name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
List.destutter'_eq_self_iff._simp_1 | Mathlib.Data.List.Destutter | [
"DecidableRel",
"List.IsChain",
"List.destutter'",
"List.cons",
"List",
"List.destutter'_eq_self_iff",
"propext",
"Eq"
] | false |
LinearEquiv.isPositive_symm_iff._simp_1 | Mathlib.Analysis.InnerProductSpace.Positive | [
"InnerProductSpace.toNormedSpace",
"LinearEquiv.symm",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"LinearEquiv.isPositive_symm_iff",
"Field.toSemifield",
"RCLike.toDenselyNormedField",
"LinearMap.IsPositive",
"RCLike",
"Semifield.toDivisionSemiring",
"Linear... | false |
_private.Lean.Elab.SetOption.0.Lean.Elab.elabSetOption.setOption | Lean.Elab.SetOption | [
"Pure.pure",
"Monad.toApplicative",
"Lean.OptionDecl",
"Applicative.toPure",
"Unit",
"Lean.MonadError",
"Lean.KVMap.instValueDataValue",
"Lean.MonadOptions.getOptions",
"Lean.Name",
"Monad.toBind",
"Lean.DataValue",
"Lean.Options.set",
"Bind.bind",
"Monad",
"Lean.Options",
"Lean.MonadO... | true |
_private.Init.Data.List.Pairwise.0.List.pairwise_and_iff.match_1_1 | Init.Data.List.Pairwise | [
"List.Pairwise",
"And.casesOn",
"List",
"And",
"And.intro"
] | false |
Std.DTreeMap.Raw.Const.get!_insert_self | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.Const.get!",
"Ord.mk",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Inhabited",
"Std.DTreeMap.Raw.insert",
"Std.DTreeMap.Internal.Impl.Const.get!_insert!_self",
"Eq",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] | true |
Turing.TM1to1.trTape_mk' | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Turing.TM1to1.trTape'",
"Inhabited.default",
"Turing.Tape.mk'",
"Turing.Tape",
"congrArg",
"instInhabitedBool",
"Turing.TM1to1.trTape",
"List.Vector",
"Turing.Tape.left",
"id",
"Turing.Tape.right₀",
"Turing.TM1to1.trTape'.congr_simp",
"Turing.Tape.mk'_right₀",
"Nat",
"True",
"List.Vec... | true |
_private.Mathlib.RingTheory.SimpleModule.Isotypic.0.isIsotypic_iff_isFullyInvariant_imp_bot_or_top.match_1_1 | Mathlib.RingTheory.SimpleModule.Isotypic | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"AddCommGroup",
"Subtype",
"IsSimpleModule",
"Submodule.instPartialOrder",
"Submodule.module",
"LE.le",
"And.casesOn",
"And",
"Exists.casesOn",
"Submodule.addCommGroup",... | false |
CompactlySupportedContinuousMap.instMulActionWithZeroOfContinuousConstSMul | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"CompactlySupportedContinuousMap.instMulActionWithZeroOfContinuousConstSMul._proof_2",
"CompactlySupportedContinuousMap.instMulActionWithZeroOfContinuousConstSMul._proof_3",
"SMulWithZero.toSMulZeroClass",
"CompactlySupportedContinuousMap",
"CompactlySupportedContinuousMap.instMulActionWithZeroOfContinuousC... | true |
CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShape.inverseImage | Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape | [
"CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShape",
"_private.Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape.0.CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShape.inverseImage.match_1",
"CategoryTheory.Functor",
"CategoryTheory.ObjectProperty.colimitsOfShape",
"CategoryTheory.ObjectP... | true |
Subring.coe_pow._simp_1 | Mathlib.Algebra.Ring.Subring.Defs | [
"Subring.instSetLike",
"Ring.toNonAssocRing",
"SubmonoidClass.instPow",
"Membership.mem",
"Subring.instSubringClass",
"Subtype",
"Monoid.toPow",
"HPow.hPow",
"Subring",
"Nat",
"Semiring.toMonoid",
"instHPow",
"Eq.symm",
"Subtype.val",
"Subring.coe_pow",
"Semiring.toNonAssocSemiring",
... | false |
RelIso.symm_symm | Mathlib.Order.RelIso.Basic | [
"RelIso.symm",
"RelIso",
"Eq",
"rfl"
] | true |
Std.ExtTreeSet.get!_empty | Std.Data.ExtTreeSet.Lemmas | [
"Inhabited.default",
"Std.ExtTreeMap.getKey!_empty",
"Ordering",
"Std.TransCmp",
"Std.ExtTreeSet.get!",
"Unit",
"Std.ExtTreeSet",
