name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Pretriangulated.rotateRotateRotateIso._proof_1 | Mathlib.CategoryTheory.Triangulated.TriangleShift | [
"NegZeroClass.toNeg",
"Units.instMulAction",
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Ring.toNonAssocRing",
"Quiver.Hom",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"AddMonoid.toAddZeroClass",
"Ca... | false |
_private.Mathlib.AlgebraicGeometry.Sites.QuasiCompact.0.AlgebraicGeometry.Scheme.mem_propQCPrecoverage_iff_exists_quasiCompactCover.match_1_1 | Mathlib.AlgebraicGeometry.Sites.QuasiCompact | [
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.Presieve",
"Exists",
"AlgebraicGeometry.Scheme.propQCPrecoverage",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.Precoverage.ZeroHypercover",
"CategoryTheory.PreZeroHypercover... | false |
Lean.Lsp.PlainTermGoal | Lean.Data.Lsp.Extra | [
"Lean.Lsp.PlainTermGoal.mk"
] | true |
Std.ExtTreeMap.le_maxKey_of_mem | Std.Data.ExtTreeMap.Lemmas | [
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.ExtTreeMap",
"Std.ExtTreeMap.inner",
"Std.ExtTreeMap.ne_empty_of_mem",
"Std.ExtTreeMap.maxKey",
"Bool",
"Std.ExtTreeMap.instMembershipOfTransCmp",
"Ordering.isLE",
"Std.ExtDTreeMap.le_maxKey_of_mem",
"Eq"
] | true |
Polynomial.IsDistinguishedAt.algEquivQuotient._proof_5 | Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | [
"MvPowerSeries.instAddCommGroup",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Nontrivial",
"Iff.mpr",
"WithBot.instPreorder",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Ide... | false |
Aesop.ClusterState.AddM.Context.rec | Aesop.Forward.State | [
"Lean.MVarId",
"Array",
"Aesop.ClusterState.AddM.Context.mk",
"Aesop.ClusterState.AddM.Context",
"Lean.LMVarId"
] | false |
CategoryTheory.PositiveCategory.mk._flat_ctor | Mathlib.CategoryTheory.MarkovCategory.Positive | [
"CategoryTheory.ComonObj.comul",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.PositiveCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.SymmetricCategory.symm... | false |
ContinuousMap.compMonoidHom'.eq_1 | Mathlib.Topology.ContinuousMap.Algebra | [
"MulOne.toOne",
"MonoidHom",
"ContinuousMap",
"OneHom.mk",
"ContinuousMap.comp",
"MulOne.toMul",
"MonoidHom.mk",
"ContinuousMap.compMonoidHom'",
"ContinuousMap.instMulOneClassOfContinuousMul",
"TopologicalSpace",
"MulOneClass.toMulOne",
"ContinuousMul",
"ContinuousMap.compMonoidHom'._proof_2... | true |
isOpen_extChartAt_target | Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | [
"Eq.mpr",
"extChartAt",
"NormedSpace",
"chartAt",
"congrArg",
"PartialEquiv.target",
"ModelWithCorners.Boundaryless",
"Set.univ",
"Set.inter_univ",
"PseudoMetricSpace.toUniformSpace",
"id",
"ModelWithCorners.toFun'",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"ModelWithCorners... | true |
ESeminormedAddCommMonoid.noConfusionType | Mathlib.Analysis.Normed.Group.Defs | [
"ESeminormedAddCommMonoid",
"AddMonoid.toAddSemigroup",
"ESeminormedAddMonoid",
"ESeminormedAddMonoid.toAddMonoid",
"ESeminormedAddCommMonoid.casesOn",
"TopologicalSpace",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"HEq",
"Eq"
] | false |
_private.Lean.Util.CollectAxioms.0.Lean.ExportedAxiomsState.recOn | Lean.Util.CollectAxioms | [
"_private.Lean.Util.CollectAxioms.0.Lean.ExportedAxiomsState.mk",
"Array",
"Lean.Name",
"Prod",
"_private.Lean.Util.CollectAxioms.0.Lean.ExportedAxiomsState.rec",
"_private.Lean.Util.CollectAxioms.0.Lean.ExportedAxiomsState"
] | false |
_private.Mathlib.RingTheory.ClassGroup.0.ClassGroup.equiv._simp_2 | Mathlib.RingTheory.ClassGroup | [
"Units.val",
"MonoidHom.range",
"CommRing",
"FractionalIdeal.spanSingleton",
"mem_principal_ideals_iff",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"Membership.mem",
