"Option.ctorIdx",
"Option.some",
"Lean.FVarId",
"Nat.hasNotBit",
"_private.Lean.Meta.Tactic.Replace.0.Lean.MVarId.withReverted._sparseCasesOn_1",
"Option"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Equiv.toList_eq._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 |
Order.IsPredLimit.ne_top | Mathlib.Order.SuccPred.Limit | [
"Preorder.toLE",
"Ne",
"OrderTop",
"OrderTop.toTop",
"Order.IsPredLimit.top_lt",
"Top.top",
"Preorder",
"LT.lt.ne",
"Order.IsPredLimit"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.size_left_le_size_union._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion.0.aux_IsBigO_mul | Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.div_congr",
"SeminormedRing.toNorm",
"Real",
"instHDiv",
"Mathlib.Meta.NormNum.IsNat.to_isNNRat",
"Grou... | true |
ProbabilityTheory.Kernel.compProd_prodMkLeft_eq_comp | Mathlib.Probability.Kernel.Composition.KernelLemmas | [
"ProbabilityTheory.Kernel.prod_apply'",
"Eq.mpr",
"ProbabilityTheory.IsZeroOrMarkovKernel.isFiniteKernel",
"MeasureTheory.Measure",
"MeasurableSet",
"ProbabilityTheory.Kernel.IsSFiniteKernel.prodMkLeft",
"congrArg",
"ProbabilityTheory.Kernel.comp",
"MeasureTheory.lintegral_dirac'",
"ProbabilityThe... | true |
MonadSatisfying.instStateRefT'._proof_2 | Batteries.Classes.SatisfiesM | [
"LawfulFunctor",
"instLawfulMonadStateRefT'",
"Monad.toApplicative",
"LawfulApplicative.toLawfulFunctor",
"LawfulMonad",
"StateRefT'",
"StateRefT'.instMonad",
"Applicative.toFunctor",
"LawfulMonad.toLawfulApplicative",
"Monad"
] | false |
BEq.rfl | Init.Core | [
"Bool.true",
"BEq.beq",
"ReflBEq.rfl",
"ReflBEq",
"Bool",
"BEq",
"Eq"
] | true |
IsLUB | Mathlib.Order.Bounds.Defs | [
"upperBounds",
"LE",
"IsLeast",
"Set"
] | true |
_private.Lean.Meta.CongrTheorems.0.Lean.Meta.mkCongrSimpCore?.mkProof.go._unsafe_rec | Lean.Meta.CongrTheorems | [
"Lean.Meta.mkEqRec",
"_private.Lean.Meta.CongrTheorems.0.Lean.Meta.mkHCongrWithArity.mkProof.match_4",
"panicWithPosWithDecl",
"Lean.Expr",
"Lean.Meta.MetaM",
"instDecidableEqBool",
"instOfNatNat",
"Lean.Meta.mkEqNDRec",
"Lean.Expr.instantiate",
"instBEqOfDecidableEq",
"_private.Lean.Meta.CongrT... | false |
Multiset.instDistribLattice | Mathlib.Data.Multiset.UnionInter | [
"Multiset.instDistribLattice._proof_5",
"Multiset.instLattice",
"Multiset",
"DistribLattice",
"DistribLattice.mk",
"DecidableEq"
] | true |
_private.Mathlib.RingTheory.AdjoinRoot.0.AdjoinRoot.map._simp_1 | Mathlib.RingTheory.AdjoinRoot | [
"RingHom",
"Polynomial.eval₂",
"Polynomial.eval₂_map",
"Polynomial",
"RingHom.comp",
"Semiring",
"Polynomial.map",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq"
] | false |
ENat.smul_sSup | Mathlib.Data.ENat.Lattice | [
"Eq.mpr",
"instHSMul",
"instCompleteLinearOrderENat",
"instSMulOfMul",
"congrArg",
"CommSemiring.toSemiring",
"iSup",
"IsScalarTower",
"CompletelyDistribLattice.toCompleteLattice",
"SMul",
"Membership.mem",
"id",
"ENat.smul_iSup",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLa... | true |
Preorder.piCongrLeft_comp_restrictLe | Mathlib.Order.Restriction | [
"Equiv.instEquivLike",
"Finset",
"Equiv.IicFinsetSet",
"Function.comp",
"Membership.mem",
"LocallyFiniteOrderBot",
"Set.Elem",
"Equiv",
"Subtype",
"Equiv.piCongrLeft",
"Preorder.restrictLe",
"Finset.instSetLike",
"Finset.Iic",
"Set.Iic",
"Preorder.frestrictLe",
"Equiv.symm",
"Subtype... | true |
Part.get_eq_get_of_eq | Mathlib.Data.Part | [
"Part",
"Eq.rec",
"Part.get",