"Inhabited",
"Std.ExtTreeSet.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq"
] | true |
Lean.Meta.Sym.Simp.instInhabitedResult | Lean.Meta.Sym.Simp.SimpM | [
"Lean.Meta.Sym.Simp.instInhabitedResult.default",
"Lean.Meta.Sym.Simp.Result",
"Inhabited",
"Inhabited.mk"
] | true |
Polynomial.rootsExpandToRoots._proof_2 | Mathlib.FieldTheory.Perfect | [
"Multiset.toFinset",
"IsDomain",
"CommRing",
"IsDomain.to_noZeroDivisors",
"Polynomial.roots",
"CommSemiring.toSemiring",
"AlgHom",
"Finset",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"AddGroupWithOne.toAddMonoidWithOne",
"RingHom",
"Membership.mem",
"ExpChar",
"Algebra.id",
"Su... | false |
Finset.cons | Mathlib.Data.Finset.Insert | [
"Finset.cons._proof_1",
"Finset",
"Membership.mem",
"Multiset.cons",
"Finset.val",
"Finset.instSetLike",
"Finset.mk",
"Not",
"SetLike.instMembership"
] | true |
Std.DTreeMap.Internal.Unit.RocSliceData.mk.sizeOf_spec | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"Std.DTreeMap.Internal.Unit.RocSliceData.mk",
"instOfNatNat",
"instHAdd",
"Unit",
"Std.DTreeMap.Internal.Impl._sizeOf_inst",
"HAdd.hAdd",
"Std.DTreeMap.Internal.Unit.RocSliceData._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Std.Roc._sizeOf_inst",
"Eq.refl",
"SizeOf",
"Std... | true |
Lean.Grind.Ring.zsmul_natCast_eq_nsmul | Init.Grind.Ring.Basic | [
"instHSMul",
"Int",
"Nat.cast",
"Lean.Grind.Ring",
"Nat",
"HSMul.hSMul",
"Lean.Grind.Ring.zsmul",
"Lean.Grind.Ring.toSemiring",
"instNatCastInt",
"Lean.Grind.Semiring.nsmul",
"Eq"
] | true |
Lean.Elab.Do.DoElemContKind.duplicable | Lean.Elab.Do.Basic | [
"Lean.Elab.Do.DoElemContKind",
"Lean.Elab.Do.DoElemContKind.duplicable"
] | true |
PartialEquiv.prod._proof_2 | Mathlib.Logic.Equiv.PartialEquiv | [
"Set.instSProd",
"SProd.sprod",
"congrArg",
"and_self",
"PartialEquiv.target",
"PartialEquiv",
"Set.mem_prod._simp_1",
"Membership.mem",
"PartialEquiv.symm",
"Eq.mp",
"id",
"Prod.mk",
"Prod.fst",
"And",
"congr",
"True",
"of_eq_true",
"PartialEquiv.source",
"PartialEquiv.toFun",
... | false |
ByteArray.utf8Decode?.go | Init.Data.String.Basic | [
"LE.le",
"instLENat",
"Array",
"Nat",
"PSigma.mk",
"ByteArray.utf8Decode?.go._unary",
"Char",
"ByteArray",
"PSigma",
"ByteArray.size",
"Option"
] | true |
Fin.orderSucc_eq | Mathlib.Data.Fin.SuccPredOrder | [
"Order.succ",
"Fin.succ",
"PartialOrder.toPreorder",
"Fin.lastCases",
"Fin.instSuccOrder",
"instOfNatNat",
"instHAdd",
"Fin.instPartialOrder",
"HAdd.hAdd",
"Nat",
"Fin.last",
"instAddNat",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
_private.Mathlib.Tactic.Module.0.Mathlib.Tactic.Module.qNF.mkAddProof._unary._proof_2 | Mathlib.Tactic.Module | [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Nat.instCanonicallyOrderedAdd",
"Lean.RArray.leaf",
"Preorder.toLT",
"Mathlib.Tactic.Module.NF",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Nat.instOne",
"Mathlib.Tactic.Module.qNF",
"congrArg",
"true_or",
... | false |
UniqueProds.instMulOpposite | Mathlib.Algebra.Group.UniqueProds.Basic | [
"MulEquiv.opOp",
"MulOpposite",
"Mul",
"UniqueProds",
"MulEquiv.uniqueProds_iff",
"UniqueProds.of_mulOpposite",
"Iff.mp",
"MulOpposite.instMul"
] | true |
MulAction.toPermHom | Mathlib.Algebra.Group.Action.End | [
"MulOne.toOne",
"MonoidHom",
"Monoid.toMulOneClass",
"OneHom.mk",
"Group",
"DivInvMonoid.toMonoid",
"MonoidHom.mk",
"MulAction.toPerm",
"Group.toDivInvMonoid",
"Equiv.Perm.permGroup",
"MulOneClass.toMulOne",
"Equiv.Perm",
"MulAction",
"MulAction.toPermHom._proof_1",
"MulAction.toPermHom.... | true |
_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithResult | Lean.Meta.Tactic.Grind.AC.Seq | [
"_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithResult.prefix",
"_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithResult.exact",
"_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithResult.false"