"nonZeroDivisors",
"Exists",
"Units",
"Subgroup",
"Units.instGroup",
"Field.toSemifield",
"Field.toCommRing... | false |
Lean.Meta.Occurrences.pos | Init.MetaTypes | [
"List",
"Lean.Meta.Occurrences.pos",
"Lean.Meta.Occurrences",
"Nat"
] | true |
linter.tacticAnalysis.omegaToLia | Mathlib.Tactic.TacticAnalysis.Declarations | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
_private.Init.Data.List.Find.0.List.lt_findIdx_of_not._simp_1_1 | Init.Data.List.Find | [
"Nat.not_lt",
"LE.le",
"instLENat",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Eq",
"Not"
] | false |
ContMDiffOn.sub_const | Mathlib.Geometry.Manifold.Algebra.Monoid | [
"NormedSpace",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"SubNegMonoid",
"Membership.mem",
"AddZeroClass.toAddZero",
"SubNegMonoid.toSub",
"TopologicalSpace",
"ModelWithCorners",
"instHSub",
"ENat",
"ContMDiffWithinAt.sub_const",
"NontriviallyNormedField",
"AddZero.toAdd",
"NontriviallyNo... | true |
AlgebraicGeometry.HasAffineProperty.diagonal_of_openCover | Mathlib.AlgebraicGeometry.Morphisms.Constructors | [
"CategoryTheory.Limits.hasPullbackVertPaste",
"CategoryTheory.Limits.limit.π",
"CategoryTheory.Limits.pullbackDiagonalMapIso",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"... | true |
_private.Mathlib.Tactic.Linter.MinImports.0.Mathlib.Linter.MinImports.minImportsLinter._sparseCasesOn_1 | Mathlib.Tactic.Linter.MinImports | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Lean.Meta.Simp.SimprocEntry._sizeOf_inst | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.Simp.SimprocEntry",
"Lean.Meta.Simp.SimprocEntry._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
SSet.Truncated.Edge.CompStruct.d₁._autoParam | Mathlib.AlgebraicTopology.SimplicialSet.CompStructTruncated | [
"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.Sieve.mem_ofArrows_iff | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve.ofArrows.mk",
"CategoryTheory.Sieve.ofArrows_mk",
"HEq.refl",
"Exists",
"CategoryTheory.Sieve.downward_closed",
"CategoryTheory.Sieve.ofArrows",
"CategoryTheory.Sieve.arrows",
"And.casesOn",
"And",
"Iff",
"Exist... | true |
SubAddAction.instSupSet.eq_1 | Mathlib.GroupTheory.GroupAction.SubMulAction | [
"Membership.mem",
"VAdd",
"SupSet.mk",
"SupSet",
"SubAddAction.mk",
"SubAddAction",
"SubAddAction.instSupSet._proof_2",
"SetLike.coe",
"SubAddAction.instSupSet",
"Eq.refl",
"Eq",
"Set.instMembership",
"Set.iUnion",
"SubAddAction.instSetLike",
"Set"
] | true |
Lean.Elab.Term.ElabElimInfo.mk._flat_ctor | Lean.Elab.App | [
"Lean.Elab.Term.ElabElimInfo.mk",
"Lean.Elab.Term.ElabElimInfo",
"Lean.Expr",
"Array",
"Nat"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof.0.Lean.Meta.Grind.Arith.Cutsat.DvdCnstr.toExprProof.match_11 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof | [
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.subst",
"Lean.Grind.CommRing.Poly",
"Lean.Meta.Grind.Arith.Cutsat.CooperSplit",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.casesOn",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.core",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₂",
"Lean.Expr",
"Lean.... | false |
DFinsupp.range_mapRangeAddMonoidHom | Mathlib.LinearAlgebra.DFinsupp | [
"AddSubgroup.comap",
"Pi.addGroup",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.range",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"AddSubgroup",
"DFinsupp.mrange_mapRangeAddMonoidHom",
"AddZero.toZero",
"AddSubgroup.toAddSu... | true |
sbtw_comm | Mathlib.Analysis.Convex.Between | [
"Eq.mpr",
"IsOrderedRing",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Iff.rfl",
"Wbtw",
"AddCommGroup.toAddGroup",
"PartialOrder",
"AddCommGroup",
"id",
"Ne",
"wbtw_comm",
"And",
"Iff",
"and_assoc",
"and_right_comm",
"AddTorsor",