"Part.Dom",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
_private.Lean.Elab.Import.0.Lean.Elab.printImports.match_1 | Lean.Elab.Import | [
"Lean.Import",
"Prod.mk",
"Lean.Position",
"Array",
"Prod",
"Prod.casesOn",
"Lean.MessageLog"
] | false |
CategoryTheory.Arrow.leftFunc_obj | Mathlib.CategoryTheory.Comma.Arrow | [
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.Comma",
"CategoryTheory.Arrow.leftFunc",
"CategoryTheory.instCategoryArrow",
"Eq.refl",
"CategoryTheory.Arrow",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
String.Slice.Pattern.Model.ForwardStringSearcher.isLongestRevMatch_iff | Init.Data.String.Lemmas.Pattern.String.Basic | [
"String.Slice.Pattern.Model.IsRevMatch",
"Eq.mpr",
"String.Slice.Pattern.Model.ForwardStringSearcher.instPatternModel",
"congrArg",
"String",
"Iff.rfl",
"String.Slice.sliceFrom",
"String.Slice",
"id",
"Ne",
"String.Slice.Pattern.Model.ForwardStringSearcher.isRevMatch_iff",
"String.Slice.Patter... | true |
Filter.Realizer.ofEquiv_F | Mathlib.Data.Analysis.Filter | [
"Equiv.instEquivLike",
"CompleteLattice.toConditionallyCompleteLattice",
"Equiv",
"Filter.Realizer.ofEquiv",
"Filter.Realizer.F",
"CompleteBooleanAlgebra.toCompleteLattice",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"Co... | true |
_private.Mathlib.AlgebraicTopology.ExtraDegeneracy.0.CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.homotopy._proof_33 | Mathlib.AlgebraicTopology.ExtraDegeneracy | [
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"of_decide_eq_true",
"Int.Linear.norm_le",
"Fin.succ",
"Lean.Grind.CommRing.Expr.var",
"Int.L... | false |
CategoryTheory.GrothendieckTopology.PreservesSheafification.transport | Mathlib.CategoryTheory.Sites.Equivalence | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Functor.IsCoverDense",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.GrothendieckTopology.PreservesSheafification",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.co... | true |
CategoryTheory.RanIsSheafOfIsCocontinuous.liftAux._proof_1 | Mathlib.CategoryTheory.Sites.CoverLifting | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Membership.mem",
"CategoryTheory.GrothendieckTopology.pullback_stable",
"CategoryTheory.Sieve",
"CategoryTheory.Functor.IsCocontinuous",
"CategoryTheory.GrothendieckTopology.Cover",
"CategoryTheory.GrothendieckTopolog... | false |
IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_of_surjective | Mathlib.FieldTheory.Relrank | [
"Cardinal",
"IntermediateField",
"AlgHom",
"AlgHom.funLike",
"Cardinal.lift",
"Algebra",
"Membership.mem",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_of_le",
"IntermediateField.instSetLike",
... | true |
_private.Mathlib.Data.Set.Image.0.Set.imageFactorization_surjective.match_1_1 | Mathlib.Data.Set.Image | [
"HEq.refl",
"Subtype.casesOn",
"Membership.mem",
"Set.Elem",
"Eq.casesOn",
"Subtype.mk",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"Set.image",
"HEq",
"Eq.symm",
"Eq",
"Set.instMembership",
"Set"
] | false |
iSup_inf_eq | Mathlib.Order.CompleteBooleanAlgebra | [
"Eq.mpr",
"CompleteLattice.toLattice",
"congrArg",
"iSup",
"iSup.eq_1",
"iSup_range",
"Membership.mem",
"id",
"SemilatticeInf.toMin",
"Order.Frame.toCompleteLattice",
"CompleteSemilatticeSup.toSupSet",
"Eq.refl",
"CompleteLattice.toCompleteSemilatticeSup",
"Set.range",
"Order.Frame",
"... | true |
Lean.Parser.Term.throwNamedErrorMacro | Lean.Parser.Term | [
"Lean.Parser.identWithPartialTrailingDot",