] | true |
Std.ExtTreeMap.instMembershipOfTransCmp | Std.Data.ExtTreeMap.Basic | [
"Ordering",
"Std.TransCmp",
"Membership",
"Bool.true",
"Std.ExtTreeMap",
"Bool",
"Membership.mk",
"Std.ExtTreeMap.contains",
"Eq"
] | true |
_private.Lean.DocString.Extension.0.Lean.VersoModuleDocs.DocContext.close._proof_2 | Lean.DocString.Extension | [
"_private.Lean.DocString.Extension.0.Lean.VersoModuleDocs.DocContext.context",
"instOfNatNat",
"_private.Lean.DocString.Extension.0.Lean.VersoModuleDocs.DocContext.close._proof_1",
"_private.Lean.DocString.Extension.0.Lean.VersoModuleDocs.DocFrame",
"_private.Lean.DocString.Extension.0.Lean.VersoModuleDocs.... | false |
LinearEquiv.det | Mathlib.LinearAlgebra.Determinant | [
"CommRing",
"Module.End.instMonoid",
"MonoidHom",
"Monoid.toMulOneClass",
"LinearMap.GeneralLinearGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"equivOfPiLEquivPi._proof_1",
"Units",
"AddCommGroup",
"MulOne.toMul",
"MonoidHom.comp",
"DivInvMonoid.toMonoid",
"LinearMap.... | true |
SemiNormedGrp.of.sizeOf_spec | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"SeminormedAddCommGroup",
"instSizeOfDefault",
"instOfNatNat",
"instHAdd",
"SemiNormedGrp.of",
"HAdd.hAdd",
"SemiNormedGrp._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"SemiNormedGrp"
] | true |
IsOrderedCancelAddMonoid.of_add_lt_add_left | Mathlib.Algebra.Order.Monoid.Defs | [
"not_le",
"Eq.mpr",
"IsOrderedMonoid._proof_1._to_additive_1",
"Preorder.toLT",
"instReflLe",
"congrArg",
"LinearOrder",
"Std.le_refl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZero",
"Eq.mp",
"DistribLatt... | true |
Matrix.isSymm_one | Mathlib.LinearAlgebra.Matrix.Symmetric | [
"One",
"Matrix",
"Matrix.transpose_one",
"Matrix.IsSymm",
"One.toOfNat1",
"Matrix.one",
"OfNat.ofNat",
"DecidableEq",
"Zero"
] | true |
IsField.toField._proof_2 | Mathlib.Algebra.Field.IsField | [
"CommSemiring.mul_comm",
"Semigroup.toMul",
"IsField.toSemifield",
"HMul.hMul",
"CommSemiring.toSemiring",
"IsField",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"Semifield.toCommSemiring",
"Ring.toSemiring",
"Eq",
"Ring",
"instHMul"
] | false |
CategoryTheory.MorphismProperty.monotone_paths | Mathlib.CategoryTheory.PathCategory.MorphismProperty | [
"CategoryTheory.MorphismProperty",
"trivial",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"Quiver.Path.nil",
"CategoryTheory.Paths.categoryPaths",
"PartialOrder.toPreorder",
"CategoryTheory.Paths",
"Monotone",
"Quiver.Path... | true |
CategoryTheory.SimplicialObject.augmentedCechNerve_map_left_app | Mathlib.AlgebraicTopology.CechNerve | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.Limits.widePullback",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.ho... | true |
compl_unique | Mathlib.Order.Heyting.Basic | [
"Lattice.toSemilatticeSup",
"Compl.compl",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"Bot.bot",
"SemilatticeInf.toMin",
"IsCompl.compl_eq",
"OrderTop.toTop",
"Max.max",
"GeneralizedHeytingAlgebra.toLattice",
"IsCo... | true |
StructureGroupoid.LocalInvariantProp.liftPropOn_congr | Mathlib.Geometry.Manifold.LocalInvariantProperties | [
"StructureGroupoid.LocalInvariantProp",
"ChartedSpace.LiftPropOn",
"Membership.mem",
"StructureGroupoid",
"StructureGroupoid.LocalInvariantProp.liftPropWithinAt_congr",
"TopologicalSpace",
"Eq",
"Set.instMembership",
"Set",
"ChartedSpace"
] | true |
_private.Lean.Meta.Basic.0.Lean.Meta.forallTelescopeReducingAux | Lean.Meta.Basic | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"Lean.Meta.instInhabitedMetaM",
"Nat",
"Bool",
"Option"
] | true |
Set.biUnionEqSigmaOfDisjoint._proof_1 | Mathlib.Data.Set.Pairwise.Lattice | [
"Membership.mem",
"Set.Elem",
"Set.biUnion_eq_iUnion",
"Subtype.val",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
LinearMap.compl₁₂.eq_1 | Mathlib.LinearAlgebra.Matrix.SesquilinearForm | [