"propext",
"Module",
"Eq.symm",
"Ring.toSemi... | true |
Lean.Lsp.LeanQueryModuleParams.mk.injEq | Lean.Data.Lsp.Internal | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Lsp.LeanQueryModuleParams",
"Array",
"And",
"Eq.ndrec",
"Eq.refl",
"Lean.Lsp.LeanQueryModuleParams.mk",
"Lean.Lsp.LeanQueryModuleParams.mk.inj",
"Lean.JsonRpc.RequestID",
"Eq",
"Lean.Lsp.LeanModuleQuery"
] | true |
List.instDecidableMapsToCoeFinsetOfDecidablePredMemSet | Mathlib.Data.Finset.Defs | [
"Finset",
"Decidable",
"Membership.mem",
"List.instDecidableMapsToCoeFinsetOfDecidablePredMemSet._aux_1",
"SetLike.coe",
"Finset.instSetLike",
"Set.MapsTo",
"DecidablePred",
"Set.instMembership",
"Set"
] | true |
IsPurelyInseparable.iterateFrobeniusₛₗ_algebraMap_base | Mathlib.FieldTheory.PurelyInseparable.Exponent | [
"Eq.mpr",
"RingHom.instRingHomClass",
"IsPurelyInseparable.iterateFrobeniusₛₗ",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"IsScalarTower",
"Nat.instMonoid",
"AddGroupWithOne.toAddMonoidWithOne",
... | true |
Lean.Meta.Match.DiscrInfo.mk._flat_ctor | Lean.Meta.Match.MatcherInfo | [
"Lean.Meta.Match.DiscrInfo.mk",
"Lean.Name",
"Lean.Meta.Match.DiscrInfo",
"Option"
] | false |
CategoryTheory.Limits.widePushoutShapeUnop_obj | Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks | [
"Opposite",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.WidePushoutShape.category",
"CategoryTheory.Category.opposite",
"CategoryTheory.Limits.widePushoutShapeUnop",
"Eq.refl",
"Eq",
"CategoryTheory.Limits.WidePushoutShape",
... | true |
_private.Lean.Meta.SynthInstance.0.Lean.Meta.SynthInstance.getInstances.match_1 | Lean.Meta.SynthInstance | [
"Lean.Expr.const",
"Lean.Expr",
"_private.Lean.Meta.SynthInstance.0.Lean.Meta.SynthInstance.getInstances._sparseCasesOn_1",
"Nat.hasNotBit",
"Lean.Level",
"List",
"Lean.Name",
"Lean.Expr.ctorIdx"
] | false |
Lean.Parser.Syntax.cat.parenthesizer | Lean.Parser.Syntax | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Parser.optPrecedence.parenthesizer",
"Lean.Parser.ident.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPrinter.Parenthesiz... | true |
CategoryTheory.ShortComplex.ShortExact.mono_f | Mathlib.Algebra.Homology.ShortComplex.ShortExact | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Mono",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.ShortExact",
"CategoryTheory.ShortComplex.f",
"CategoryTheory.Category",
"CategoryTheory.ShortComplex.X₂"
] | true |
_private.Mathlib.MeasureTheory.Integral.PeakFunction.0.tendsto_integral_comp_smul_smul_of_integrable._simp_1_2 | Mathlib.MeasureTheory.Integral.PeakFunction | [
"Real.instLE",
"Real",
"Membership.mem",
"LE.le",
"PseudoMetricSpace",
"propext",
"Metric.mem_closedBall",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Metric.closedBall",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Data.Int.CardIntervalMod.0.Int.Ioc_filter_dvd_eq._simp_1_1 | Mathlib.Data.Int.CardIntervalMod | [
"Finset",
"Finset.map",
"Membership.mem",
"Exists",
"Function.Embedding",
"And",
"Finset.instSetLike",
"propext",
"Finset.mem_map",
"Function.instFunLikeEmbedding",
"Eq",
"DFunLike.coe",
"SetLike.instMembership"
] | false |
exists_of_not_isMeagre_biUnion | Mathlib.Topology.GDelta.Basic | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Eq.mpr",
"Mathlib.Tactic.Push.not_and_eq",
"Mathlib.Tactic.Contrapose.contrapose₂",
"IsMeagre",
"isMeagre_biUnion",
"Membership.mem",
"Exists",
"id",
"Classical.not_not._simp_2",
"TopologicalSpace",
"And",
"binderNameHint",
"implies_congr",
"Eq.... | true |
Order.Ideal.biSup_finset_mem_iff._simp_1 | Mathlib.Order.Ideal | [
"iSup",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Finset.instSetLike",
"propext",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"Order.Ide... | false |
