name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.MonadFileMap | Lean.Data.Position | [
"Lean.MonadFileMap.mk"
] | true |
AddSubgroup.SubgroupNormal.mem_comm | Mathlib.Algebra.Group.Subgroup.Basic | [
"AddGroup.toSubtractionMonoid",
"add_neg_cancel",
"NegZeroClass.toNeg",
"AddMonoid.toAddSemigroup",
"congrArg",
"add_assoc",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddSubgroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAdd... | true |
NormedAddGroupHom.smul.match_1 | Mathlib.Analysis.Normed.Group.Hom | [
"Norm.norm",
"Real.instLE",
"Real",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"HMul.hMul",
"Exists",
"LE.le",
"SeminormedAddCommGroup.toNorm",
"Exists.casesOn",
"Real.instMul",
"Exists.intro",
"NormedAddGroupHom.toFun",
"instHMul"
] | false |
CategoryTheory.Comonad.Coalgebra.casesOn | Mathlib.CategoryTheory.Monad.Algebra | [
"CategoryTheory.Comonad",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comonad.Coalgebra.mk",
"CategoryTheory.Comonad.δ",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Functor.map",
"CategoryTheory.Comonad... | false |
Submodule.map₂_eq_span_image2 | Mathlib.Algebra.Module.Submodule.Bilinear | [
"Eq.mpr",
"Submodule",
"congrArg",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"id",
"Submodule.span_eq",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"Submodule.map₂_span_span",
"SetLike.coe",
"CommMonoid.toMonoid",
"Set.image2",
"S... | true |
Lean.Export.OfState.noConfusion | Mathlib.Util.Export | [
"HEq.refl",
"Lean.Export.Alloc",
"Lean.Export.OfState",
"Lean.Export.OfState.noConfusionType",
"Lean.Export.State",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Hashable",
"BEq",
"Eq",
"Lean.Export.OfState.casesOn"
] | false |
AddSubgroup.isFiniteRelIndex_of_finiteIndex | Mathlib.GroupTheory.Index | [
"AddSubgroup.instCompleteLattice",
"AddSubgroup.FiniteIndex",
"congrArg",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Eq.mp",
"AddSubgroup.isFiniteRelIndex_top_iff",
"AddSubgroup.isFiniteRelIndex_of_le_right",
"AddSubgroup",
"A... | true |
Graph.disjoint_iff._simp_1 | Mathlib.Combinatorics.Graph.Lattice | [
"Disjoint",
"SemilatticeInf.toPartialOrder",
"Graph.disjoint_iff",
"BiheytingAlgebra.toHeytingAlgebra",
"Graph",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanAlgebra.toBiheytingAlgebra",
"Graph.instOrderBot",
"Set.instBooleanAlgebra",
"propext",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra"... | false |
_private.Mathlib.LinearAlgebra.Matrix.ToLin.0.Matrix.ker_mulVecLin_eq_bot_iff._simp_1_1 | Mathlib.LinearAlgebra.Matrix.ToLin | [
"Submodule",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Bot.bot",
"AddCommMonoid",
"AddZero.toZero",
"Submodule.instBot",
"Submodule.setLike",
"propext",
"Semiring",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"Submodule.eq_bot_iff",
"Module",
"OfNat.ofN... | false |
Lean.Elab.Term.ToDepElimPattern.Context.explicitPatternVars._default | Lean.Elab.Match | [
"id",
"Lean.FVarId",
"List.toArray",
"Array",
"List.nil"
] | false |
CategoryTheory.ShortComplex.leftHomologyMap_comp | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.leftHomologyMap'_comp",
"CategoryTheory.ShortComplex.leftHomologyData",
"CategoryTheory.ShortComplex.leftHomologyMap",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComp... | true |
Std.TreeSet.min_erase_eq_of_not_compare_eq_min | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet.min",
"Std.TreeSet",
"Std.TreeSet.isEmpty",
"Ordering",
"Std.TreeSet.inner",
"Ordering.eq",
"Std.TreeMap.minKey_erase_eq_of_not_compare_eq_minKey",
"Std.TreeSet.isEmpty_eq_false_of_isEmpty_erase_eq_false",
"Std.TransCmp",
"Unit",
"Bool",
"Std.TreeSet.erase",
"Bool.false",
"Eq"... | true |
Mathlib.Tactic.Linarith.CompSource | Mathlib.Tactic.Linarith.Oracle.FourierMotzkin | [
"Mathlib.Tactic.Linarith.CompSource.scale",