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"Lean.Parser.interpolatedStr",
"instHAndThenOfAndThen",
"HOrElse.hOrElse",
"instOfNatNat",
"Lean.Parser.symbol",
"Lean.Parser.ppSpace",
"Lean.Parser.withAntiquot",
"Bool.true",
"U... | true |
QuaternionAlgebra.coe_natCast | Mathlib.Algebra.Quaternion | [
"AddCommGroupWithOne",
"AddGroupWithOne.toAddMonoidWithOne",
"QuaternionAlgebra",
"AddMonoidWithOne.toNatCast",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Nat.cast",
"QuaternionAlgebra.coe",
"Nat",
"AddCommGroup.toDivi... | true |
CategoryTheory.IndParallelPairPresentation.parallelPairIsoParallelPairCompYoneda._proof_4 | Mathlib.CategoryTheory.Limits.Indization.ParallelPair | [
"CategoryTheory.Limits.Types.hasColimitsOfShape",
"CategoryTheory.Functor",
"CategoryTheory.IndParallelPairPresentation.φ",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"Catego... | false |
Std.Sat.AIG.RefVec.MapTarget.recOn | Std.Sat.AIG.RefVecOperator.Map | [
"Std.Sat.AIG.RefVec.MapTarget",
"Std.Sat.AIG.RefVec.MapTarget.mk",
"Std.Sat.AIG.Entrypoint",
"Std.Sat.AIG.RefVec.MapTarget.rec",
"Std.Sat.AIG.Ref",
"Std.Sat.AIG",
"Nat",
"Std.Sat.AIG.RefVec.LawfulMapOperator",
"Hashable",
"Std.Sat.AIG.RefVec",
"Std.Sat.AIG.LawfulOperator",
"DecidableEq"
] | false |
Std.DTreeMap.Internal.Impl.getKeyD_union!_of_contains_eq_false_left | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.getKeyD",
"Eq.mpr",
"Ord",
"congrArg",
"Std.TransOrd",
"id",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Std.DTreeMap.Internal.Impl.contains",
"Std.DTreeMap.Internal.Impl.union!",
"Std.DTreeMap.Internal.Impl.getKeyD_union_of_contains_eq... | true |
Sat.Fmla.reify.mk | Mathlib.Tactic.Sat.FromLRAT | [
"Sat.Fmla",
"Sat.Fmla.reify.mk",
"Sat.Valuation.satisfies_fmla",
"Sat.Valuation",
"Sat.Fmla.reify",
"Not"
] | true |
Std.ExtHashMap.ext_getKey_getElem?_iff | Std.Data.ExtHashMap.Lemmas | [
"HEq.refl",
"Membership.mem",
"Eq.casesOn",
"Std.ExtHashMap.ext_getKey_getElem?",
"LawfulHashable",
"Std.ExtHashMap",
"And.casesOn",
"And",
"Iff",
"EquivBEq",
"And.intro",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Hashable",
"GetElem?.getElem?",
"Std.ExtHashMap.instGetElem?Mem",
... | true |
CategoryTheory.Limits.spanCompIso._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"Option.some.noConfusion",
"CategoryTheory.Limits.WidePushoutShape.struct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Option.ctorIdx",
"congrArg",
"HEq.refl",
"False.elim",
"CategoryTheory.Limits.WidePushoutShape.Hom.i... | false |
Lean.Elab.TerminationMeasure.mk.noConfusion | Lean.Elab.PreDefinition.TerminationMeasure | [
"Lean.Syntax",
"Lean.Expr",
"id",
"Lean.Elab.TerminationMeasure.mk",
"Bool",
"Lean.Elab.TerminationMeasure.noConfusion",
"Lean.Elab.TerminationMeasure",
"Eq"
] | false |
Lean.Elab.MonadParentDecl.noConfusionType | Lean.Elab.InfoTree.Types | [
"Lean.Elab.MonadParentDecl.casesOn",
"Lean.Elab.MonadParentDecl",
"Lean.Name",
"HEq",
"Option"
] | false |
CategoryTheory.Abelian.Ext.bilinearComp | Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | [
"CategoryTheory.Abelian.Ext.instAddCommGroup",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"CategoryTheory.Abelian",
"AddZeroClass.toAddZero",
"CategoryTheory.Abelian.Ext.bilinearComp._proof_2",
"CategoryTheory.HasExt",
"CategoryTheory.Abelian.Ext.comp",
"instHAdd",
"AddGroup.toSubNegMo... | true |
BialgHom.toAlgHom._proof_2 | Mathlib.RingTheory.Bialgebra.Hom | [