CategoryTheory.Endofunctor.Algebra.mk._flat_ctor | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Endofunctor.Algebra.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | false |
LieSubalgebra.add_mem | Mathlib.Algebra.Lie.Subalgebra | [
"CommRing",
"AddSubmonoidClass.toAddMemClass",
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddSubgroupClass.toAddSubmonoidClass",
"instHAdd",
"LieRing",
"AddGroup.toSubNegMonoid... | true |
CategoryTheory.WithTerminal.Hom.eq_3 | Mathlib.CategoryTheory.WithTerminal.Basic | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"id",
"CategoryTheory.WithTerminal.Hom",
"PEmpty",
"CategoryTheory.WithTerminal",
"_private.Mathlib.CategoryTheory.WithTerminal.Basic.0.CategoryTheory.WithTerminal.Hom.match_1.eq_3",
"CategoryTheory.WithTerminal.Hom.matc... | true |
List.zipIdx.eq_1 | Init.Data.List.Impl | [
"List",
"Nat",
"Eq.refl",
"Prod",
"List.zipIdx",
"Eq",
"List.nil"
] | true |
NonUnitalSubsemiring.toSubsemiring_toNonUnitalSubsemiring | Mathlib.Algebra.Ring.Subsemiring.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Membership.mem",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Subsemiring.toNonUnitalSubsemiring",
"NonUnitalSubsemiring.toSubsemiring",
"AddMonoidWithOne.toOne",
"NonAssocSemiring",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalSubsemiring.inst... | true |
_private.Batteries.Lean.Meta.UnusedNames.0.Lean.LocalContext.getUnusedUserNames.loop._sunfold | Batteries.Lean.Meta.UnusedNames | [
"_private.Batteries.Lean.Meta.UnusedNames.0.Lean.LocalContext.getUnusedUserNames.loop",
"Array.push",
"instOfNatNat",
"_private.Batteries.Lean.Meta.UnusedNames.0.Lean.LocalContext.getUnusedUserNames.loop.match_1",
"Array",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat",
"Lean.Name.appendIndexAfter",
"in... | false |
CategoryTheory.Limits.IsLimit.ofIsZero._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.isZero_iff",
"CategoryTheory.Limits.Cone.pt",
"Catego... | false |
Lean.Parser.Term.doFor | Lean.Parser.Do | [
"Lean.Parser.Term.doSeq",
"Lean.Parser.Parser",
"HAndThen.hAndThen",
"Lean.Parser.leadingNode",
"instHAndThenOfAndThen",
"instOfNatNat",
"Lean.Parser.sepBy1",
"Lean.Parser.symbol",
"Lean.Parser.withAntiquot",
"Bool.true",
"Lean.Parser.Term.doForDecl",
"Unit",
"Nat",
"Lean.Parser.withCache"... | true |
exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow' | Mathlib.FieldTheory.SeparablyGenerated | [
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"False",
"CommRing",
"Nat.Prime",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"eq_false",
"outParam",
"Iff.of_eq",
"congrArg",
"IntermediateField",
"HEq.refl",
"Compl.compl",
"true_or",
"Finset",
"False.elim",
"... | true |
Mathlib.Tactic.getDSimpArgs | Mathlib.Tactic.Core | [
"Pure.pure",
"Lean.Syntax.TSepArray.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Syntax.getArgs",
"Lean.Meta.State",
"Lean.Syntax.TSepArray.getElems",
"Lean.Syntax.isOfKind",
"Lean.Elab.Tactic.Context",
"Lean.Syntax",
"Lean.Syntax.TSepArray",
"Lean.Me... | true |
List.sorted_mergeSort | Init.Data.List.Sort.Lemmas | [
"List.pairwise_mergeSort",
"List.Pairwise",
"Bool.true",
"List",
"Bool",
"Bool.or",
"Eq",
"List.mergeSort"
] | true |
CategoryTheory.End.ext | Mathlib.CategoryTheory.Endomorphism | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.End",
"CategoryTheory.End.asHom",
"CategoryTheory.CategoryStruct",
"Eq"
] | true |
Fin.neg | Init.Data.Fin.Basic | [
"Neg.mk",
"HSub.hSub",
"Fin.mk",
"Nat.instMod",
"instHMod",
"instSubNat",
"Fin.val",
"Neg",
"HMod.hMod",
"instHSub",
"Nat",
"Fin",
"Fin.neg._proof_1"
] | true |
AlgebraicGeometry.isLimitOpensCone._proof_4 | Mathlib.AlgebraicGeometry.AffineTransitionLimit | [