"Mathlib.Tactic.Linarith.CompSource.assump",
"Mathlib.Tactic.Linarith.CompSource.add"
] | true |
Nat.avg_le_left | Batteries.Data.Nat.Bisect | [
"Nat.div_le_of_le_mul",
"Lean.RArray.leaf",
"HMul.hMul",
"Nat.Linear.Expr.mulL",
"Lean.RArray.branch",
"Nat.Linear.ExprCnstr.eq_of_toNormPoly_eq",
"id",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"Nat",
"True",
"eq_true",
"Bool",
"of... | true |
Turing.TM1to1.trTape'_move_left | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Turing.TM1to1.trTape'",
"Eq.mpr",
"Turing.ListBlank.mk",
"Inhabited.default",
"List.replicate",
"Turing.Tape.mk'",
"Turing.Tape.move_left_mk'",
"Turing.Tape",
"congrArg",
"instInhabitedBool",
"Turing.ListBlank.flatMap",
"HEq.refl",
"List.length_reverse",
"List.Vector",
"List.reverseAux"... | true |
Set.BijOn.prodMap | Mathlib.Data.Set.Function | [
"Set.instSProd",
"SProd.sprod",
"Set.SurjOn",
"Prod.mk",
"Set.BijOn.injOn",
"Prod.fst",
"Set.BijOn.surjOn",
"Set.InjOn.prodMap",
"And",
"Set.MapsTo",
"Set.SurjOn.prodMap",
"And.intro",
"Set.MapsTo.prodMap",
"Set.BijOn",
"Set.BijOn.mapsTo",
"Set.InjOn",
"Prod",
"Prod.snd",
"Set"
] | true |
CoalgHom.noConfusion | Mathlib.RingTheory.Coalgebra.Hom | [
"CoalgebraStruct",
"Semiring.toModule",
"CommSemiring.toSemiring",
"CoalgHom",
"HEq.refl",
"TensorProduct.addCommMonoid",
"CoalgebraStruct.counit",
"TensorProduct.map",
"LinearMap",
"AddCommMonoid",
"CoalgebraStruct.comul",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Line... | false |
Subtype.relEmbedding_apply | Mathlib.Order.RelIso.Basic | [
"Subtype.relEmbedding",
"Subtype",
"RelEmbedding",
"Eq.refl",
"Subtype.val",
"Eq",
"DFunLike.coe",
"RelEmbedding.instFunLike",
"Order.Preimage"
] | true |
Lean.Widget.RpcEncodablePacket.mk.injEq._@.Lean.Widget.InteractiveGoal.3114798910._hygCtx._hyg.1 | Lean.Widget.InteractiveGoal | [
"Lean.Json",
"Lean.Widget.RpcEncodablePacket._@.Lean.Widget.InteractiveGoal.3114798910._hygCtx._hyg.1",
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Widget.RpcEncodablePacket.mk.inj._@.Lean.Widget.InteractiveGoal.3114798910._hygCtx._hyg.1",
"And",
"Lean.Widget.RpcEncodablePacket.mk._@.Lean.Widget.Interact... | false |
MonoidAlgebra.mul_def | Mathlib.Algebra.MonoidAlgebra.Defs | [
"MonoidAlgebra.addCommMonoid",
"HMul.hMul",
"Finsupp.sum",
"Mul",
"MonoidAlgebra.instMul",
"instDistribOfSemiring",
"Distrib.toMul",
"MonoidAlgebra",
"Semiring",
"Eq.refl",
"Eq",
"MulZeroClass.toZero",
"MonoidAlgebra.single",
"instMulZeroClassOfSemiring",
"instHMul"
] | true |
FormalMultilinearSeries.ofScalars_apply_zero | Mathlib.Analysis.Analytic.OfScalars | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"List.replicate",
"False",
"Nat.instMulZeroClass",
"instHSMul",
"HMul.hMul",
"ContinuousMultilinearMap.mkPiAlgebraFin",
"Nat.instOne",
"Ring.toNonAssocRing",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"MulZe... | true |
CategoryTheory.LocalizerMorphism.LeftResolution.instCategory._proof_2 | Mathlib.CategoryTheory.Localization.Resolution | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.LocalizerMorphism.LeftResolution",
"CategoryTheory.LocalizerMorphism.LeftResolution.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.LocalizerMorphism.LeftResolution.X₁",
"CategoryTheory.LocalizerMorphism.LeftR... | false |
Lean.Language.instInhabitedSnapshotLeaf.default | Lean.Language.Basic | [
"Inhabited.default",
"Lean.Language.SnapshotLeaf.mk",
"Lean.Language.instInhabitedSnapshot",
"Lean.Language.Snapshot",
"Lean.Language.SnapshotLeaf"
] | true |
Lean.Parser.LeadingIdentBehavior.casesOn | Lean.Parser.Basic | [
"Lean.Parser.LeadingIdentBehavior",
"Lean.Parser.LeadingIdentBehavior.default",
"Lean.Parser.LeadingIdentBehavior.symbol",
"Lean.Parser.LeadingIdentBehavior.rec",
"Lean.Parser.LeadingIdentBehavior.both"
] | false |
Lean.Lsp.FileSystemWatcher.mk | Lean.Data.Lsp.Workspace | [
"String",
