name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Bipointed.swap._proof_1 | Mathlib.CategoryTheory.Category.Bipointed | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Bipointed.toProd",
"CategoryTheory.CategoryStruct.id",
"Bipointed.Hom.map_snd",
"id",
"Bipointed.X",
"Bipointed",
"Bipointed.Hom.mk",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Prod.swap",
"Bipointed.Hom.map_fst",
"Bipoi... | false |
TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_addGroup | Mathlib.Topology.Algebra.Group.Compact | [
"Filter.instMembership",
"mem_interior_iff_mem_nhds",
"TopologicalSpace.PositiveCompacts.instSetLike",
"TopologicalSpace.PositiveCompacts.interior_nonempty",
"Membership.mem",
"nhds",
"_private.Mathlib.Topology.Algebra.Group.Compact.0.TopologicalSpace.PositiveCompacts.locallyCompactSpace_of_addGroup.mat... | true |
_private.Lean.Meta.Transform.0.Lean.Meta.transformWithCache.visit.visitPost._unsafe_rec | Lean.Meta.Transform | [
"Pure.pure",
"Monad.toApplicative",
"instMonadLiftT",
"Option.getD",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.MonadCacheT",
"liftM",
"MonadLiftT",
"Applicative.toPure",
"Lean.MonadCacheT.instMonad",
"MonadControlT",
"ST",
"Lean.ExprStructEq.instHashable",
"_private.Lean.Me... | false |
_private.Lean.Elab.Tactic.Do.ProofMode.Refine.0.Lean.Elab.Tactic.Do.ProofMode.patAsTerm.match_1 | Lean.Elab.Tactic.Do.ProofMode.Refine | [
"Lean.TSyntax",
"Nat.hasNotBit",
"List.cons",
"Lean.Parser.Tactic.MRefinePat",
"Lean.Name.mkStr2",
"Lean.Parser.Tactic.MRefinePat.ctorIdx",
"Lean.SyntaxNodeKind",
"Lean.Parser.Tactic.MRefinePat.pure",
"Lean.Name.mkStr1",
"_private.Lean.Elab.Tactic.Do.ProofMode.Refine.0.Lean.Elab.Tactic.Do.ProofMod... | false |
Order.cof_ne_one._simp_1 | Mathlib.SetTheory.Cardinal.Cofinality.Basic | [
"False",
"Cardinal.instOne",
"eq_false",
"Cardinal",
"Order.cof_ne_one",
"Preorder.toLE",
"NoTopOrder",
"One.toOfNat1",
"Order.cof",
"OfNat.ofNat",
"Eq",
"Preorder"
] | false |
_private.Mathlib.FieldTheory.Finite.Basic.0._aux_Mathlib_FieldTheory_Finite_Basic___macroRules__private_Mathlib_FieldTheory_Finite_Basic_0_termQ_1 | Mathlib.FieldTheory.Finite.Basic | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr... | false |
MeasureTheory.Filtration.mk.inj | Mathlib.Probability.Process.Filtration | [
"MeasurableSpace.instLE",
"MeasureTheory.Filtration.mk",
"MeasurableSpace.instPartialOrder",
"PartialOrder.toPreorder",
"Monotone",
"MeasureTheory.Filtration",
"LE.le",
"MeasurableSpace",
"eq_of_heq",
"HEq",
"MeasureTheory.Filtration.mk.noConfusion",
"Eq",
"Preorder"
] | true |
String.Slice.Pattern.Model.CharPred.not_matchesAt_of_get | Init.Data.String.Lemmas.Pattern.Pred | [
"False",
"Iff.of_eq",
"congrArg",
"Bool.false_eq_true",
"String.Slice",
"Exists",
"Ne",
"Bool.true",
"String.Slice.endPos",
"exists_false._simp_1",
"String.Slice.Pattern.Model.CharPred.instPatternModelForallCharBool",
"exists_prop_congr",
"True",
"propext",
"Bool",
"of_eq_true",
"Eq.... | true |
AddSubgroup.isComplement'_bot_top | Mathlib.GroupTheory.Complement | [
"AddSubgroup.instBot",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Bot.bot",
"AddSubgroup",
"AddSubgroup.isComplement_singleton_univ",
"AddZero.toZero",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Zero.toOfNat0",
"SubNegMonoid.toAddMonoid",
"AddSubgroup.IsComplement'",
"Top.top",
"O... | true |
NonUnitalAlgHom.rec | Mathlib.Algebra.Algebra.NonUnitalHom | [
"DistribMulActionHom.toMulActionHom",
"Monoid",
"NonUnitalAlgHom.mk",
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"Monoid.toMulOneClass",
"DistribMulActionHom",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"NonU... | false |
String.Slice.copy_slice_next._proof_1 | Init.Data.String.Lemmas.Splits | [
"String.instLEPos_1",
"String.Slice.Pos.le_next._simp_1",
"String.Slice",
"String.Slice.Pos.next",
"Ne",
"LE.le",
"String.Slice.endPos",
"of_eq_true",
"String.Slice.Pos"
] | false |
Set.mul_mem_center | Mathlib.Algebra.Group.Center | [