"CategoryTheory.Limits.ConeMorphism.mk",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"AlgebraicGeometry.isLimitOpensC... | false |
Part.Fix.approx._sunfold | Mathlib.Control.Fix | [
"Part",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Part.instPartialOrder",
"Pi.instBotForall",
"Bot.bot",
"Stream'",
"Part.instOrderBot",
"Unit",
"Nat",
"Part.Fix.approx.match_1",
"Part.Fix.approx"
] | false |
_private.Std.Data.Iterators.Lemmas.Equivalence.Basic.0.Std.quotOfQuot._proof_1 | Std.Data.Iterators.Lemmas.Equivalence.Basic | [
"Quot.sound",
"Quot",
"Eq",
"Quot.mk"
] | false |
WellFounded.sigma_lex_of_wellFoundedOn_fiber | Mathlib.Order.WellFoundedSet | [
"PSigma.snd",
"Iff.mpr",
"PSigma.subtype_ext",
"Eq.mpr",
"PSigma.Lex",
"_private.Mathlib.Order.WellFoundedSet.0.WellFounded.sigma_lex_of_wellFoundedOn_fiber._proof_1_1",
"Function.onFun",
"PSigma.Lex.left",
"Sigma.Lex",
"HEq.refl",
"Membership.mem",
"Exists",
"PSigma.Lex.right",
"Sigma.lex... | true |
TopCat.homeoOfIso_symm_apply | Mathlib.Topology.Category.TopCat.Basic | [
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap",
"CategoryTheory.Iso",
"TopCat.str",
"TopCat.homeoOfIso",
"Homeomorph.instEquivLike",
"TopCat.carrier",
"Homeomorph.symm",
"Homeomorph",
"Eq.refl",
"TopCat.instConcreteCategoryContinuousMapCarrier",
"TopCat",
"Eq... | true |
HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst | Mathlib.RingTheory.HahnSeries.Lex | [
"Preorder.toLT",
"Equiv.instEquivLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Lex",
"WithTop.coe_untop",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"HahnSeries.orderTop",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGr... | true |
CategoryTheory.Square.opFunctor._proof_2 | Mathlib.CategoryTheory.Square | [
"CategoryTheory.Square.category",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Square.op",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Square.Hom.τ₄",
"Quiver.Hom.unop",
"CategoryTheory.Square.Hom.comm₃₄",
"CategoryTheory.Square",
"CategoryTheory.Square.... | false |
Mathlib.Tactic.Bound.lt_max_of_lt_left_or_lt_right | Mathlib.Tactic.Bound | [
"Iff.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"Max.max",
"LT.lt",
"Or",
"instDistribLatticeOfLinearOrder",
"lt_max_iff",
"Lattice.toSemilatticeInf"
] | true |
RatFunc.setOf_polynomial_valuation_lt_one_and_ne_zero_nonempty | Mathlib.NumberTheory.RatFunc.Ostrowski | [
"Iff.mpr",
"lt_iff_le_and_ne",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"False",
"DivInvMonoid.toInv",
"Preorder.toLT",
"instHDiv",
"InvOneClass.toOne",
"GroupWithZero.toDivInvMonoid",
"DivisionCommMonoid.toDivisionMonoid",... | true |
Mathlib.Tactic.BicategoryLike.WhiskerLeft.whisker | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.Mor₂",
"Mathlib.Tactic.BicategoryLike.Atom₁",
"Mathlib.Tactic.BicategoryLike.WhiskerLeft",
"Mathlib.Tactic.BicategoryLike.WhiskerLeft.whisker"
] | true |
_private.Aesop.Search.Expansion.0.Aesop.runFirstUnsafeRule.loop | Aesop.Search.Expansion | [
"Inhabited.default",
"Aesop.UnsafeQueue",
"Aesop.SearchM.instInhabited",
"Aesop.GoalRef",
"Aesop.Queue",
"Aesop.SearchM",
"Aesop.RuleResult",
"Prod"
] | true |
CategoryTheory.InjectiveResolution.isLimitKernelFork._proof_5 | Mathlib.CategoryTheory.Preadditive.Injective.Resolution | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.HasHomology",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"HomologicalComplex",
"HomologicalComplex.instHasHomologyObjSingle",
"Nat.instAddCancelCom... | false |
AddSemiconjBy.neg_neg_symm_iff | Mathlib.Algebra.Group.Semiconj.Basic | [
"neg_add_rev",
"Eq.mpr",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"AddSemiconjBy",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"eq_comm... | true |
HahnSeries.single | Mathlib.RingTheory.HahnSeries.Basic | [