"Nat",
"Lean.Lsp.FileSystemWatcher.mk",
"Lean.Lsp.FileSystemWatcher",
"Option"
] | true |
Aesop.GoalData.recOn | Aesop.Tree.Data | [
"Aesop.GoalData",
"Aesop.GoalData.rec",
"Lean.instBEqMVarId",
"Aesop.ForwardState",
"Aesop.GoalId",
"Lean.MVarId",
"Aesop.NormalizationState",
"Aesop.UnsafeQueue",
"Array",
"Aesop.GoalState",
"Aesop.ForwardRuleMatches",
"Aesop.UnorderedArraySet",
"Nat",
"Aesop.Iteration",
"Aesop.GoalData... | false |
_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.ParamMap.rec | Lean.Compiler.LCNF.InferBorrow | [
"Lean.instBEqFVarId",
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.ParamMap.instHashableKey",
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.ParamMap.instBEqKey",
"Std.HashSet",
"Lean.FVarId",
"Std.HashMap",
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.Pa... | false |
_private.Lean.Compiler.LCNF.ExplicitBoxing.0.Lean.Compiler.LCNF.State.auxDecls._default | Lean.Compiler.LCNF.ExplicitBoxing | [
"Lean.Compiler.LCNF.Decl",
"id",
"List.toArray",
"Array",
"Lean.Compiler.LCNF.Purity.impure",
"List.nil"
] | false |
AlgebraicGeometry.LocallyRingedSpace.Hom.mk._flat_ctor | Mathlib.Geometry.RingedSpace.LocallyRingedSpace | [
"CommRingCat.Hom.hom",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.PresheafedSpace.Hom.stalkMap",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory... | false |
Set.range_eq_empty_iff | Mathlib.Data.Set.Image | [
"Eq.mpr",
"Set.range_nonempty_iff_nonempty",
"congrArg",
"Set.not_nonempty_iff_eq_empty",
"Iff.rfl",
"id",
"IsEmpty",
"not_nonempty_iff",
"Iff",
"Set.Nonempty",
"propext",
"Set.instEmptyCollection",
"Nonempty",
"Set.range",
"EmptyCollection.emptyCollection",
"Eq.symm",
"Eq",
"Not",... | true |
Affine.Simplex.PointsWithCircumcenterIndex.circumcenterIndex.elim | Mathlib.Geometry.Euclidean.Circumcenter | [
"PULift.up",
"Affine.Simplex.PointsWithCircumcenterIndex.ctorElim",
"Nat",
"Affine.Simplex.PointsWithCircumcenterIndex.ctorIdx",
"Affine.Simplex.PointsWithCircumcenterIndex",
"Eq.symm",
"Affine.Simplex.PointsWithCircumcenterIndex.circumcenterIndex",
"Eq"
] | false |
CategoryTheory.ShortComplex.abToCycles._proof_2 | Mathlib.Algebra.Homology.ShortComplex.Ab | [
"Eq.mpr",
"Subtype.mk.congr_simp",
"AddMonoidHom.instAddMonoidHomClass",
"AddCommGrpCat.instCategory",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"AddCommGroup.toA... | false |
_private.Lean.Elab.MutualDef.0.Lean.Elab.Term.elabHeaders.match_5 | Lean.Elab.MutualDef | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Syntax",
"Option.none",
"Unit",
"Option"
] | false |
Subgroup.relIndex_bot_right | Mathlib.GroupTheory.Index | [
"Eq.mpr",
"Subgroup.subgroupOf",
"congrArg",
"Group",
"Membership.mem",
"id",
"Subtype",
"Subgroup",
"instOfNatNat",
"Bot.bot",
"Subgroup.relIndex",
"Subgroup.relIndex.eq_1",
"Nat",
"Subgroup.index",
"Subgroup.instTop",
"Eq.refl",
"Subgroup.index_top",
"Subgroup.instBot",
"Top.to... | true |
Metric.tendstoUniformlyOnFilter_iff | Mathlib.Topology.MetricSpace.Pseudo.Basic | [
"Filter.instMembership",
"Real",
"Real.instZero",
"SProd.sprod",
"Filter.Eventually",
"uniformity",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"TendstoUniformlyOnFilter",
"Membership.mem",
"Exists",
"Prod.mk",
"Prod.fst",
"And.casesOn",
"Filter.Eventually.mono",
"GT.... | true |
Batteries.RBNode.depthLB.eq_1 | Batteries.Data.RBMap.Depth | [
"instOfNatNat",
"instHAdd",
"Batteries.RBColor.red",
"HAdd.hAdd",
"Batteries.RBNode.depthLB",
"Nat",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
tsub_pos_iff_lt | Mathlib.Algebra.Order.Sub.Basic | [
"not_le",
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"LinearOrder",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZero",
"DistribLattice.toLattice",
"id",
"OrderedSub",
"LE.le",
"Canonic... | true |
Std.Internal.IO.Async.System.CPUInfo._sizeOf_inst | Std.Internal.Async.System | [