"CoalgebraStruct",
"CoalgHom.toLinearMap",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Algebra",
"LinearMap.map_zero",
"AddZeroClass.toAddZero",
"Algebra.toModule",
"LinearMap",
"CommSemiring",
"BialgHom",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"A... | false |
Lean.Meta.Match.State.mk.injEq | Lean.Meta.Match.Match | [
"Lean.Meta.Match.Example",
"Eq.propIntro",
"Lean.injEq_helper",
"Std.HashSet",
"Lean.Meta.Match.State.mk",
"Lean.Meta.Match.Overlaps",
"instHashableNat",
"instBEqOfDecidableEq",
"List",
"And",
"Nat",
"Eq.ndrec",
"Eq.refl",
"instDecidableEqNat",
"Eq",
"Lean.Meta.Match.State.mk.inj",
"... | true |
CategoryTheory.Limits.preservesProduct_of_preservesBiproduct | Mathlib.CategoryTheory.Preadditive.Biproducts | [
"CategoryTheory.Limits.PreservesBiproduct",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.IsLimit.postcomposeInvEquiv",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.PreservesLimit",
"Equiv.instEquivLike",
"CategoryTheory.Functor.mapBicone",
"CategoryTheory.... | true |
ENat.coe_lt_coe | Mathlib.Data.ENat.Basic | [
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ENat.instNatCast",
"instLinearOrderENat",
"congrArg",
"CommSemiring.toSemiring",
"Nat.cast_lt._simp_1",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"instPreorderENat",
"Nat.cast",
"iff_self",
"NonUnitalNonAssocSemiring.toAddCo... | true |
CategoryTheory.CountableAB4Star.of_hasExactLimitsOfShape_nat | Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.instHasProductsOfShapeOfHasCountableProductsOfCountable",
"Finite",
"CategoryTheory.Limits.HasFiniteBiproducts",
"inferInstance",
"CategoryTheory.Limits.HasCountableProducts",
"CategoryTheory.CountableAB4Star.of_hasExactLimitsOfShape_nat_a... | true |
Std.ExtHashMap.getElem?_filter' | Std.Data.ExtHashMap.Lemmas | [
"Iff.mpr",
"Std.ExtHashMap.filter",
"Option.pfilter",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Std.ExtHashMap.getElem?_filter",
"Std.ExtHashMap.getKey_eq",
"Option.some",
"LawfulBEq",
"Membership.mem",
"Option.pfilter_congr",
"Std.ExtHashMap.mem_iff_isSome_getElem?",
"Std.ExtHashMap",
... | true |
Holor.instAddMonoid._aux_3 | Mathlib.Data.Holor | [
"instHSMul",
"AddMonoid.toNSMul",
"List",
"Nat",
"AddMonoid",
"HSMul.hSMul",
"Holor",
"HolorIndex"
] | false |
IsAzumaya.recOn | Mathlib.Algebra.Azumaya.Defs | [
"instSMulOfMul",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"MulOpposite.instAlgebra",
"MulOpposite",
"Module.End.instSemiring",
"MulOpposite.instModule",
"Module.Projective",
"Algebra",
"Algebra.toSMul",
"Algebra.toModule",
"IsScalarTower.left",
"smulCommClass_self",
"instDi... | false |
CommMonoidWithZero.zero_mul | Mathlib.Algebra.GroupWithZero.Defs | [
"CommMonoidWithZero.toCommMonoid",
"Semigroup.toMul",
"HMul.hMul",
"CommMonoid.toMonoid",
"CommMonoidWithZero.toZero",
"CommMonoidWithZero",
"Monoid.toSemigroup",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"instHMul"
] | true |
Frm.hom_ext_iff | Mathlib.Order.Category.Frm | [
"FrameHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"Eq.casesOn",
"Frm.Hom.hom",
"Frm.str",
"Iff",
"Order.Frame.toCompleteLattice",
"Frm.hom_ext",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"CategoryTheory.Category.toCategoryStruct",
"Frm.carrier",
"Frm",
... | true |
Nat.choose_mul_factorial_mul_factorial | Mathlib.Data.Nat.Choose.Basic | [
"Nat.choose",
"Nat.choose_mul_factorial_mul_factorial._f",
"HMul.hMul",
"HSub.hSub",
"Nat.brecOn",