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.lcomp._proof_1",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"LinearMap.comp",
"LinearMap.addCommMonoid",
"Semiring.toMonoid",
"Semiring",... | true |
_private.Lean.Server.Completion.SyntheticCompletion.0.Lean.Server.Completion.findSyntheticFieldCompletion? | Lean.Server.Completion.SyntheticCompletion | [
"Pure.pure",
"_private.Lean.Server.Completion.SyntheticCompletion.0.Lean.Server.Completion.findSyntheticFieldCompletion?.match_4",
"instAlternativeOption",
"Lean.Syntax.missing",
"Bool.not",
"Lean.Server.Completion.HoverInfo.after",
"Lean.FileMap",
"Lean.LocalContext.empty",
"Lean.Elab.CompletionInf... | true |
Complex.exists_continuousOn_pow_eq | Mathlib.Analysis.Complex.BranchLogRoot | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"False",
"DivInvMonoid.toInv",
"Continuous",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Set.piecewise_eq_of_notMem",
"HMul.hMul",
"eq_false",
"congrArg",
"IsSemitopological... | true |
Lean.Lsp.DocumentChange.create.injEq | Lean.Data.Lsp.Basic | [
"Eq.propIntro",
"Lean.Lsp.CreateFile",
"Lean.Lsp.DocumentChange",
"Lean.Lsp.DocumentChange.create",
"Lean.Lsp.DocumentChange.create.inj",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.coequalizerCoconeIsColimit | Mathlib.CategoryTheory.Limits.Constructions.Equalizers | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.HasCoequalizersOfHasPushoutsAndBinaryCoproducts.coequalizerCoconeIsColimit._proof_4",
"CategoryTheory.Limits.coprod.desc",
"CategoryTheory.Functor.category",
"CategoryTheory.Limi... | true |
Std.TreeMap.getKeyD_eq_of_contains | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.inner",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.TreeMap.contains",
"Std.LawfulEqCmp",
"Bool",
"Std.TreeMap.getKeyD",
"Std.DTreeMap.getKeyD_eq_of_contains",
"Eq",
"Std.TreeMap"
] | true |
TopologicalSpace.Closeds.isUniformEmbedding_coe | Mathlib.Topology.UniformSpace.Closeds | [
"UniformSpace",
"TopologicalSpace.Closeds.uniformSpace",
"IsUniformEmbedding",
"uniformity",
"TopologicalSpace.Closeds.instSetLike",
"Prod.mk",
"SetLike.coe_injective",
"Prod.fst",
"SetLike.coe",
"IsUniformEmbedding.mk",
"IsUniformInducing.mk",
"Prod",
"UniformSpace.hausdorff",
"UniformSpa... | true |
Filter.bliminf_eq_liminf_subtype | Mathlib.Order.LiminfLimsup | [
"Filter.liminf",
"setOf",
"ConditionallyCompleteLattice",
"Function.comp",
"Membership.mem",
"Filter.bliminf",
"Subtype",
"Filter.blimsup_eq_limsup_subtype",
"OrderDual.instConditionallyCompleteLattice",
"OrderDual",
"Subtype.val",
"Eq",
"Set.instMembership",
"Filter",
"Filter.comap",
... | true |
Lean.PrettyPrinter.OneLine.State._sizeOf_1 | Lean.PrettyPrinter.Formatter | [
"Lean.PrettyPrinter.OneLine.State.rec",
"instOfNatNat",
"Lean.PrettyPrinter.OneLine.State",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"List._sizeOf_inst",
"SizeOf.sizeOf",
"Std.Format._sizeOf_inst",
"Std.Format",
"instAddNat",
"instSizeOfNat",
"Prod._sizeOf_inst",
"Prod",
"OfNat.ofNat"
] | false |
AddOpposite.instAddCommMonoid.eq_1 | Mathlib.Algebra.Group.Opposite | [
"AddOpposite.instAddCommMonoid",
"AddOpposite",
"AddOpposite.instAddCommMonoid._proof_1",
"AddCommMonoid",
"AddOpposite.instAddMonoid",
"Eq.refl",
"AddCommMonoid.toAddMonoid",
"Eq",
"AddCommMonoid.mk"
] | true |
FirstOrder.Field.FieldAxiom.toSentence._proof_3 | Mathlib.ModelTheory.Algebra.Field.Basic | [
"instNeZeroNatHAdd_1",
"Zero.ofOfNat0",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"NeZero",
"OfNat.ofNat"
] | false |
Subsemiring.instSMulWithZeroSubtypeMem | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"SMulWithZero.toSMulZeroClass",
"SubsemiringClass.toAddSubmonoidClass",
"SubsemiringClass",
"AddMonoid.toAddZeroClass",
"Subsemiring.instSMulWithZeroSubtypeMem._proof_1",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"Subtype",