"Std.Internal.IO.Async.System.CPUInfo._sizeOf_1",
"Std.Internal.IO.Async.System.CPUInfo",
"SizeOf.mk",
"SizeOf"
] | false |
TopologicalSpace.PositiveCompacts.interior_nonempty | Mathlib.Topology.Sets.Compacts | [
"TopologicalSpace.PositiveCompacts.instSetLike",
"TopologicalSpace.PositiveCompacts.interior_nonempty'",
"TopologicalSpace",
"Set.Nonempty",
"SetLike.coe",
"interior",
"TopologicalSpace.PositiveCompacts"
] | true |
_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable._proof_10 | Init.Data.String.Pattern.String | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance._proof_1",
"Int.add_one_l... | false |
_private.Mathlib.Tactic.ComputeDegree.0.Mathlib.Tactic.ComputeDegree.getCongrLemma._sparseCasesOn_3 | Mathlib.Tactic.ComputeDegree | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
Lean.instInhabitedImport | Lean.Setup | [
"Lean.Import",
"Lean.instInhabitedImport.default",
"Inhabited",
"Inhabited.mk"
] | true |
CategoryTheory.Pretriangulated.Triangle.add_hom₁ | Mathlib.CategoryTheory.Triangulated.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.shiftFunctor",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Triangle",
"CategoryTheory.Preadditi... | true |
exists_nhds_one_split | Mathlib.Topology.Algebra.Monoid | [
"Filter.instMembership",
"MulOne.toOne",
"HMul.hMul",
"Membership.mem",
"Exists",
"nhds",
"_private.Mathlib.Topology.Algebra.Monoid.0.exists_nhds_one_split.match_1_1",
"MulOne.toMul",
"TopologicalSpace",
"MulOneClass.toMulOne",
"ContinuousMul",
"And",
"exists_open_nhds_one_split",
"And.int... | true |
Real.fourierIntegral_eq' | Mathlib.Analysis.Fourier.FourierTransform | [
"InnerProductSpace.toNormedSpace",
"Real",
"instHSMul",
"Real.pi",
"measureSpaceOfInnerProductSpace",
"HMul.hMul",
"NormedSpace",
"Inner.inner",
"Real.instRCLike",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"Measure... | true |
_private.Mathlib.Geometry.Convex.ConvexSpace.Defs.0.Convexity.StdSimplex.restrict_singleton._simp_1_6 | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"Finsupp.mem_support_iff",
"Finsupp.instFunLike",
"Finset",
"Finsupp.support",
"Membership.mem",
"Ne",
"Finset.instSetLike",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"SetLike.instMembership",
"Finsupp",
"Zero"
] | false |
List.pairwise_of_forall_sublist | Init.Data.List.Pairwise | [
"Iff.mpr",
"List.Pairwise",
"List.pairwise_iff_forall_sublist",
"List.cons",
"List",
"List.Sublist",
"List.nil"
] | true |
catalan_one | Mathlib.Combinatorics.Enumerative.Catalan.Basic | [
"Nat.instCanonicallyOrderedAdd",
"catalan",
"Nat.instOrderedSub",
"instHSMul",
"HMul.hMul",
"Finset.univ",
"congrArg",
"Finset",
"Fin.instUnique",
"AddMonoid.toAddZeroClass",
"tsub_self",
"HSub.hSub",
"AddMonoid.toNSMul",
"Nat.instMulOneClass",
"Fin.instUnique._proof_1",
"Membership.me... | true |
cfc_predicate_algebraMap | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"cfc",
"IsTopologicalSemiring",
"ContinuousStar",
"PseudoMetricSpace.toUniformSpace",
"Algebra",
"RingHom",
"Eq.rec",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"StarAddMonoid.toInvolutiveStar",
"NonAssocRing.t... | true |
_private.Mathlib.Analysis.Meromorphic.TrailingCoefficient.0.MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_add._proof_1_1 | Mathlib.Analysis.Meromorphic.TrailingCoefficient | [
"False",
"Lean.Grind.not_not",
"NormedSpace",
"eq_false",
"Classical.byContradiction",
"Eq.mp",
"id",
"meromorphicOrderAt",
"Int",
"WithTop.top",
"True",
"eq_true",
"NontriviallyNormedField",
"Lean.Grind.intro_with_eq",
"NontriviallyNormedField.toNormedField",
"Top.top",
"Eq.symm",
... | false |
AddSubmonoid.topologicalClosure._proof_2 | Mathlib.Topology.Algebra.Monoid | [
"AddSubmonoid.zero_mem",
"subset_closure",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid",
"TopologicalSpace",
"AddZero.toZero",