"Eq.mpr",
"HMul.hMul",
"_private.Mathlib.Algebra.Group.Center.0.Set.mul_mem_center._simp_1_2",
"congrArg",
"Mul",
"Commute",
"Membership.mem",
"Eq.mp",
"id",
"Set.center",
"_private.Mathlib.Algebra.Group.Center.0.Set.mul_mem_center._simp_1_1",
"_private.Mathlib.Algebra.Group.Center.0.Set.mul_m... | true |
Nat.xor_mod_two_eq_one._simp_1 | Init.Data.Nat.Bitwise.Lemmas | [
"Nat.instXorOp",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"HMod.hMod",
"Iff",
"Nat",
"HXor.hXor",
"propext",
"Nat.xor_mod_two_eq_one",
"OfNat.ofNat",
"Eq",
"Not",
"instHXorOfXorOp"
] | false |
Function.IsPeriodicPt.piMap | Mathlib.Dynamics.PeriodicPts.Defs | [
"Iff.mpr",
"Function.isPeriodicPt_piMap",
"Pi.map",
"Function.IsPeriodicPt",
"Nat"
] | true |
Std.ExtTreeSet.get_min? | Std.Data.ExtTreeSet.Lemmas | [
"Std.ExtTreeSet.min?",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Std.ExtTreeMap.getKey_minKey?",
"Bool.true",
"Unit",
"Option.get",
"Std.ExtTreeSet.isSome_min?_of_contains",
"Std.ExtTreeSet.get",
"Std.ExtTreeSet",
"Bool",
"Std.ExtTreeSet.contains",
"Eq"
] | true |
Mathlib.Tactic.BicategoryLike.MonadMor₂Iso.noConfusion | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.Mor₂Iso",
"HEq.refl",
"Mathlib.Tactic.BicategoryLike.CoherenceHom",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.StructuralAtom",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"Mathlib.Tactic.BicategoryLike.MonadMor₂Iso",
"Mathlib.Tactic.BicategoryLike.MonadMor₂Iso.casesOn",
"e... | false |
_private.Init.Data.BitVec.Lemmas.0.BitVec.msb_twoPow._simp_1_2 | Init.Data.BitVec.Lemmas | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
CategoryTheory.Limits.limit.hom_ext_iff | Mathlib.CategoryTheory.Limits.HasLimits | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Limits.HasLimit",
"Eq.casesOn",
"CategoryTheory.Limits.limit.hom_ext",
"CategoryTheory.Limits.limit",
"Iff",
"Iff.intro",
"CategoryTheory.CategoryStruc... | true |
Lean.ModuleDoc.mk._flat_ctor | Lean.DocString.Extension | [
"Lean.ModuleDoc.mk",
"String",
"Lean.DeclarationRange",
"Lean.ModuleDoc"
] | false |
ConvexCone.hull_min | Mathlib.Geometry.Convex.Cone.Basic | [
"ConvexCone.instCompleteSemilatticeInf",
"ConvexCone.instPartialOrder",
"SMul",
"ConvexCone.hull",
"PartialOrder.toPreorder",
"setOf",
"ConvexCone.instSetLike",
"Preorder.toLE",
"PartialOrder",
"HasSubset.Subset",
"LE.le",
"AddCommMonoid",
"SetLike.coe",
"sInf_le",
"ConvexCone",
"Semir... | true |
InverseSystem.piEquivLim | Mathlib.Order.DirectedInverseSystem | [
"InverseSystem.IsNatEquiv",
"Preorder.toLT",
"InverseSystem.invLimEquiv",
"Equiv.instEquivLike",
"Order.IsSuccPrelimit",
"LinearOrder.toDecidableEq",
"Equiv.trans",
"LinearOrder",
"PartialOrder.toPreorder",
"InverseSystem.limit",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOr... | true |
_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation.0.CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁._proof_1_3 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation | [
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"Set.Ici",
"NormedSpace",
"eq_false",
"Lean.Grind.iff_eq",
"Set.subset_def",
"Real.instZero",
"CommSemiring.toSemiring",
"NormedSpace.toModule",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"Lean.Grind.eq_false_of_imp_eq_tru... | false |
Equiv.prodEmpty | Mathlib.Logic.Equiv.Prod | [
"Equiv",
"Prod.isEmpty_right",
"Empty",
"Empty.instIsEmpty",
"Prod",
"Equiv.equivEmpty"
] | true |
ContRepresentation.Equiv.coe_toContinuousLinearMap | Mathlib.RepresentationTheory.Continuous.Basic | [
"Monoid",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"ContRepresentation",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"ContRepresentation.Equiv.toContinuousLinearEquiv",
"ContRepresentation.Equiv.instEquivLike",
"ContRepresentation.Equiv",
"ContinuousLinearMap",
"TopologicalS... | true |
CategoryTheory.instCategoryComonad._proof_4 | Mathlib.CategoryTheory.Monad.Basic | [