"instSubNat",
"instMulNat",
"LE.le",
"instLENat",
"instHSub",
"Nat.factorial",
"Nat",
"Eq",
"instHMul"
] | true |
Subring.op_top | Mathlib.Algebra.Ring.Subring.MulOpposite | [
"MulOpposite",
"MulOpposite.instNonAssocRing",
"NonAssocRing",
"Subring",
"Subring.instTop",
"Subring.op",
"Top.top",
"Eq",
"rfl"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.mem_lattice._simp_1_2 | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | [
"Submodule",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"Set.instSingletonSet",
"Insert.insert",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"Set.instInsert",
"HAdd.hAd... | false |
ZFSet.Definable | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"Nat",
"ZFSet.Definable.mk",
"Fin"
] | true |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.toFunctorToCategoricalPullback._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.CategoricalPullback.Hom.mk.congr_simp",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.CategoricalPullback.mk",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.... | false |
Finset.notMem_singleton | Mathlib.Data.Finset.Insert | [
"Finset.mem_singleton",
"Finset",
"Membership.mem",
"Ne",
"Iff",
"Finset.instSetLike",
"Finset.instSingleton",
"Singleton.singleton",
"Eq",
"Not",
"SetLike.instMembership",
"not_congr"
] | true |
Plausible.SampleableExt.sample | Plausible.Sampleable | [
"Plausible.SampleableExt.proxy",
"Plausible.Arbitrary",
"Plausible.SampleableExt"
] | true |
NNReal.coe_sInf | Mathlib.Data.NNReal.Defs | [
"Eq.mpr",
"Real.instLE",
"Real",
"Set.Ici",
"Real.instZero",
"congrArg",
"PartialOrder.toPreorder",
"subset_sInf_emptyset",
"Membership.mem",
"Set.Elem",
"id",
"Subtype",
"NNReal",
"LE.le",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"subsetInfSet",
"Or.casesOn... | true |
_private.Init.Data.Range.Polymorphic.Internal.SignedBitVec.0.BitVec.Signed.instRxcLawfulHasSize.match_5 | Init.Data.Range.Polymorphic.Internal.SignedBitVec | [
"BitVec",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.zero",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Measurable.of_discrete | Mathlib.MeasureTheory.MeasurableSpace.Defs | [
"MeasurableSet",
"MeasurableSet.of_discrete",
"DiscreteMeasurableSpace",
"Measurable",
"MeasurableSpace",
"Set.preimage",
"Set"
] | true |
LinearEquiv.toContinuousLinearEquivOfBounds | Mathlib.Analysis.Normed.Operator.ContinuousLinearMap | [
"Norm.norm",
"Real.instLE",
"LinearEquiv.symm",
"Real",
"SeminormedAddCommGroup",
"HMul.hMul",
"ContinuousLinearEquiv.mk",
"LinearEquiv.toContinuousLinearEquivOfBounds._proof_1",
"AddCommGroup.toAddCommMonoid",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"LE.le",
"RingHomInvPair",
"Semi... | true |
_private.Mathlib.Analysis.SumIntegralComparisons.0.integral_le_sum_mul_Ico_of_antitone_monotone._proof_1_3 | Mathlib.Analysis.SumIntegralComparisons | [
"Lean.RArray.leaf",
"False",
"Preorder.toLT",
"of_decide_eq_true",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"Preorder.toLE",
"Eq.mp",
"Lean.RArray.branch",
"Na... | false |
Std.Http.Body.Empty.ctorIdx | Std.Internal.Http.Data.Body.Empty | [
"Std.Http.Body.Empty",
"Nat"
] | false |
Lean.Compiler.LCNF.Simp.ConstantFold.Folder.leftRightAnnihilator._auto_1 | Lean.Compiler.LCNF.Simp.ConstantFold | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
UniformEquiv.piCongrRight | Mathlib.Topology.UniformSpace.Equiv | [
"Pi.uniformSpace",
"UniformSpace",