... | true |
_private.Mathlib.Algebra.Group.Units.Defs.0.AddUnits.isAddUnit_add_addUnits.match_1_1 | Mathlib.Algebra.Group.Units.Defs | [
"AddUnits.val",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"IsAddUnit",
"instHAdd",
"Exists.casesOn",
"HAdd.hAdd",
"AddMonoid",
"Exists.intro",
"AddZero.toAdd",
"Eq",
"AddUnits"
] | false |
instAddCommGroupPadic._proof_14 | Mathlib.NumberTheory.Padics.PadicNumbers | [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"instAddCommGroupPadic._proof_12",
"instAddCommGroupPadic._aux_9",
"instAddPadic",
"Nat.Prime",
"NormedRing.toRing",
"AddMonoid.toAddSemigroup",
"instZeroPadic",
"SubNegMonoid.mk",
"Ring.neg_add_cancel",
"Rat",
"AddMonoid.toZ... | false |
StieltjesFunction.mono' | Mathlib.MeasureTheory.Measure.Stieltjes | [
"Real",
"LinearOrder",
"PartialOrder.toPreorder",
"Monotone",
"SemilatticeInf.toPartialOrder",
"StieltjesFunction.toFun",
"DistribLattice.toLattice",
"TopologicalSpace",
"StieltjesFunction",
"instDistribLatticeOfLinearOrder",
"Real.instPreorder",
"Lattice.toSemilatticeInf"
] | true |
_private.Mathlib.AlgebraicTopology.SimplexCategory.MorphismProperty.0.SimplexCategory.Truncated.morphismProperty_eq_top._proof_1 | Mathlib.AlgebraicTopology.SimplexCategory.MorphismProperty | [
"Lean.RArray.leaf",
"False",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"Eq.mp",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegIn... | false |
CategoryTheory.yonedaMonObjIsoOfRepresentableBy._proof_2 | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.Functor",
"MonoidHom.instFunLike",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"MonCat.hom_ext",
"MulEquiv.toMonCatIso",
"CategoryTheory.Functor.RepresentableBy.homEquiv'",
"CategoryTheory.Functor.comp",
"MonoidHom.ex... | false |
_private.Mathlib.NumberTheory.DiophantineApproximation.Basic.0.Real.aux₁._proof_1_8 | Mathlib.NumberTheory.DiophantineApproximation.Basic | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"Int.Linear.le_unsat",
"Eq.mp",
"id",
"Lean.RArray",
"Int.instNegInt",
"Int.Linear.eq_le_subst_nonneg",
"instOfNatNat",
"Int",
"LE.le",
"Int.Linear.Poly.num",
"Int.instMul",
"Int.Linear.Poly.add"... | false |
ContinuousAt.snd' | Mathlib.Topology.Constructions.SumProd | [
"ContinuousAt",
"instTopologicalSpaceProd",
"Prod.mk",
"TopologicalSpace",
"ContinuousAt.comp",
"Prod",
"Prod.snd",
"continuousAt_snd"
] | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.minEntry?_insertEntry._simp_1_5 | Std.Data.Internal.List.Associative | [
"Ordering.gt",
"Ordering",
"Std.OrientedCmp",
"Ordering.lt",
"Std.OrientedCmp.gt_iff_lt",
"propext",
"Eq"
] | false |
irreducible_pow_sup_of_ge | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"CommRing",
"Semiring.toModule",
"IsScalarTower.right",
"ENat.instNatCast",
"CommSemiring.toSemiring",
"SemilatticeSup.toMax",
"Irreducible",
"Algebra.id",
"Ne",
"Bot.bot",
"LE.le",
"Ideal",
"Nat.cast",
"multiplicity",
"instLEENat",
"IdemSemiring.toSemilatticeSup",
"NonUnitalNonAssoc... | true |
circleAverage_log_norm_sub_const₂ | Mathlib.Analysis.SpecialFunctions.Integrals.PosLogEqCircleAverage | [
"AddGroup.toSubtractionMonoid",
"Real.instIsOrderedRing",
"Norm.norm",
"Mathlib.Tactic.Ring.Common.neg_zero",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib... | true |
RegularWreathProduct | Mathlib.GroupTheory.RegularWreathProduct | [
"RegularWreathProduct.mk"
] | true |
MeasurableSet.setOf_infinite | Mathlib.MeasureTheory.MeasurableSpace.Constructions | [
"MeasurableSet",
"Finite",
"setOf",
"MeasurableSet.setOf_finite",
"Set.instMeasurableSpace",
"Set.Elem",
"MeasurableSet.compl",
"Countable",
"Set.Infinite",
"Set"
] | true |
SetRel.finiteDimensional_iff | Mathlib.Order.RelSeries | [
"SetRel",
"Exists",
"SetRel.FiniteDimensional.casesOn",
"RelSeries.length",
"LE.le",
"RelSeries",
"instLENat",