"CategoryTheory.Comonad",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Comonad.δ",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Category.comp_id",
"CategoryTh... | false |
AddSemigroupAction.casesOn | Mathlib.Algebra.Group.Action.Defs | [
"VAdd",
"AddSemigroup",
"HVAdd.hVAdd",
"AddSemigroupAction.mk",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"instHVAdd",
"AddSemigroupAction",
"Eq",
"AddSemigroupAction.rec"
] | false |
Polynomial.expand_pow | Mathlib.Algebra.Polynomial.Expand | [
"Function.iterate_succ_apply'",
"Eq.mpr",
"MulOne.toOne",
"id.eq_1",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"Nat.instMonoid",
"Function.iterate_zero",
"AlgHom.funLike",
"Polynomial.expand_one",
"Polynomial.algebraOfAlgebra",
"Algebra.id",
... | true |
CategoryTheory.OplaxFunctor.PseudoCore.mk._flat_ctor | Mathlib.CategoryTheory.Bicategory.Functor.Oplax | [
"CategoryTheory.OplaxFunctor.PseudoCore.mapCompIso_hom._autoParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.OplaxFunctor.mapComp",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.OplaxFunctor.PseudoCore",
"CategoryTheor... | false |
NNRat.instMetricSpace._aux_14 | Mathlib.Topology.Instances.Rat | [
"Rat.instOfNat",
"Rat",
"uniformity",
"PseudoMetricSpace.toUniformSpace",
"Subtype",
"Prod.mk",
"NNRat",
"LE.le",
"Rat.instLE",
"Prod.fst",
"MetricSpace.toPseudoMetricSpace",
"Rat.instMetricSpace",
"Prod",
"OfNat.ofNat",
"Subtype.val",
"Prod.snd",
"Filter",
"Filter.comap"
] | false |
_private.Init.Data.Ord.Vector.0.Vector.instLawfulBEqOrd._proof_1 | Init.Data.Ord.Vector | [
"Vector.instLawfulBEqCmpCompareLex",
"Vector",
"Ord",
"Ord.compare",
"Vector.instBEq",
"Nat",
"Vector.instOrd",
"Std.LawfulBEqOrd",
"BEq"
] | false |
_private.Mathlib.Order.Height.0.Set.one_le_chainHeight_iff._simp_1_1 | Mathlib.Order.Height | [
"instAddMonoidWithOneENat",
"CommSemiring.toSemiring",
"AddMonoidWithOne.toOne",
"ENat",
"LT.lt",
"propext",
"instCommSemiringENat",
"One.toOfNat1",
"Zero.toOfNat0",
"instLTENat",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero",
"instMulZeroClassOfSemiring",
"ENat.lt_one_iff_eq_zero"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality.0.Polynomial.Chebyshev.integral_eval_T_real_mul_self_measureT_zero._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Chebyshev.Orthogonality | [
"Polynomial.eval",
"HMul.hMul",
"CommSemiring.toSemiring",
"Polynomial.eval_mul",
"Polynomial",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"Polynomial.instMul",
"Eq.symm",
"Eq",
"instHMul"
] | false |
CategoryTheory.Limits.Trident.app_zero_assoc | Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers | [
"CategoryTheory.Limits.WalkingParallelFamily.one",
"CategoryTheory.Limits.Trident.app_zero",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.WalkingParallelFamily",
... | true |
SignType.pos | Mathlib.Data.Sign.Defs | [
"SignType.pos",
"SignType"
] | true |
IterateMulAct.instCommMonoid._proof_5 | Mathlib.GroupTheory.GroupAction.IterateAct | [
"Mul.mk",
"HMul.hMul",
"IterateMulAct.mk",
"IterateMulAct.val",
"instHAdd",
"IterateMulAct",
"HAdd.hAdd",
"Nat",
"instAddNat",
"IterateMulAct.ext",
"Eq",
"instHMul",
"Nat.add_comm"
] | false |
OrderedFinpartition.compAlongOrderedFinpartitionₗ._proof_1 | Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno | [
"Function.update",
"NormedSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"ContinuousMultilinearMap.addCommMonoid",
"instDecidableEqFin",
"ContinuousMultilinearMap.map_update_add",
"OrderedFinpartition.compAlongOrderedFinpartition",
"PseudoMetricSpace.toUniformSpace",
... | false |
Lean.Meta.Tactic.Backtrack.BacktrackConfig.mk._flat_ctor | Lean.Meta.Tactic.Backtrack | [
"Lean.MVarId",
"Lean.Meta.MetaM",
"List",
"Nat",
"Bool",
"Lean.Meta.Tactic.Backtrack.BacktrackConfig.mk",
"Lean.Meta.Tactic.Backtrack.BacktrackConfig",
"Option"
] | false |
_private.Init.Control.Lawful.Instances.0.EStateM.bind.match_1.eq_1 | Init.Control.Lawful.Instances | [
"EStateM.Result",