"Classical.propDecidable",
"PartialOrder",
"HahnSeries.instZero",
"HahnSeries.mk",
"Pi.single",
"ZeroHom.mk",
"ZeroHom",
"HahnSeries.single._proof_1",
"HahnSeries.single._proof_3",
"HahnSeries",
"Eq",
"Zero"
] | true |
_private.Qq.Macro.0.Qq.Impl.isBad.match_1 | Qq.Macro | [
"String",
"Lean.Expr.const",
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Level",
"Lean.Name.ctorIdx",
"dite",
"Lean.Name.str",
"List",
"Eq.ndrec_symm",
"instDecidableEqString",
"_private.Qq.Macro.0.Qq.Impl.isBad._sparseCasesOn_1",
"Lean.Name",
"Lean.Expr.ctorIdx",
"Eq",
"Not",
"_private.Qq.M... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.isEmpty_alter_eq_isEmpty_erase._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 |
LinearMap.isNilpotent_mulRight_iff._simp_1 | Mathlib.RingTheory.Nilpotent.Lemmas | [
"Module.End.instMonoid",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.toModule",
"LinearMap",
"Monoid.toPow",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"LinearMap.isNilpotent_mulRight_iff",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring.to... | false |
_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.IsPrime.notMem_of_isCoprime_of_mem.match_1_1 | Mathlib.RingTheory.Ideal.Operations | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"CommSemiring.toSemiring",
"Exists",
"Distrib.toAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSemiring",
"CommSemiring",
"AddMonoidWithOne.toOne",
"instHAdd",
"Exists.casesOn",
"Distrib.toMul",
"HAdd.hAdd",
"Exists.in... | false |
CategoryTheory.CommShift₂Setup.mk.noConfusion | Mathlib.CategoryTheory.Shift.CommShiftTwo | [
"CategoryTheory.Functor",
"CategoryTheory.CatCenter",
"HMul.hMul",
"AddMonoidHom.fst",
"CategoryTheory.CommShift₂Setup.mk",
"HEq.refl",
"Prod.instAddZeroClass",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"Units",
"AddZeroClass.toAddZero",
"id"... | false |
CategoryTheory.preservesLimitsOfShape_presheafToSheaf | Mathlib.CategoryTheory.Sites.LeftExact | [
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.GrothendieckTopology.sheafification",
"CategoryTheory.FinCategory.categoryAsType",
"Opposite",
"CategoryTheory.CreatesLimitsOfShape.CreatesLimit",
"CategoryTheory.Limits.HasColimi... | true |
Lean.Meta.Simp.instInhabitedBuiltinSimprocs.default | Lean.Meta.Tactic.Simp.Simproc | [
"Inhabited.default",
"Lean.Meta.SimpTheoremKey",
"Sum",
"Std.HashMap",
"Array",
"Lean.Meta.Simp.DSimproc",
"Lean.Name",
"Lean.Meta.Simp.BuiltinSimprocs",
"Lean.Meta.Simp.BuiltinSimprocs.mk",
"Lean.Name.instBEq",
"Std.HashMap.instInhabited",
"Lean.instHashableName",
"Lean.Meta.Simp.Simproc"
] | true |
Mathlib.Tactic.Reassoc.reassocExprHom | Mathlib.Tactic.CategoryTheory.Reassoc | [
"Pure.pure",
"Lean.Meta.simpType",
"Lean.mkAppN",
"Lean.MetavarKind.natural",
"Lean.MVarId.assignIfDefEq",
"Lean.MVarId.setKind",
"Lean.Meta.State",
"Lean.MVarId",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Prod.mk",
"instOfNatNat",
"Lean.MetavarKind.synthetic",
"Applicative.toPure... | true |
Subgroup.focalSubgroupOf_eq_closure | Mathlib.GroupTheory.Focal | [
"Subgroup.map_focalSubgroupOf",
"Eq.mpr",
"MonoidHom.instFunLike",
"Subgroup.map_subtype_inj",
"Subgroup.closure",
"MonoidHom",
"Iff.of_eq",
"Subgroup.map",
"Monoid.toMulOneClass",
"congrArg",
"Subgroup.subtype",
"Bracket.bracket",
"setOf",
"Group",
"Membership.mem",
"Subgroup.focalSub... | true |
Array.isSome_findSome? | Init.Data.Array.Find | [
"congrArg",
"Array.any",
"Array.any_toList",
"instOfNatNat",
"Array.toList",
"Array",
"Array.findSome?",
"List.findSome?",
"Nat",
"_private.Init.Data.Array.Find.0.Array.isSome_findSome?._simp_1_1",
"True",
"eq_self",
"Bool",
"of_eq_true",
"List.any",
"congrFun'",
"Option.isSome",
"... | true |
Mathlib.Tactic.ITauto.Context.add | Mathlib.Tactic.ITauto | [