"SetLike.coe",
"closure",
"AddMonoid",
"Zero.toOfNat0",
"OfNat.ofNat",
"AddSubmonoid.instSetLike",
"Set.instMembership"... | false |
Graph.IsSubgraph.casesOn | Mathlib.Combinatorics.Graph.Subgraph | [
"Graph.IsSubgraph.mk",
"Graph.IsSubgraph.rec",
"Graph.IsSubgraph",
"HasSubset.Subset",
"Graph",
"Graph.IsLink",
"Graph.vertexSet",
"Set.instHasSubset",
"Set"
] | false |
Mathlib.Linter.linter.style.show | Mathlib.Tactic.Linter.Style | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
SetLike.GradeZero.instSemiring._proof_3 | Mathlib.Algebra.DirectSum.Internal | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semigroup.toMul",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"SetLike.GradeZero.instMonoid",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
"SetLike.GradeZero.subsemiring",
"Subtype",
"AddSubmo... | false |
SetLike.GradeZero.submonoid._proof_1 | Mathlib.Algebra.GradedMonoid | [
"SetLike",
"Monoid",
"HMul.hMul",
"Monoid.toMulOneClass",
"AddMonoid.toAddZeroClass",
"SetLike.mul_mem_graded",
"Membership.mem",
"Eq.rec",
"AddZeroClass.toAddZero",
"MulOne.toMul",
"AddZero.toZero",
"instHAdd",
"MulOneClass.toMulOne",
"SetLike.GradedMonoid.toGradedMul",
"SetLike.coe",
... | false |
Rep.resFunctor | Mathlib.RepresentationTheory.Rep.Res | [
"Monoid",
"Rep.V",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"Rep.resFunctor._proof_1",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"CategoryTheory.Functor.mk",
"Rep.of",
"Module.End.instSemiring",
"Rep.resFunctor.... | true |
_private.Mathlib.CategoryTheory.Presentable.IsCardinalFiltered.0.CategoryTheory.IsCardinalFiltered.of_final._simp_1_1 | Mathlib.CategoryTheory.Presentable.IsCardinalFiltered | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
AffineIsometryEquiv.comp_continuousOn_iff._simp_1 | Mathlib.Analysis.Normed.Affine.Isometry | [
"AffineIsometryEquiv.instEquivLike",
"SeminormedAddCommGroup",
"NormedSpace",
"PseudoMetricSpace.toUniformSpace",
"Function.comp",
"AffineIsometryEquiv",
"NormedField",
"TopologicalSpace",
"PseudoMetricSpace",
"propext",
"ContinuousOn",
"AffineIsometryEquiv.comp_continuousOn_iff",
"UniformSp... | false |
CompleteSublattice.comap._proof_2 | Mathlib.Order.CompleteSublattice | [
"Sublattice",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"CompleteSublattice.toSublattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"InfTopHomClass.toInfHomClass",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"Sublattice.infClosed",
"Semil... | false |
Finset.Iic_mul_Iic_subset' | Mathlib.Algebra.Group.Pointwise.Finset.Interval | [
"Eq.mpr",
"HMul.hMul",
"Finset.coe_Iic",
"congrArg",
"Finset",
"Preorder.toLE",
"Mul",
"Finset.coe_mul",
"LocallyFiniteOrderBot",
"MulLeftMono",
"id",
"MulRightMono",
"HasSubset.Subset",
"Finset.mul",
"Set.Iic_mul_Iic_subset'",
"SetLike.coe",
"Finset.instSetLike",
"congr",
"Iff.m... | true |
FractionalIdeal.zero_le | Mathlib.RingTheory.FractionalIdeal.Basic | [
"Eq.mpr",
"CommRing",
"outParam",
"congrArg",
"CommSemiring.toSemiring",
"HEq.refl",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"Eq.casesOn",
"id",
"LE.le",
"Membership",
"FractionalIdeal.mem_zero_iff",
"MulZeroOneClass.toMulOneClass",
"FractionalIdeal.i... | true |
_private.Batteries.Data.List.Lemmas.0.List.exists_of_replaceF.match_1_1 | Batteries.Data.List.Lemmas | [
"False",
"Option.ctorIdx",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Option.some",
"Eq.casesOn",
"Option.none",
"Eq.refl",
"HEq",
"Eq",
"Option"
] | false |
Matrix.rank.eq_1 | Mathlib.LinearAlgebra.Matrix.Rank | [
"Pi.Function.module",
"Submodule",
"CommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"CommSemiring.toSemiring",
"Matrix",
"Submodule.addCommMonoid",
"Membership.mem",
"Matrix.rank",
"LinearMap.range",
"Subtype",
"Submodule.module",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRin... | true |