"EStateM.bind.match_1",
"Eq.refl",
"EStateM.Result.ok",
"EStateM.Result.error",
"Eq"
] | true |
TopHom._sizeOf_inst | Mathlib.Order.Hom.Bounded | [
"TopHom._sizeOf_1",
"SizeOf.mk",
"TopHom",
"SizeOf",
"Top"
] | false |
εNFA.εClosure.below.step | Mathlib.Computability.EpsilonNFA | [
"εNFA.εClosure.step",
"εNFA.εClosure.below",
"Membership.mem",
"εNFA.εClosure.below.step",
"Option.none",
"εNFA.step",
"Set.instMembership",
"εNFA",
"εNFA.εClosure",
"Set"
] | true |
ModularGroup.one_lt_normSq_T_zpow_smul | Mathlib.NumberTheory.Modular | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Real.instIsOrderedRing",
"Int.cast",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"ModularGroup.fd._proof_1",
"Mathlib.Meta.NormNum.isNat_add",
"R... | true |
not_addDissociated | Mathlib.Combinatorics.Additive.Dissociation | [
"_private.Mathlib.Combinatorics.Additive.Dissociation.0.not_addDissociated._proof_1_1",
"AddCommGroup.toAddCommMonoid",
"Finset",
"Exists",
"AddCommGroup",
"HasSubset.Subset",
"Ne",
"And",
"Iff",
"SetLike.coe",
"Finset.instSetLike",
"Eq",
"Not",
"AddDissociated",
"Finset.sum",
"Set.ins... | true |
Std.Internal.List.List.getValueD_filter_containsKey_of_containsKey_right | Std.Data.Internal.List.Associative | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"congrArg",
"Option.getD",
"Eq.rec",
"id",
"Sigma.fst",
"Bool.true",
"List",
"Std.Internal.List.containsKey",
"EquivBEq",
"Std.Internal.List.getValue?",
"List.filter",
"Bool",
"Eq.refl",
"Std.Internal.List.List.getValue?_filter_containsKey_of... | true |
CochainComplex.mappingConeHomOfDegreewiseSplitIso | Mathlib.Algebra.Homology.HomotopyCategory.DegreewiseSplit | [
"HomologicalComplex.instCategory",
"CochainComplex.cocycleOfDegreewiseSplit._proof_10",
"HomologicalComplex.Hom.isoOfComponents",
"CategoryTheory.ShortComplex",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"CochainComplex.instHasShiftInt",
"CategoryTheory.ShortComple... | true |
_private.Lean.Server.FileWorker.WidgetRequests.0.Lean.Widget.findTaggedTextMatches | Lean.Server.FileWorker.WidgetRequests | [
"String",
"Lean.Widget.TaggedText.rewrite",
"String.Pos.Raw",
"Lean.Widget.TaggedText",
"Array",
"Empty",
"Lean.Widget.TaggedText.text",
"Lean.Widget.TaggedText.stripTags",
"_private.Lean.Server.FileWorker.WidgetRequests.0.Lean.Widget.kmpSearch"
] | true |
Lean.Meta.InductionSubgoal.fields | Lean.Meta.Tactic.Induction | [
"Lean.Meta.InductionSubgoal",
"Lean.Expr",
"Array"
] | true |
Tuple.lt_card_le_iff_apply_le_of_monotone | Mathlib.Data.Fin.Tuple.Sort | [
"Finset.univ",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"Fin.lt_card_filter_univ_iff_apply_of_imp",
"LE.le",
"Fin.val",
"Fin.fintype",
"DecidableLE",
"Iff",
"Fin.instPartialOrder",
"Nat",
"LT.lt",
"Finset.card",
"_private.Mathlib.Data.Fin.Tuple.Sort.0.Tuple.lt_card_le_iff_... | true |
GrpCat.sectionsSubgroup._proof_2 | Mathlib.Algebra.Category.Grp.Limits | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"GrpCat.hasForgetToMonCat",
"CategoryTheory.Functor",
"GrpCat",
"MonoidHom.instFunLike",
"HMul.hMul",
"MonoidHom",
"GrpCat.str",
"Monoid.toMulOneClass",
"Submonoid.toSubsemigroup",
"CategoryTheory.Functor.comp",
"Membership.mem",
"MulOne.toMul",... | false |
_private.Init.Data.List.Monadic.0.List.mapM'.match_1.splitter | Init.Data.List.Monadic | [
"List.cons",
"List",
"Unit",
"List.mapM'.match_1",
"List.nil"
] | true |
CategoryTheory.EnrichedCategory.id_comp._autoParam | Mathlib.CategoryTheory.Enriched.Basic | [
"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.Functor.hasStrongEpiMonoFactorisations_imp_of_isEquivalence | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.MonoFactorisation.fac",
"CategoryTheory.Limits.MonoFactorisation.I",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Limits.MonoFactorisation.m_mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.categor... | true |
OrderIso.sumLexIioIci._proof_1 | Mathlib.Order.Hom.Lex | [
"Set.ext",
"Preorder.toLT",