"SetRel.FiniteDimensional.mk",
"Iff",
"Nat",
"Iff.intro",
"SetRel.FiniteDimensional"
] | true |
Multiset.countP_False | Mathlib.Data.Multiset.Count | [
"List.countP",
"False",
"List.countP_false",
"Quot.inductionOn",
"Multiset",
"instOfNatNat",
"List",
"congrFun",
"Nat",
"instDecidableFalse",
"Function.const",
"List.isSetoid",
"OfNat.ofNat",
"Multiset.countP",
"Bool.false",
"Eq",
"Setoid.r"
] | true |
Lean.RecursorVal.mk._flat_ctor | Lean.Declaration | [
"Lean.Expr",
"Lean.ConstantVal.mk",
"Lean.RecursorRule",
"List",
"Nat",
"Bool",
"Lean.RecursorVal",
"Lean.Name",
"Lean.RecursorVal.mk"
] | false |
Lean.RecursorRule.mk.injEq | Lean.Declaration | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Expr",
"Lean.RecursorRule",
"And",
"Nat",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Lean.RecursorRule.mk",
"Lean.RecursorRule.mk.inj",
"Eq"
] | true |
AdicCompletion.instAlgebra._proof_6 | Mathlib.RingTheory.AdicCompletion.Algebra | [
"Submodule",
"RingHom.instRingHomClass",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"AdicCompletion.instAlgebra._proof_1",
"Semiring.toModule",
"instSMulOfMul",
"HMul.hMul",
"IsScalarTower.right",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoi... | false |
_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.insertIfNew._proof_1 | Std.Data.DTreeMap.Internal.Operations | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Std.DTreeMap.Internal.Impl.size",
... | false |
CategoryTheory.Functor.CoconeTypes.IsColimitCore.ctorIdx | Mathlib.CategoryTheory.Limits.Types.ColimitType | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.CoconeTypes.IsColimitCore",
"CategoryTheory.Functor.CoconeTypes",
"Nat",
"CategoryTheory.types",
"CategoryTheory.Category"
] | false |
CategoryTheory.ChosenPullbacksAlong.isoInv_pullback_obj_right_as | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | [
"CategoryTheory.Over",
"CategoryTheory.Comma.right",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso",
"CategoryTheory.instCategoryOver",
"CategoryTheory.Discrete.as",
"CategoryTheory.discreteCategory",
"PUnit",
"Eq.refl",
"PUnit.unit",
"CategoryTheory.Functor.fromPUnit",
"CategoryTheory.Chos... | true |
List.get_permutations'Aux | Mathlib.Data.List.Permutation | [
"congrArg",
"List.get",
"List.insertIdx",
"Fin.isLt",
"Fin.mk",
"List",
"List.getElem_permutations'Aux",
"Nat",
"LT.lt",
"True",
"List.permutations'Aux",
"eq_self",
"of_eq_true",
"congrFun'",
"instLTNat",
"Eq",
"List.length",
"Eq.trans"
] | true |
Ideal.pow_multiset_sum_mem_span_pow | Mathlib.RingTheory.Ideal.Basic | [
"Multiset.sum",
"Multiset.toFinset",
"add_mul",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"MulOne.toOne",
"Nat.instMulZeroClass",
"Submodule.addSubmonoidClass",
"Nat.instOrderedSub",
"Semigroup.toMul",
"add_tsub_assoc_of_le",
"Preord... | true |
conditionallyCompleteLatticeOfLatticeOfsSup._proof_2 | Mathlib.Order.ConditionallyCompleteLattice.Defs | [
"Iff.mpr",
"Lattice",
"lowerBounds",
"PartialOrder.toPreorder",
"Preorder.toLE",
"forall_eq",
"Membership.mem",
"Exists",
"inf_le_right",
"SemilatticeInf.toPartialOrder",
"Set.instSingletonSet",
"Insert.insert",
"Set.forall_insert_of_forall",
"SemilatticeInf.toMin",
"LE.le",
"Set.instI... | false |
AffineMap.pi | Mathlib.LinearAlgebra.AffineSpace.AffineMap | [
"AffineMap.mk",
"AffineMap.instFunLike",
"AddCommGroup.toAddCommMonoid",
"AffineMap.pi._proof_1",
"Pi.module",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"AffineMap",
"LinearMap.pi",
"Pi.instAddTorsor",
"Pi.addCommGroup",
"AffineMap.linear",
"AddTorsor",
"Module",
"Ring.toSemiring",
"D... | true |
Submonoid.mem_op._simp_2 | Mathlib.Algebra.Group.Submonoid.MulOpposite | [
"Submonoid.op",
"MulOpposite",
"Membership.mem",
"propext",
"Submonoid.mem_op",
"MulOpposite.instMulOneClass",
"MulOpposite.unop",
"Submonoid.instSetLike",
"MulOneClass",
"Eq",