"Inhabited.default",
"Mathlib.Tactic.ITauto.IProp",
"instInhabitedExcept",
"Mathlib.Tactic.ITauto.Context",
"Pi.instInhabited",
"Mathlib.Tactic.ITauto.Proof",
"Inhabited",
"Except",
"Inhabited.mk"
] | true |
AlgebraicGeometry.Scheme.IdealSheafData.glueData_t | Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme | [
"CategoryTheory.GlueData.t",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"AlgebraicGeometry.Scheme.IdealSheafData.glueDataT",
"Quiver.Hom",
"AlgebraicGeometry.Scheme.IdealSheafData.glueData",
"Set.Elem",
"AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjPullback",
"Algebr... | true |
Finset.subtractionCommMonoid._proof_4 | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Finset",
"Finset.coe_sub",
"HSub.hSub",
"SubtractionMonoid.toSubNegMonoid",
"SubtractionCommMonoid.toSubtractionMonoid",
"SubNegMonoid.toSub",
"instHSub",
"SetLike.coe",
"Set.sub",
"Finset.instSetLike",
"Finset.sub",
"SubtractionCommMonoid",
"Eq",
"DecidableEq",
"Set"
] | false |
RootPairing.chainBotCoeff_add_chainTopCoeff_le_three | Mathlib.LinearAlgebra.RootSystem.Chain | [
"RootPairing.chainTopIdx",
"Int.instAddCommGroup",
"Nat.cast_ofNat",
"Eq.mpr",
"RootPairing.IsReduced",
"IsDomain",
"False",
"Int.instIsStrictOrderedRing",
"Nat.instMulZeroClass",
"CommRing",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"instConditionallyCompleteLinearOrder",
"eq_fals... | true |
NumberField.AdeleRing.instInhabited | Mathlib.NumberTheory.NumberField.AdeleRing | [
"CommRing",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"NumberField.instCommRingAdeleRing",
"Field.toSemifield",
"CommRing.toCommSemiring",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"IsDedekindDomain",
"NumberField.AdeleRing",
"Inhabited",
"Zero.toOfNat0",
... | true |
ContinuousMap.piEquiv._proof_1 | Mathlib.Topology.ContinuousMap.Basic | [
"Function.LeftInverse",
"ContinuousMap.eval",
"Pi.topologicalSpace",
"ContinuousMap",
"ContinuousMap.comp",
"TopologicalSpace",
"Eq.refl",
"ContinuousMap.pi"
] | false |
WithCStarModule.instNormedAddCommGroupProd._proof_8 | Mathlib.Analysis.CStarAlgebra.Module.Constructions | [
"Norm.norm",
"UniformSpace.comap._proof_1",
"NegZeroClass.toNeg",
"Bornology.induced._proof_1",
"NonUnitalNormedRing.toNorm",
"instUniformSpaceProd",
"Real",
"ENNReal.ofNNReal",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"Equiv.instEquivLike",
"CStarModule.normedSpaceCore",
"PseudoMetricSp... | false |
_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.RequestOverview.noConfusion | Lean.Server.ProtocolOverview | [
"_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.ProtocolExtensionKind",
"String",
"Array",
"_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.RequestOverview.noConfusionType",
"Eq.ndrec",
"Eq.refl",
"_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.RequestOverview",
... | false |
List.Perm.cons | Init.Data.List.Basic | [
"List.Perm.cons",
"List.Perm",
"List.cons",
"List"
] | true |
_private.Mathlib.Order.Interval.Set.LinearOrder.0.Set.Ioo_union_Ioo._proof_1_1 | Mathlib.Order.Interval.Set.LinearOrder | [
"instLawfulOrderLT_mathlib",
"Lean.Grind.of_eq_eq_true",
"Set.mem_union",
"Lean.Grind.eq_false_of_not_eq_true",
"Set.ext",
"of_eq_false",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Preorder.toLT",
"Set.mem_Ioo",
"Lattice.toSemilatticeSup",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind... | false |
_private.Init.Data.Fin.Lemmas.0.Fin.zero_mul._simp_1_1 | Init.Data.Fin.Lemmas | [
"Fin.ext_iff",
"Fin.val",
"Nat",
"propext",
"Fin",
"Eq"
] | false |
_private.Init.Data.String.Lemmas.Pattern.Find.Pred.0.String.find?_prop_eq_some_iff._simp_1_2 | Init.Data.String.Lemmas.Pattern.Find.Pred | [
"Decidable",
"decide_eq_false_iff_not",