"Set.Ici",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"iff_self",
"not_lt._simp_1",
"funext",
"Iff",
"congr",
"LT.lt",
"True",
... | false |
ContDiffWithinAt._proof_3 | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"Field.toSemifield",
"Field.toCommRing",
"smulCommClass_self",
"Semifield.toDivisionSemiring",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
... | false |
Batteries.Tactic.GeneralizeProofs.withGeneralizedProofs | Batteries.Tactic.GeneralizeProofs | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Batteries.Tactic.GeneralizeProofs.Config",
"Lean.MessageData",
"Batteries.Tactic.GeneralizeProofs.abstractProofs",
"Lean.indentD",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"Lean.Expr.instBEq",
"String",
"Lean.instMonadT... | true |
Submonoid.toCommMonoid.eq_1 | Mathlib.Algebra.Group.Submonoid.Defs | [
"Monoid.toMulOneClass",
"Membership.mem",
"Subtype",
"CommMonoid.toMonoid",
"Eq.refl",
"Submonoid.toCommMonoid._proof_1",
"Submonoid.instSetLike",
"Submonoid.toCommMonoid",
"Eq",
"CommMonoid",
"SubmonoidClass.toCommMonoid",
"SetLike.instMembership",
"Submonoid"
] | true |
Metric.infEDist_biUnion | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"iInf",
"congrArg",
"Membership.mem",
"Metric.infEDist",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"PseudoEMetricSpace",
"funext",
"CompleteLinearOrder.toConditionallyCompleteLinearOrderBot",
"Metric.infEDist_iUnion",
"True",
"eq_self",
"ENNReal",
"of_eq_true",
"Co... | true |
RingHom.Smooth.holdsForLocalizationAway | Mathlib.RingTheory.RingHom.Smooth | [
"Eq.mpr",
"CommRing",
"Algebra.algebraMap",
"Algebra.Smooth.mk",
"congrArg",
"CommSemiring.toSemiring",
"Algebra.FormallySmooth.of_isLocalization",
"IsLocalization.Away.finitePresentation",
"RingHom.HoldsForLocalizationAway",
"IsLocalization.Away",
"Algebra",
"id",
"RingHom.Smooth",
"CommR... | true |
List.tail_append_of_ne_nil | Init.Data.List.Lemmas | [
"False",
"eq_false",
"congrArg",
"id",
"instDecidableEqBool",
"Ne",
"List.tail",
"Bool.true",
"instHAppendOfAppend",
"List",
"List.isEmpty",
"List.tail_append",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"List.instAppend",
"ite_cond_eq_false",
"Eq",
"Not",
"HAppe... | true |
Lean.Meta.Grind.Extension.addEMatchTheorem | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"Lean.Meta.Grind.EMatchTheoremConstraint",
"Lean.Core.instMonadResolveNameCoreM",
"Lean.Meta.State",
"Lean.Meta.Grind.Entry.ematch",
"Lean.Meta.Grind.EMatchTheorem",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Meta.Grind.mkEMatchTheorem",
"ReaderT.instMonadLift",
"Lean.ScopedEnvExtensi... | true |
MeasureTheory.SignedMeasure.haveLebesgueDecomposition_neg | Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue | [
"MeasureTheory.JordanDecomposition.posPart",
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"MeasureTheory.SignedMeasure.HaveLebesgueDecomposition.negPart",
"congrArg",
"MeasureTheory.SignedMeasure.HaveLebesgueDecomposition.mk",
"MeasureTheory.SignedMeasure.HaveLebesgueDecomposition.posPart",
"PseudoMet... | true |
Mathlib.Meta.Positivity.Strictness.nonnegative.injEq | Mathlib.Tactic.Positivity.Core | [
"Mathlib.Meta.Positivity.Strictness.nonnegative.inj",
"Mathlib.Meta.Positivity.Strictness",
"Eq.propIntro",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Mathlib.Meta.Positivity.Strictness.nonnegative",
"Lean.Literal.natVal",
"Qq.Quoted",
"Eq.ndrec",
"Lean.Name.mkStr2",
"L... | true |
Matrix.updateRow_reindex | Mathlib.LinearAlgebra.Matrix.RowCol | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.updateRow_submatrix_equiv",
"Equiv",
"Matrix.reindex",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"Matrix.updateRow",
"EquivLike.toFunLike",
"DecidableEq"
] | true |
_private.Mathlib.LinearAlgebra.RootSystem.Chain.0.RootPairing.root_add_nsmul_mem_range_iff_le_chainTopCoeff._proof_1_5 | Mathlib.LinearAlgebra.RootSystem.Chain | [
"Lean.Grind.of_eq_eq_true",
"Int.Linear.eq_of_core",
"IsDomain",
"Lean.RArray.leaf",