instNoZeroDivisorsENat._proof_1 | Mathlib.Data.ENat.Basic | [
"IsDomain.to_noZeroDivisors",
"CommSemiring.toSemiring",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Nat.instIsDomain",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"instDistribOfSemiring",
"NoZeroDivisors",
"Distrib.toMul",
"Nat",
"ENat",
"instCommSemiringENat",
"Semiring.toNonUnitalSemi... | false |
String.startsWith_string_iff | Init.Data.String.Lemmas.Pattern.TakeDrop.String | [
"String.toSlice",
"congrArg",
"String",
"String.Slice.startsWith_string_iff._simp_1",
"String.Slice.startsWith",
"String.startsWith",
"iff_self",
"Bool.true",
"String.Slice.copy",
"List",
"Iff",
"List.IsPrefix",
"String.toList",
"True",
"Bool",
"of_eq_true",
"congrFun'",
"Char",
... | true |
CategoryTheory.Pi.δ_def | Mathlib.CategoryTheory.Pi.Monoidal | [
"CategoryTheory.Pi.instMonoidalForallEval",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pi.monoidalCategory",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Pi.eval",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"CategoryTheory.pi",
... | true |
MeasurableDiv.measurable_const_div._autoParam | Mathlib.MeasureTheory.Group.Arithmetic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
sbtw_sub_const_iff | Mathlib.Analysis.Convex.Between | [
"AddCommGroup.toAddCommMonoid",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"PartialOrder",
"AddCommGroup",
"addGroupIsAddTorsor",
"sbtw_vsub_const_iff",
"SubNegMonoid.toSub",
"Iff",
"instHSub",
"AddGroup.toSubNegMonoid",
"Module",
"Ring.toSemiring",
"Ring",
"Sbtw"
] | true |
groupHomology.H0 | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"CommRing",
"ModuleCat",
"CommSemiring.toSemiring",
"Group",
"DivInvMonoid.toMonoid",
"instOfNatNat",
"groupHomology",
"Group.toDivInvMonoid",
"CommRing.toCommSemiring",
"Rep",
"Nat",
"CommRing.toRing",
"OfNat.ofNat"
] | true |
tendsto_birkhoffAverage_apply_sub_birkhoffAverage | Mathlib.Dynamics.BirkhoffSum.NormedSpace | [
"Filter.Tendsto.div_atTop",
"Real.instIsOrderedRing",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"Real.instArchimedean",
"dist_eq_norm",
"div_le_div_of_nonneg_right",
"PseudoMetricSpace.toBornology",
"NormedSpace",
"MulZero... | true |
Lat.recOn | Mathlib.Order.Category.Lat | [
"Lattice",
"Lat.mk",
"Lat.rec",
"Lat"
] | false |
Lean.Doc.DocHighlight.ctorIdx | Lean.Elab.DocString.Builtin | [
"Lean.Doc.DocHighlight",
"Lean.FVarId",
"Lean.Doc.DocHighlight.casesOn",
"Nat",
"Std.Format",
"Lean.Name",
"Lean.SyntaxNodeKind",
"Option"
] | false |
Sym2.sortEquiv._proof_1 | Mathlib.Data.Sym.Sym2.Order | [
"Lattice.toSemilatticeSup",
"Sym2.mk",
"congrArg",
"and_self",
"inf_of_le_left",
"true_or",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"inf_of_le_right",
"DistribLattice.toLattice",
"Prod.mk",
"le_total",
"LE.le",
"Sym2.inf",
"Prod.fst... | false |
WeierstrassCurve.isCharThreeJNeZeroNF_iff | Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms | [
"CommRing",
"CommSemiring.toSemiring",
"WeierstrassCurve.IsCharThreeJNeZeroNF.casesOn",
"WeierstrassCurve",
"WeierstrassCurve.a₃",
"And.casesOn",
"And",
"CommRing.toCommSemiring",
"Iff",
"WeierstrassCurve.IsCharThreeJNeZeroNF.mk",
"And.intro",
"Iff.intro",
"WeierstrassCurve.IsCharThreeJNeZer... | true |
EuclideanGeometry.Sphere.nonempty_iff | Mathlib.Geometry.Euclidean.Sphere.Basic | [
"Nontrivial",
"Iff.mpr",
"Norm.norm",
"Eq.mpr",
"Real.instLE",
"Real",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"Real.instZero",
"congrArg",
"NormedAddCommGroup.toMetricSpace",
"sub_zero",
"EuclideanGeometry.Sphere",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Eq.mp"... | true |
AddEquiv.coprodAssoc | Mathlib.GroupTheory.Coprod.Basic | [
"AddMonoid.Coprod.inst",
"AddMonoid.toAddZeroClass",
"AddMonoid.Coprod.inr",
"AddMonoidHom.id",
"AddZeroClass.toAddZero",
"AddMonoid.Coprod.lift",