"SetLike.instMembership",
"Submonoid"
] | false |
_private.Mathlib.Algebra.Homology.SpectralSequence.Basic.0.CategoryTheory.SpectralSequence._proof_9 | Mathlib.Algebra.Homology.SpectralSequence.Basic | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"CategoryTheory.SpectralSequence._auto_3",
"Int.not_le_eq",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNeg... | false |
Std.ExtTreeMap.minKey_insert_of_isEmpty | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtDTreeMap.minKey_insert_of_isEmpty",
"Std.ExtTreeMap.isEmpty",
"Ordering",
"Std.TransCmp",
"Std.ExtTreeMap.insert_ne_empty",
"Bool.true",
"Std.ExtTreeMap",
"Std.ExtTreeMap.inner",
"Bool",
"Std.ExtTreeMap.insert",
"Eq",
"Std.ExtTreeMap.minKey"
] | true |
convexHullAddMonoidHom._proof_1 | Mathlib.Analysis.Convex.Combination | [
"ChainCompletePartialOrder.instOfCompleteLattice",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribLattice.toLattice",
"ClosureOperator.instFunLike",
"ClosureO... | false |
_private.Init.Data.Iterators.Lemmas.Consumers.Loop.0.Std.Iter.forIn'_eq_match_step.match_3.splitter | Init.Data.Iterators.Lemmas.Consumers.Loop | [
"Std.Iter.forIn'_eq_match_step.match_3",
"Std.IterStep",
"Std.IterStep.skip",
"Id",
"Std.Iterator",
"Subtype.mk",
"Std.Iter",
"Std.IterStep.yield",
"Std.Iter.IsPlausibleStep",
"Std.IterStep.done",
"Std.Iter.Step"
] | true |
Sublattice.mem_iInf | Mathlib.Order.Sublattice | [
"Sublattice",
"Eq.mpr",
"Lattice",
"SetLike.mem_coe._simp_1",
"iInf",
"Sublattice.instInfSet",
"congrArg",
"Set.iInter",
"Membership.mem",
"id",
"Set.mem_iInter._simp_1",
"iff_self",
"Iff",
"SetLike.coe",
"SetLike.mem_coe",
"True",
"propext",
"of_eq_true",
"Sublattice.instSetLike... | true |
LinearMap.sub_mem_ker_iff | Mathlib.Algebra.Module.Submodule.Ker | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Submodule",
"map_sub",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"sub_eq_zero",
"AddCommGroup.toAddCommMonoid",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"LinearMap.instFunLike",
"HSub.hSub",
"AddCommGroup.toAddG... | true |
MultilinearMap.dfinsuppFamily_compLinearMap_lsingle | Mathlib.LinearAlgebra.Multilinear.DFinsupp | [
"MultilinearMap.dfinsuppFamily_single",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"MultilinearMap",
"AddCommMonoid",
"AddZero.toZero",
"MultilinearMap.compLinearMap",
"Fintype",
"Fintype.decidablePiFintype",
"DFinsupp.addCommMonoid",
"MultilinearMap.ext",
"Semiring",
"DFinsupp",
... | true |
Submodule.Quotient.module'._proof_2 | Mathlib.LinearAlgebra.Quotient.Defs | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"AddMonoid.toAddZeroClass",
"Submodule.hasQuotient",
"AddZeroClass.toAddZero",
"AddCommGroup",
"HasQuotient.Quotient",
"instHAdd",
"HAdd.hAdd",
"AddZero.toAdd",
"Eq.refl",
"AddCommMono... | false |
_private.Mathlib.Analysis.Normed.Algebra.Exponential.0.NormedSpace.star_exp._simp_1_2 | Mathlib.Analysis.Normed.Algebra.Exponential | [
"Monoid",
"Monoid.toMulOneClass",
"StarMul",
"MulOne.toMul",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"StarMul.toInvolutiveStar",
"InvolutiveStar.toStar",
"instHPow",
"Eq.symm",
"Eq",
"Star.star",
"star_pow"
] | false |
Mathlib.Tactic.BicategoryCoherence.assoc_liftHom₂ | Mathlib.Tactic.CategoryTheory.BicategoryCoherence | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Mathlib.Tactic.BicategoryCoherence.LiftHom",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.BicategoryCoherence.LiftHom₂",
"CategoryTheory.Bicategory",
"CategoryTheory.CategoryStruct.comp",
"Cate... | true |
CategoryTheory.uliftYonedaEquiv._proof_4 | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"TypeCat.instFunLikeFun",
"CategoryTheory.yoneda",
"CategoryTheory.CategoryStruct.id",
"TypeCat.o... | false |
_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.add_factorial_succ_lt_factorial_add_succ._proof_1_3 | Mathlib.Data.Nat.Factorial.Basic | [