"False",
"Exists.choose_spec",
"CommRing",
"instHSMul",
"HMul.hMul",
"instConditionallyCompleteLinearOrder",
"of_decide_eq_true",
"Int.Linear.norm_le",
"Lean.Grind.nestedProof",
"Lean.Grind.not_and",
"eq... | false |
Filter.ofCardinalUnion._proof_1 | Mathlib.Order.Filter.CardinalInter | [
"Eq.mpr",
"lt_of_le_of_lt",
"Preorder.toLT",
"Set.compl_sInter",
"Cardinal",
"congrArg",
"Compl.compl",
"PartialOrder.toPreorder",
"setOf",
"Set.sUnion",
"Cardinal.mk",
"Set.mem_image",
"Membership.mem",
"Exists",
"Cardinal.mk_image_le",
"Eq.mp",
"Set.Elem",
"id",
"HasSubset.Subs... | false |
MeasureTheory.MeasurePreserving.preErgodic_of_preErgodic_semiconj | Mathlib.Dynamics.Ergodic.Ergodic | [
"MeasureTheory.ae",
"MeasureTheory.MeasurePreserving",
"Eq.mpr",
"MeasureTheory.Measure",
"Function.Semiconj.comp_eq",
"MeasurableSet",
"congrArg",
"MeasurableSet.nullMeasurableSet",
"PreErgodic._auto_1",
"Filter.EventuallyConst",
"Function.comp",
"PreErgodic",
"id",
"Set.preimage_comp",
... | true |
Interval.subtractionCommMonoid._proof_2 | Mathlib.Algebra.Order.Interval.Basic | [
"AddCommGroup.toAddCommMonoid",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toZero",
"PartialOrder.toPreorder",
"Preorder.toLE",
"instNegInterval",
"PartialOrder",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"Interval",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"... | false |
Ring.ofMinimalAxioms._proof_13 | Mathlib.Algebra.Ring.MinimalAxioms | [
"One",
"One.mk",
"AddMonoid.toAddSemigroup",
"Zero.zero",
"Add.mk",
"AddGroup.ofLeftAxioms",
"Neg.mk",
"AddMonoid.toZero",
"Add.add",
"instOfNatNat",
"Nat.cast",
"One.one",
"instHAdd",
"Neg",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"Nat",
"NatCast.mk",
"In... | false |
String.decEq._proof_1 | Init.Prelude | [
"ByteArray.mk",
"String",
"List",
"Array.mk",
"UInt8",
"Eq",
"String.ofByteArray",
"rfl",
"ByteArray.IsValidUTF8"
] | false |
CategoryTheory.Functor.hasColimit_map_comp_ι_comp_grothendieckProj | Mathlib.CategoryTheory.Functor.KanExtension.Adjunction | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.ι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CostructuredArrow.grothendieckProj",
"CategoryTheory.Functor.comp",
"CategoryTheory.Grothendieck",
"CategoryTheory.Cat.str",
"CategoryTh... | true |
IsPrimitiveRoot.casesOn | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"IsPrimitiveRoot.mk",
"MulOne.toOne",
"Dvd.dvd",
"Monoid.toMulOneClass",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat.instDvd",
"CommMonoid.toMonoid",
"Nat",
"One.toOfNat1",
"instHPow",
"IsPrimitiveRoot",
"OfNat.ofNat",
"Eq",
"CommMonoid",
"IsPrimitiveRoot.rec"
] | false |
AddMonCat.id_apply | Mathlib.Algebra.Category.MonCat.Basic | [
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"CategoryTheory.ConcreteCategory.hom",
"AddMonoid.toAddZeroClass",
"CategoryTheory.CategoryStruct.id",
"AddZeroClass.toAddZero",
"AddMonCat.str",
"AddMonCat",
"AddMonCat.instCategory",
"eq_self",
"of_eq_true",
"CategoryTheory.Category.toCatego... | true |
IO.Process.runCmdWithInput'.match_1 | Batteries.Lean.IO.Process | [
"IO.Process.SpawnArgs.toStdioConfig",
"IO.Process.StdioConfig.stdin",
"IO.Process.StdioConfig.stderr",
"String",
"IO.Process.SpawnArgs.mk",
"IO.Process.StdioConfig.mk",
"Prod.mk",
"IO.Process.Stdio.null",
"IO.Process.Child",
"List.toArray",
"Array",
"Bool.true",
"Option.none",
"Prod",
"I... | false |
Set.Nonempty.of_vsub_right | Mathlib.Algebra.Group.Pointwise.Set.Scalar | [
"Set.vsub",
"VSub.vsub",
"Set.Nonempty",
"Set.Nonempty.of_image2_right",
"VSub",
"Set"
] | true |
OmegaCompletePartialOrder.ContinuousHom.ωScottContinuous.map | Mathlib.Order.OmegaCompletePartialOrder | [
"Pure.pure",
"Part",
"Eq.mpr",
"instOmegaCompletePartialOrderForall",
"congrArg",
"Monad.toApplicative",
"Function.comp",
"id",
"Applicative.toPure",
"OmegaCompletePartialOrder.ωScottContinuous.const",
"OmegaCompletePartialOrder",
"funext",
"Part.instLawfulMonad",
"Function.const",