"UniformEquiv.piCongrRight._proof_1",
"Equiv",
"UniformEquiv.mk",
"Equiv.piCongrRight",
"UniformEquiv.piCongrRight._proof_2",
"UniformEquiv.toEquiv",
"UniformEquiv"
] | true |
AlgebraicGeometry.Scheme.isAffine_affineBasisCover | Mathlib.AlgebraicGeometry.AffineScheme | [
"AlgebraicGeometry.Scheme",
"Opposite",
"CommRingCat.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"AlgebraicGeometry.Scheme.affineBasisCover",
"TopCat.instCategory",
"PartialOrder.toPreorder",
"Localization.Away",
"AlgebraicGeometry.Scheme.affineCover._proof_5",
"Topologic... | true |
Array.append_inj_left' | Init.Data.Array.Lemmas | [
"Array.instAppend",
"Array.append_inj'",
"Array",
"instHAppendOfAppend",
"And.left",
"Nat",
"Eq",
"Array.size",
"HAppend.hAppend"
] | true |
not_covBy_bot._simp_1 | Mathlib.Order.BoundedOrder.Basic | [
"False",
"Preorder.toLT",
"eq_false",
"CovBy",
"OrderBot.toBot",
"Preorder.toLE",
"OrderBot",
"Bot.bot",
"not_covBy_bot",
"Eq",
"Preorder"
] | false |
RingHomInvPair.mk._flat_ctor | Mathlib.Algebra.Ring.CompTypeclasses | [
"outParam",
"RingHom",
"RingHomInvPair",
"RingHom.comp",
"Semiring",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"RingHomInvPair.mk"
] | false |
MeasureTheory.AddQuotientMeasureEqMeasurePreimage.addHaarMeasure_quotient | Mathlib.MeasureTheory.Measure.Haar.Quotient | [
"instWeaklyLocallyCompactSpaceOfLocallyCompactSpace",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"MeasureTheory.Measure.IsAddHaarMeasure.smul",
"lt_of_le_of_lt",
"instHSMul",
"MeasureTheory.Measure",
"instSeparatelyContinuousAddOfContinuousAdd",
"instSMulOfMul",
"IsScalarTower.right",
"interior_s... | true |
_private.Lean.Meta.ExprDefEq.0.Lean.Meta.isDefEqArgs._sparseCasesOn_1 | Lean.Meta.ExprDefEq | [
"Nat.ne_of_beq_eq_false",
"Lean.Meta.DefEqArgsFirstPassResult.rec",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Meta.DefEqArgsFirstPassResult.ctorIdx",
"Array",
"Nat.land",
"Lean.Meta.DefEqArgsFirstPassResult.failed",
"Nat",
"Lean.Meta.DefEqArgsFirstPassResult.ok",
"Lean.Meta.DefE... | false |
LightDiagram.diagram | Mathlib.Topology.Category.LightProfinite.Basic | [
"CategoryTheory.Functor",
"Opposite",
"Finite",
"FintypeCat",
"Preorder.smallCategory",
"LightDiagram",
"Nat.instPreorder",
"Nat",
"CategoryTheory.types",
"CategoryTheory.Category.opposite",
"CategoryTheory.ObjectProperty.FullSubcategory.category"
] | true |
_private.Mathlib.LinearAlgebra.TensorAlgebra.Basic.0.instSMulCommClassTensorAlgebra._proof_1 | Mathlib.LinearAlgebra.TensorAlgebra.Basic | [
"FreeAlgebra.instSemiring",
"FreeAlgebra.instAlgebra",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"FreeAlgebra.instSMulCommClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"RingQuot.instSMulCommClass",
"DistribSMul.to... | false |
_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.doubling_lt_golden_ratio._simp_1_21 | Mathlib.Combinatorics.Additive.VerySmallDoubling | [
"Finset",
"Membership.mem",
"HasSubset.Subset",
"Finset.instSetLike",
"Finset.subset_iff",
"propext",
"Finset.instHasSubset",
"Eq",
"SetLike.instMembership"
] | false |
DifferentiableAt.smul_const | Mathlib.Analysis.Calculus.FDeriv.Mul | [
"instHSMul",
"NormedRing.toRing",
"NormedSpace",
"ContinuousLinearMap.smulRight",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"DifferentiableAt",
"IsScalarTower",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"SeminormedRing.toRin... | true |
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