"Lean.RArray.leaf",
"False",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"Nat.Linear.ExprCnstr.eq_of_toNormPo... | false |
AlgebraicGeometry.Scheme.openCoverOfIsOpenCover | Mathlib.AlgebraicGeometry.Restrict | [
"CategoryTheory.PreZeroHypercover.mk",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"AlgebraicGeometry.Scheme.openCoverOfIsOpenCover._proof_1",
"CommRingCat",
"AlgebraicGeometry.Scheme.OpenCover",
"CommRin... | true |
_private.Batteries.Data.RBMap.WF.0.Batteries.RBNode.RedRed.imp.match_1_1 | Batteries.Data.RBMap.WF | [
"Batteries.RBNode",
"HEq.refl",
"Batteries.RBNode.RedRed.balanced",
"Batteries.RBNode.RedRed",
"Batteries.RBColor.red",
"Batteries.RBColor",
"Nat",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Batteries.RBNode.RedRed.redred",
"Batteries.RBNode.RedRed.casesOn",
"Eq.symm",
"Batteries.RBNode... | false |
_private.Mathlib.RingTheory.Polynomial.GaussNorm.0.Polynomial.gaussNorm_zero_right._simp_1_4 | Mathlib.RingTheory.Polynomial.GaussNorm | [
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"Finset.sup'_le_iff",
"Finset.instSetLike",
"propext",
"Finset.Nonempty",
"SemilatticeSup.toPartialOrder",
"Finset.sup'",
"Eq",
"SemilatticeSup",
"SetLike.instMembership"
] | false |
CategoryTheory.ComposableArrows.homMk_app | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.homMk._proof_2",
"CategoryTheory.ComposableArrows.map'._proof_8",
"PartialOrder.toPreorder",
"CategoryTheory.ComposableArrows",
"Fin.mk",
"Preorder.smallCategory",
"instOfNatNat",
"instHAdd",
"Fin.instPartia... | true |
MulActionWithZero.rec | Mathlib.Algebra.GroupWithZero.Action.Defs | [
"instHSMul",
"MulActionWithZero",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"MulAction",
"Monoid.toSemigroup",
"Zero.toOfNat0",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulZeroOneClass.toMulZeroClass",
"MulAction.toSemigroupAction",
"OfNat.ofNat",
"Eq",
"MulActionWithZero.mk",... | false |
AlgebraicGeometry.Scheme.homOfLE | Mathlib.AlgebraicGeometry.Restrict | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"AlgebraicGeometry.Scheme.homOfLE._proof_1",
"CommRingCat",
... | true |
Std.TransCmp.eq_trans | Init.Data.Order.Ord | [
"Eq.mpr",
"congrArg",
"Ordering",
"Ordering.eq",
"id",
"Std.TransCmp",
"Ordering.swap",
"Bool.true",
"Ordering.isLE_of_eq_eq",
"Std.TransCmp.isLE_trans",
"Bool",
"Ordering.eq_eq_of_isLE_of_isLE_swap",
"Std.OrientedCmp.eq_symm",
"Std.OrientedCmp.eq_swap",
"Eq.symm",
"Ordering.isLE",
"... | true |
Lean.Compiler.LCNF.LetValue._auto_15 | Lean.Compiler.LCNF.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Parser.Tactic.vcAlt | Std.Tactic.Do.Syntax | [
"Lean.ParserDescr.nodeWithAntiquot",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.sepBy1",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"Lean.Parser.Tactic.caseArg",
"Bool.false",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | true |
ProbabilityTheory.uncenteredCovarianceBilinDual._proof_2 | Mathlib.Probability.Moments.CovarianceBilinDual | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
CompactlySupportedContinuousMap.instAddMonoidOfContinuousAdd | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"CompactlySupportedContinuousMap.instAddMonoidOfContinuousAdd._proof_7",
"Nat.instMulZeroClass",
"instHSMul",
"AddMonoid.toAddSemigroup",
"SMulWithZero.toSMulZeroClass",
"CompactlySupportedContinuousMap",
"ContinuousMap.mk",
"AddMonoid.toAddZeroClass",
"instSMulWithZeroNat",
"AddMonoid.mk",
"Add... | true |
Std.ge_refl | Mathlib.Order.RelClasses | [
"Std.Refl.refl",
"GE.ge",
"Std.Refl",
"LE.le",
"LE"
] | true |
_private.Mathlib.Data.Matrix.Mul.0.Matrix.vecMulVec_eq_zero._simp_1_1 | Mathlib.Data.Matrix.Mul | [
"Matrix",
"propext",
"Matrix.ext_iff",
"Eq.symm",
"Eq"
] | false |
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