"Appl... | true |
Int.ediv_nonneg | Init.Data.Int.DivMod.Lemmas | [
"Int.instDiv",
"instHDiv",
"Exists",
"HDiv.hDiv",
"Int",
"LE.le",
"Nat.cast",
"Int.eq_ofNat_of_zero_le",
"instOfNat",
"Nat",
"Nat.instDiv",
"instNatCastInt",
"OfNat.ofNat",
"Eq",
"_private.Init.Data.Int.DivMod.Lemmas.0.Int.ediv_nonneg.match_1_1",
"Int.instLEInt",
"Int.natCast_nonneg"... | true |
_private.Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory.0.CategoryTheory.Limits.Concrete.Pi.map_ext.match_1_1 | Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory | [
"CategoryTheory.Discrete.mk",
"CategoryTheory.Discrete.casesOn",
"CategoryTheory.Discrete"
] | false |
IsOpen.measure_eq_zero_iff | Mathlib.MeasureTheory.Measure.OpenPos | [
"ENNReal.instCanonicallyOrderedAdd",
"MeasureTheory.Measure",
"Preorder.toLT",
"congrArg",
"instIsBotZeroClass",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Eq.mp",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LE.le",
"MeasurableSpace",
"TopologicalSpace",
"Meas... | true |
CategoryTheory.FunctorToTypes.binaryCoproductIso._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.FunctorToTypes | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.functorCategoryHasColimit",
"UnivLE.small",
"CategoryTheory.Limits.Types.hasColimit",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.instSmallDiscrete",
"CategoryTheory.discreteCa... | false |
continuousFunctionalCalculus._proof_2 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"IsTopologicalSemiring.toContinuousMul",
"Complex.instNormedField",
"IsTopologicalDivisionRing.toIsTopologicalRing",
"PseudoMetricSpace.toUniformSpace",
"NormedDivisionR... | false |
Sigma.Lex.preorder.match_1 | Mathlib.Data.Sigma.Order | [
"Lex",
"Sigma.mk",
"Sigma.casesOn",
"Sigma"
] | false |
_private.Mathlib.Lean.Meta.RefinedDiscrTree.Encode.0.Lean.Meta.RefinedDiscrTree.etaPossibilities._sunfold | Mathlib.Lean.Meta.RefinedDiscrTree.Encode | [
"Pure.pure",
"_private.Mathlib.Lean.Meta.RefinedDiscrTree.Encode.0.Lean.Meta.RefinedDiscrTree.etaPossibilities",
"StateT.run",
"_private.Mathlib.Lean.Meta.RefinedDiscrTree.Encode.0.Lean.Meta.RefinedDiscrTree.Context",
"Bool.not",
"instMonadReaderOfReaderTOfMonad",
"ReaderT",
"Lean.Meta.State",
"inst... | false |
_private.Init.Data.String.Slice.0.String.Slice.Pos.skipWhile.match_1.eq_1 | Init.Data.String.Slice | [
"_private.Init.Data.String.Slice.0.String.Slice.Pos.skipWhile.match_1",
"String.Slice.sliceFrom",
"Option.some",
"String.Slice",
"Eq.refl",
"String.Slice.Pos",
"Eq",
"Option"
] | true |
Std.Channel.Sync.recv | Std.Sync.Channel | [
"Task",
"Std.Channel.Sync",
"instMonadBaseIO",
"Monad.toBind",
"Inhabited",
"Std.Channel.recv",
"Bind.bind",
"BaseIO",
"IO.wait"
] | true |
_private.Mathlib.RingTheory.Congruence.Basic.0.RingCon.instIsCentralScalarQuotient._proof_1 | Mathlib.RingTheory.Congruence.Basic | [
"RingCon.toCon",
"RingCon.instSMulQuotient",
"instSMulOfMul",
"IsScalarTower",
"SMul",
"MulOpposite",
"RingCon",
"MulOne.toMul",
"RingCon.Quotient",
"MulOneClass.toMulOne",
"IsCentralScalar",
"IsScalarTower.op_left",
"Con.instIsCentralScalar",
"MulOneClass",
"Add"
] | false |
CategoryTheory.ShortComplex.LeftHomologyData.map._proof_2 | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex.LeftHomologyData.f'",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.Walk... | false |
Lean.Meta.FunIndParamKind.dropped.elim | Lean.Meta.Tactic.FunIndInfo | [
"PULift.up",
"Lean.Meta.FunIndParamKind.dropped",
"Nat",
"Lean.Meta.FunIndParamKind",
"Eq.symm",
"Eq",
"Lean.Meta.FunIndParamKind.ctorElim",
"Lean.Meta.FunIndParamKind.ctorIdx"
] | false |
Lean.ProjectionFunctionInfo | Lean.ProjFns | [
"Lean.ProjectionFunctionInfo.mk"
] | true |
LinearMap.vecEmpty_apply | Mathlib.LinearAlgebra.Pi | [
"Pi.Function.module",
"Pi.addCommMonoid",
"LinearMap.instFunLike",
"LinearMap.vecEmpty",
"instOfNatNat",
"LinearMap",
"AddCommMonoid",
"Nat",
"Matrix.vecEmpty",
"Semiring",
"Module",
"OfNat.ofNat",