"propext",
"Bool",
"Bool.false",
"Decidable.decide",
"Eq",
"Not"
] | false |
Std.Sat.AIG.RefVec.IfInput.rhs | Std.Sat.AIG.If | [
"Std.Sat.AIG.RefVec.IfInput",
"Std.Sat.AIG",
"Nat",
"Hashable",
"Std.Sat.AIG.RefVec",
"DecidableEq"
] | true |
_private.Batteries.Data.RBMap.Lemmas.0.Batteries.RBNode.toStream.match_1.eq_2 | Batteries.Data.RBMap.Lemmas | [
"Batteries.RBNode",
"Batteries.RBNode.nil",
"Batteries.RBNode.Stream",
"Batteries.RBColor",
"Eq.refl",
"Batteries.RBNode.toStream.match_1",
"Batteries.RBNode.node",
"Eq"
] | true |
_private.Lean.Meta.Tactic.LibrarySearch.0.Lean.Meta.LibrarySearch.librarySearchSymm.match_1 | Lean.Meta.Tactic.LibrarySearch | [
"Option.ctorIdx",
"Option.some",
"Lean.MVarId",
"Nat.hasNotBit",
"_private.Lean.Meta.Tactic.LibrarySearch.0.Lean.Meta.LibrarySearch.librarySearchSymm._sparseCasesOn_1",
"Option"
] | false |
_private.Lean.PrivateName.0.Lean.isPrivateName.match_1 | Lean.PrivateName | [
"String",
"namedPattern",
"Lean.Name.num",
"Lean.Name.str",
"Lean.Name.anonymous",
"Lean.Name.casesOn",
"Nat",
"Lean.Name",
"Eq.refl",
"Eq"
] | false |
Lean.Elab.Level.Context.recOn | Lean.Elab.Level | [
"Lean.Elab.Level.Context.rec",
"Lean.Syntax",
"Lean.Elab.Level.Context.mk",
"Lean.Elab.Level.Context",
"Bool",
"Lean.Options"
] | false |
WeakFEPair.mk.congr_simp | Mathlib.NumberTheory.LSeries.HurwitzZetaEven | [
"Real.instPow",
"Real",
"Set.Ioi",
"instHSMul",
"instHDiv",
"HMul.hMul",
"NormedSpace",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Real.instDivInvMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"WeakFEPair",
"Asymptotics.IsBigO",
"C... | true |
LinearMap.injective_of_linearIndependent | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Submodule",
"instHSMul",
"Semiring.toModule",
"SemilinearMapClass.toMulActionSemiHomClass",
"Finsupp.module",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
... | true |
MeasureTheory.integral_mono_of_nonneg | Mathlib.MeasureTheory.Integral.Bochner.Basic | [
"MeasureTheory.ae",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"ClosedIciTopology",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"MeasureTheory.integral_undef",
"PartialOrder.toPreorder",
"PseudoMe... | true |
perfect_def | Mathlib.Topology.Perfect | [
"Perfect",
"Preperfect",
"Perfect.mk",
"And.casesOn",
"IsClosed",
"TopologicalSpace",
"And",
"Iff",
"And.intro",
"Iff.intro",
"Perfect.casesOn",
"Set"
] | true |
CategoryTheory.Subgroupoid.instTop._proof_2 | Mathlib.CategoryTheory.Groupoid.Subgroupoid | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Set.univ",
"Membership.mem",
"CategoryTheory.Groupoid",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Groupoid.toCategory",
"Set.instMembership",
"True.intro",
"Set"
] | false |
CategoryTheory.Functor.addGrpObjObj._proof_4 | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.Monoidal.toUnit_ε_assoc",
"CategoryTheory.AddGrpObj.right_neg",
"CategoryTheory.Functor.Monoidal.lift_μ_assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.addMonObjObj",
"CategoryTheory.Functor.LaxMono... | false |
RingHom.snd_comp_prod | Mathlib.Algebra.Ring.Prod | [
"RingHom",
"RingHom.ext",
"RingHom.snd",
"RingHom.comp",
"NonAssocSemiring",
"RingHom.instFunLike",
"Prod.instNonAssocSemiring",
"Prod",
"Eq",
"DFunLike.coe",
"RingHom.prod",
"rfl"
] | true |
AlgebraicGeometry.instIsIntegralPullbackSchemeOfGeometricallyIntegralOfFlatOfUniversallyOpenOfIsLocallyNoetherian_1 | Mathlib.AlgebraicGeometry.Geometrically.Integral | [
"AlgebraicGeometry.IsIntegral",
"AlgebraicGeometry.Flat",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.UniversallyOpen",
"AlgebraicGeometry.Flat.instFstScheme",
"AlgebraicGeometry.IsLocallyNoetherian",
"Alg... | true |
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