"AddEquiv.coprodAssoc._proof_2",
"AddMonoid.Coprod.instAddZeroClass",
"AddMonoid",
"AddEquiv",
"AddZero.toAdd",
"AddMonoid.Coprod.inl",
"AddEquiv... | true |
CategoryTheory.Pairwise.diagramMap._proof_1 | Mathlib.CategoryTheory.Category.Pairwise | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeInf.toMin",
"LE.le",
"SemilatticeInf",
"inf_le_left",
"Min.min"
] | false |
Std.DTreeMap.Internal.Impl.Const.get_insertMany!_list_of_contains_eq_false | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"Std.DTreeMap.Internal.Impl.Const.insertMany!",
"congrArg",
"instForInOfForIn'",
"Std.DTreeMap.Internal.Impl.insert!",
"List.map",
"Std.TransOrd",
"List.contains",
"Std.DTreeMap.Internal.Impl.Balanced",
"inferInstance",
"E... | true |
Computation.runFor | Mathlib.Data.Seq.Computation | [
"Option.some",
"instOfNatNat",
"Computation",
"Stream'",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Subtype.val",
"Eq",
"Option"
] | true |
FirstOrder.Language.Term.ctorIdx | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.Term.casesOn",
"FirstOrder.Language.Term",
"Nat",
"FirstOrder.Language.Functions",
"FirstOrder.Language",
"Fin"
] | false |
Algebra.intNorm_eq_zero._simp_1 | Mathlib.RingTheory.IntegralClosure.IntegralRestrict | [
"IsDomain",
"FractionRing.field",
"CommRing",
"IsDomain.to_noZeroDivisors",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"MonoidHom",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"OreLocalization.ins... | false |
Subgroup.conj_smul_subgroupOf | Mathlib.Algebra.Group.Subgroup.Pointwise | [
"instHSMul",
"Subgroup.subgroupOf",
"MonoidHom.instFunLike",
"MulAut.applyMulDistribMulAction",
"MonoidHom",
"Monoid.End.instMonoid",
"Monoid.toMulOneClass",
"Subgroup.subtype",
"MulAut.instGroup",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Membership.mem",
"MulAut",
"MulOne.t... | true |
Lean.Meta.Grind.Arith.CommRing.EqCnstrProof.mul.sizeOf_spec | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Meta.Grind.Arith.CommRing.EqCnstr._sizeOf_inst",
"instOfNatNat",
"Int",
"Lean.Meta.Grind.Arith.CommRing.EqCnstrProof",
"instHAdd",
"Lean.Meta.Grind.Arith.CommRing.EqCnstrProof._sizeOf_inst",
"HAdd.hAdd",
"Nat",
"Int._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Lean.Meta.Gr... | true |
Filter.ofCountableUnion.congr_simp | Mathlib.Topology.Compactness.Lindelof | [
"Set.sUnion",
"Membership.mem",
"Eq.rec",
"HasSubset.Subset",
"Filter.ofCountableUnion",
"Eq.ndrec",
"Eq.refl",
"Set.Countable",
"Eq",
"Set.instMembership",
"Filter",
"Set.instHasSubset",
"Set"
] | true |
Submodule.toAddSubgroup_eq_top | Mathlib.Algebra.Module.Submodule.Lattice | [
"Submodule",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Submodule.instTop",
"AddSubgroup",
"iff_self",
"Iff",
"Submodule.toAddSubgroup",
"True",
"of_eq_true",
"Module",
"Top.top",
"AddSubgroup.instTop",
"Ring.toSemiring",
"Eq",
"Ring",
... | true |
AddAction.isPretransitive_compHom | Mathlib.Algebra.Group.Action.Hom | [
"AddAction.exists_vadd_eq",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"Exists",
"AddZeroClass.toAddZero",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"Exists.casesOn",
"AddAction.compHom",
"AddSemigroupAction.toVAdd",
"AddMonoid",
"Exists.intro",
"instHVAdd"... | true |
IsAddCyclic.card_addOrderOf_eq_totient | Mathlib.GroupTheory.SpecificGroups.Cyclic | [
"Dvd.dvd",
"Finset.univ",
"addOrderOf",
"Classical.propDecidable",
"IsAddCyclic.card_nsmul_eq_zero_le",
"Fintype.card",
"Nat.totient",
"AddGroup",
"Fintype",
"AddGroup.toSubNegMonoid",
"Nat.instDvd",
"Nat",
"Finset.card",
"card_addOrderOf_eq_totient_aux₂",
"instDecidableEqNat",
"SubNeg... | true |
Std.Time.Modifier.k.injEq | Std.Time.Format.Basic | [
"Eq.propIntro",
"Std.Time.Modifier.k.inj",
"Std.Time.Number",
"Eq.ndrec",
"Eq.refl",
"Std.Time.Modifier",
"Eq",
"Std.Time.Modifier.k"
] | true |