"Fin",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
Quiver.arborescenceMk._proof_1 | Mathlib.Combinatorics.Quiver.Arborescence | [
"Nat.recAux",
"Quiver.Hom",
"Quiver.Path.nil",
"HEq.refl",
"False.elim",
"Exists",
"Eq.casesOn",
"Nat.lt_add_one",
"instOfNatNat",
"LE.le",
"instLENat",
"Nonempty.intro",
"Or.casesOn",
"Quiver.Path",
"instHAdd",
"Quiver.Path.cons",
"Exists.casesOn",
"Nat.lt_succ_iff",
"HAdd.hAdd"... | false |
PMF.toMeasure_ofMultiset_apply | Mathlib.Probability.Distributions.Uniform | [
"MeasureTheory.Measure",
"instHDiv",
"MeasurableSet",
"ENNReal.instAddCommMonoid",
"PMF.ofMultiset",
"PMF.toOuterMeasure",
"Classical.propDecidable",
"Membership.mem",
"PMF.toMeasure_apply_eq_toOuterMeasure_apply",
"Multiset.count",
"MeasureTheory.OuterMeasure",
"Multiset",
"HDiv.hDiv",
"A... | true |
WithBot.one | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"WithBot.some",
"WithBot",
"One",
"One.mk",
"One.toOfNat1",
"OfNat.ofNat"
] | true |
instMulActionElemFixedPointsSubtypeMemSubgroupOfNormal._aux_1 | Mathlib.GroupTheory.GroupAction.SubMulAction | [
"fixedPointsSubMulOfNormal",
"SubMulAction.instSetLike",
"instHSMul",
"instSMulOfMul",
"Monoid.toMulOneClass",
"Group",
"Membership.mem",
"Set.Elem",
"MulOne.toMul",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"MulAction.instMulAction",
"IsScalarTower.left",
"Subtype.mk",
"Group.to... | false |
CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.isLimit | Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf | [
"CategoryTheory.GrothendieckTopology.superset_covering",
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"CategoryTheory.GrothendieckTopology.OneHypercover.mem₀",
"Opposite",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.GrothendieckTopology.OneHypercoverFamily... | true |
ChainComplex.prev | Mathlib.Algebra.Homology.HomologicalComplex | [
"One",
"AddRightCancelSemigroup.toAddSemigroup",
"ComplexShape.prev",
"ComplexShape.prev_eq'",
"instHAdd",
"AddSemigroup.toAdd",
"AddRightCancelSemigroup",
"HAdd.hAdd",
"One.toOfNat1",
"ComplexShape.down",
"OfNat.ofNat",
"Eq",
"rfl",
"AddRightCancelSemigroup.toIsRightCancelAdd"
] | true |
AlgebraicGeometry.Scheme.coe_homeoOfIso | Mathlib.AlgebraicGeometry.Scheme | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
"AlgebraicGeometry.Scheme.homeoOfIso",
"CommRingCat.instCategory... | true |
ZeroAtInftyContinuousMap.instNonUnitalNormedRing._proof_2 | Mathlib.Topology.ContinuousMap.ZeroAtInfty | [
"Norm.norm",
"Real",
"ZeroAtInftyContinuousMap.instNonUnitalSeminormedRing",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toAddCommGroup",
"PseudoMetricSpace.toUniformSpace",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddCommGroup.toAddGroup",
"NonUnitalSeminormedRing.dist_eq",
"NonUnitalR... | false |
CategoryTheory.Limits.mapPair._proof_11 | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Functor",
"ULift.casesOn",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Discrete.functor_map_id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.WalkingPair.right",
"id",
"PLift",
"CategoryTheory.Category.comp_id",
"CategoryThe... | false |
_private.Mathlib.MeasureTheory.Function.Piecewise.0.IndexedPartition.stronglyMeasurable_piecewise._simp_1_7 | Mathlib.MeasureTheory.Function.Piecewise | [
"Fin.ext_iff",
"Fin.val",
"Nat",
"propext",
"Fin",
"Eq"
] | false |
autEquivZmod._proof_1 | Mathlib.FieldTheory.KummerExtension | [
"Iff.mpr",
"Polynomial.C",
"ne_zero_of_irreducible_X_pow_sub_C",
"Finset",
"HSub.hSub",
"RingHom",
"Membership.mem",
"Exists",
"Field.toDivisionRing",
"Irreducible",
"DivisionRing.toRing",
"Field.toSemifield",
"Field.toCommRing",
"instIsDomain",
"Polynomial",
"Monoid.toPow",
"Nat.pos... | false |
CategoryTheory.Presieve.hasPullback | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.Presieve.HasPullbacks.hasPullback",
"CategoryTheory.Presieve.HasPullbacks",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
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