CategoryTheory.StrongEpiCategory.recOn | Mathlib.CategoryTheory.Limits.Shapes.StrongEpi | [
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.StrongEpiCategory.rec",
"CategoryTheory.StrongEpi",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.StrongEpiCategory.mk",
"CategoryTheory.StrongEpiCategory",
"CategoryTheory.Category"
] | false |
OrderDual.instAddCommMonoid | Mathlib.Algebra.Order.Group.Synonym | [
"AddCommMonoid",
"OrderDual.instAddMonoid",
"OrderDual.instAddCommMonoid._proof_1",
"AddCommMonoid.toAddMonoid",
"OrderDual",
"AddCommMonoid.mk"
] | true |
ContinuousMap.UniqueHom.rec | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Continuous",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"IsTopologicalSemiring",
"ContinuousStar",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"Algebra",
"Membership.mem",
"ContinuousMap.UniqueHom.mk",
"StarAlgHom.instFunLike",
"Set.Elem",
"Algebra.id",
"ContinuousMap.inst... | false |
Function.bijective_of_subsingleton._simp_1 | Mathlib.Logic.Function.Basic | [
"Function.bijective_of_subsingleton",
"True",
"eq_true",
"Function.Bijective",
"Subsingleton",
"Eq"
] | false |
Lean.instInhabitedFVarIdSet | Lean.Expr | [
"Lean.instInhabitedFVarIdSet._aux_1",
"Inhabited",
"Lean.FVarIdSet",
"Inhabited.mk"
] | true |
_private.Mathlib.Topology.Compactness.Lindelof.0.IsLindelof.adherence_nhdset.match_1_1 | Mathlib.Topology.Compactness.Lindelof | [
"Compl.compl",
"Membership.mem",
"Exists",
"Filter.instInf",
"Set.instCompl",
"And.casesOn",
"TopologicalSpace",
"ClusterPt",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Filter.principal",
"Set.instMembership",
"Filter",
"Min.min",
"Set"
] | false |
Vector.Perm.extract | Init.Data.Vector.Perm | [
"instGetElem?OfGetElemOfDecidable",
"Array.Perm.extract",
"Vector",
"congrArg",
"Vector.instGetElemNatLt",
"HSub.hSub",
"Vector.extract",
"Vector.casesOn",
"Eq.rec",
"Eq.mp",
"id",
"instSubNat",
"instOfNatNat",
"Vector.getElem?_mk",
"LE.le",
"instLENat",
"Vector.Perm",
"Array",
"... | true |
AlgebraicGeometry.Scheme.Modules.instAbelian._proof_8 | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"AlgebraicGeometry.Scheme.Modules.instAbelian._proof_4",
"CategoryTheory.Limits.hasFiniteLimits_of_hasLimits",
"CategoryTheory.GrothendieckTopology.instPreservesSheafificationForgetOfPreservesLimitsOfHasColimitsOfShapeOfPreservesColimitsOfShapeOppositeCoverOfHasLimitsOfShapeWalkingMulticospanOfReflectsIsomorphi... | false |
Std.ExtDHashMap.get?_diff | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"instLawfulHashableOfLawfulBEq",
"Std.ExtDHashMap.instDecidableMem",
"Std.ExtDHashMap.inductionOn₂",
"LawfulBEq",
"Membership.mem",
"SDiff.sdiff",
"Option.none",
"Std.DHashMap.get?_diff",
"Std.ExtDHashMap",
"Hashable",
"instEquivBEqOf... | true |
irrational_div_intCast_iff._simp_1 | Mathlib.NumberTheory.Real.Irrational | [
"Int.cast",
"Real",
"instHDiv",
"Real.instDivInvMonoid",
"HDiv.hDiv",
"irrational_div_intCast_iff",
"Ne",
"Int",
"And",
"Irrational",
"instOfNat",
"Real.instIntCast",
"propext",
"DivInvMonoid.toDiv",
"OfNat.ofNat",
"Eq"
] | false |
_private.Mathlib.Topology.VectorBundle.Riemannian.0.eventually_norm_symmL_trivializationAt_self_comp_lt._simp_1_1 | Mathlib.Topology.VectorBundle.Riemannian | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace",
"ContinuousSMul",
"FiberBundle",
"ContinuousLinearMap.topologicalSpace",
"ContinuousAt",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",... | false |
CategoryTheory.GlueData.ofGlueData'._proof_6 | Mathlib.CategoryTheory.GlueData | [
"CategoryTheory.Limits.pullbackSymmetry",
"CategoryTheory.GlueData'.t''",
"dite_cond_eq_true",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.Cone.π",
"of_eq_false",
"CategoryTheory.Functor",
"CategoryTheory.GlueData'.t''._proof_1",
"CategoryTheory.GlueDa... | false |
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