name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CircleDeg1Lift.translate._proof_1 | Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | [
"Real",
"Equiv.instEquivLike",
"Monotone",
"Equiv",
"Real.instAdd",
"Multiplicative",
"instHAdd",
"HAdd.hAdd",
"Real.instAddCommMonoid",
"Multiplicative.toAdd",
"Real.instIsOrderedAddMonoid",
"add_right_mono",
"DFunLike.coe",
"Real.instPreorder",
"EquivLike.toFunLike",
"IsOrderedAddMon... | false |
Lean.Lsp.WorkspaceEditClientCapabilities._sizeOf_inst | Lean.Data.Lsp.Capabilities | [
"Lean.Lsp.WorkspaceEditClientCapabilities",
"SizeOf.mk",
"Lean.Lsp.WorkspaceEditClientCapabilities._sizeOf_1",
"SizeOf"
] | false |
MonoidHom.map_mulIndicator | Mathlib.Algebra.Group.Indicator | [
"One",
"Set.mulIndicator",
"Function.comp",
"OneHomClass",
"map_mulIndicator",
"Eq",
"DFunLike.coe",
"FunLike",
"Set"
] | true |
DyckWord.instUniqueAddUnits._proof_1 | Mathlib.Combinatorics.Enumerative.DyckWord | [
"Iff.mpr",
"Inhabited.default",
"AddMonoid.toAddSemigroup",
"DyckWord.toList_eq_nil",
"AddMonoid.toAddZeroClass",
"AddCancelMonoid.toAddRightCancelMonoid",
"Eq.rec",
"AddZeroClass.toAddZero",
"DyckWord",
"instAddCancelMonoidDyckWord",
"instZeroDyckWord",
"And.casesOn",
"AddZero.toZero",
"i... | false |
mem_asymptoticCone_iff | Mathlib.Topology.Algebra.AsymptoticCone | [
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"Iff.rfl",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"Field.toSemifield",
"Filter.Frequently",
"TopologicalSpace",
"Iff",
"asymptoticCone",
"Semifield.toDivisionSemiring",
"AddTorsor",
"DivisionSemiring.toSemiring",
"Modul... | true |
indiscreteTopology_iff_forall_norm_eq_zero' | Mathlib.Analysis.Normed.Group.Basic | [
"Norm.norm",
"not_exists._simp_1",
"Real",
"Real.instZero",
"congrArg",
"SeminormedGroup",
"PseudoMetricSpace.toUniformSpace",
"SeminormedGroup.toPseudoMetricSpace",
"Exists",
"Eq.mp",
"Iff.not",
"Ne",
"Decidable.not_not._simp_1",
"IndiscreteTopology",
"Iff",
"SeminormedGroup.toNorm",
... | true |
SimpleGraph.Subgraph.deleteEdges_coe_eq | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"SimpleGraph.deleteEdges",
"Eq.mpr",
"Sym2.Rel",
"Sym2.map",
"Sym2.mk",
"congrArg",
"SimpleGraph.Subgraph",
"HEq.refl",
"Mathlib.Tactic.Contrapose.contrapose₃",
"SimpleGraph.Adj",
"Sym2.Rel.casesOn",
"SimpleGraph.Subgraph.deleteEdges",
"Subtype.casesOn",
"Membership.mem",
"Exists",
"Se... | true |
CategoryTheory.Limits.hasLimit_of_equalizer_and_product | Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.HasLimit",
"CategoryTheory.Limits.HasEqualizers",
"CategoryTheory.SmallCategory",
"Sigma.fst",
"Prod.fst",
"CategoryTheory.discreteCategory",
"CategoryTheor... | true |
_private.Mathlib.Lean.Meta.RefinedDiscrTree.Encode.0.Lean.Meta.RefinedDiscrTree.encodingStepAux._sparseCasesOn_5 | Mathlib.Lean.Meta.RefinedDiscrTree.Encode | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
Lean.Order.CompleteLattice.mk.noConfusion | Init.Internal.Order.Basic | [
"Lean.Order.CompleteLattice.noConfusion",
"Exists",
"id",
"Lean.Order.CompleteLattice",
"heq_of_eq",
"Lean.Order.PartialOrder",
"Eq.refl",
"HEq",
"Eq",
"Lean.Order.CompleteLattice.mk",
"Lean.Order.is_sup"
] | false |
_private.Mathlib.RingTheory.SimpleModule.Isotypic.0.IsIsotypic.submodule_linearEquiv_fun.match_1_1 | Mathlib.RingTheory.SimpleModule.Isotypic | [
"Pi.Function.module",
"Submodule",
"Nat.instMulZeroClass",
"Pi.addCommMonoid",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Membership.mem",
"Exists",
"AddCommGroup",
"Subtype",
"IsSimpleModule",
"Submodule.module",
"Nonempty.intro",
"And.casesOn",
"And",
"Exists.casesOn... | false |
TruncatedWittVector.zmodEquivTrunc | Mathlib.RingTheory.WittVector.Compare | [
"Nat.Prime",
"ZMod.commRing",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"ZMod.fintype",
"TruncatedWittVector.instAdd",
"TruncatedWittVector.instCommRing",
"Fact",
"Distrib.toAdd",
"TruncatedWittVector.charP_zmod",
"ZMod",
"TruncatedWittVector.instFintype",
"instDistribOfSemiring",
"Mono... | true |
Polynomial.nthRootsFinset.congr_simp | Mathlib.Algebra.Polynomial.Roots | [
"IsDomain",
"CommRing",
"CommSemiring.toSemiring",
"Finset",
"Eq.rec",
"CommRing.toCommSemiring",
"Nat",
"Polynomial.nthRootsFinset",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_hom | Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Functor.OplaxRightLinear.δᵣ_unitality_inv",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionUnitIso",
"Cate... | true |
SubAddAction.fixingAddSubgroupInsertEquiv._proof_1 | Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | [
"AddMonoid.toAddSemigroup",
"AddSubgroup.toAddGroup",
"Membership.mem",
"Subtype",
"Insert.insert",
"HVAdd.hVAdd",
"AddSubgroup",
"AddAction",
"AddAction.toAddSemigroupAction",
"SubAddAction.ofStabilizer",
"AddGroup",
"SubAddAction",
"Set.instInsert",
"AddSemigroupAction.toVAdd",
"AddGro... | false |
CategoryTheory.Prod.swap_obj | Mathlib.CategoryTheory.Products.Basic | [
"Prod.mk",
"Prod.fst",
"CategoryTheory.prod'",
"Eq.refl",
"CategoryTheory.Prod.swap",
"Prod",
"Eq",
"Prod.snd",
"CategoryTheory.Functor.obj",
"CategoryTheory.Category"
] | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.toNat_div_toNat_lt._proof_1_2 | Init.Data.BitVec.Lemmas | [
"instPowNat",
"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'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Bi... | false |
Lean.Meta.Grind.Order.Cnstr.noConfusionType | Lean.Meta.Tactic.Grind.Order.Types | [
"Lean.Expr",
"Int",
"Lean.Meta.Grind.Order.Cnstr.casesOn",
"Lean.Meta.Grind.Order.CnstrKind",
"HEq",
"Eq",
"Lean.Meta.Grind.Order.Cnstr",
"Option"
] | false |
Multiset.toDFinsupp_replicate | Mathlib.Data.DFinsupp.Multiset | [
"DFinsupp.ext",
"Eq.recOn",
"Nat.instMulZeroClass",
"dite_congr",
"Multiset.count_replicate",
"congrArg",
"DFinsupp.single",
"AddMonoid.toAddZeroClass",
"DFinsupp.addZeroClass'",
"Multiset.instAddCancelCommMonoid",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"Multiset.count",
"Multiset"... | true |
Matrix.trace_blockDiagonal' | Mathlib.LinearAlgebra.Matrix.Trace | [
"dite_cond_eq_true",
"Matrix.diag",
"Finset.univ",
"congrArg",
"Matrix",
"Finset",
"AddMonoid.toAddZeroClass",
"cast",
"Membership.mem",
"AddZeroClass.toAddZero",
"Matrix.trace",
"Finset.sigma",
"Sigma.fst",
"Matrix.blockDiagonal'._proof_1",
"Finset.sum_sigma'",
"AddCommMonoid",
"Add... | true |
Std.Sat.AIG.ShiftTarget.rec | Std.Sat.AIG.Basic | [
"Std.Sat.AIG.ShiftTarget.mk",
"Std.Sat.AIG",
"Nat",
"Hashable",
"Std.Sat.AIG.ShiftTarget",
"Std.Sat.AIG.RefVec",
"DecidableEq"
] | false |
Lat.ofHom_id | Mathlib.Order.Category.Lat | [
"Lattice",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Lat.of",
"CategoryTheory.CategoryStruct.id",
"Lat.instCategory",
"LatticeHom.id",
"CategoryTheory.Category.toCategoryStruct",
"Lat",
"Eq",
"Lat.ofHom",
"rfl"
] | true |
Action.forget_linear | Mathlib.CategoryTheory.Action.Limits | [
"Monoid",
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Linear",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Linear",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"Action.in... | true |
Set.div_subset_div_left | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"instHDiv",
"HDiv.hDiv",
"Div",
"HasSubset.Subset",
"Set.image2_subset_left",
"Set.div",
"Set.instHasSubset",
"Set"
] | true |
DirectSum.sigmaUncurry._proof_2 | Mathlib.Algebra.DirectSum.Basic | [
"DFinsupp.sigmaUncurry_add",
"AddMonoid.toAddZeroClass",
"DFinsupp.hasAdd₂",
"AddZeroClass.toAddZero",
"Sigma.fst",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"DFinsupp.instZero",
"DFinsupp.sigmaUncurry",
"DFinsupp.instAdd",
"DFinsupp",
"AddCommMonoid.toAddMonoid",
"Sigm... | false |
BoxIntegral.Integrable.convergenceR_cond | Mathlib.Analysis.BoxIntegral.Basic | [
"BoxIntegral.Integrable.convergenceR",
"Eq.mpr",
"Exists.choose_spec",
"Real.instLE",
"Real",
"Set.Ioi",
"BoxIntegral.Integrable",
"NormedSpace",
"Real.instZero",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Real.decidableLT",
"PseudoMetricSpace.toUniformSpace",
"... | true |
Submodule.Quotient.seminormedAddCommGroup._proof_19 | Mathlib.Analysis.Normed.Group.Quotient | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Submodule",
"Bornology.ofDist._proof_2",
"Real.instLE",
"Bornology.ofDist._proof_3",
"Real",
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"AddGroupSeminorm.toSeminormedAddGroup._proof_9",
"AddMonoid.toAddZeroClass",
"PartialOr... | false |
Nonneg.coe_add | Mathlib.Algebra.Order.Nonneg.Basic | [
"AddLeftMono",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"Subtype",
"LE.le",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"Nonneg.add",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Subtype.val",
"Eq",
"rfl",
"Preorder"
] | true |
CategoryTheory.NonemptyParallelPairPresentationAux.isColimit₁._proof_1 | Mathlib.CategoryTheory.Limits.Indization.ParallelPair | [
"CategoryTheory.Limits.IndObjectPresentation.I",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.IndObjectPresentation.instFinalICostructuredArrowFunctorOppositeTypeYonedaToCostructuredArrow",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.fst",
"CategoryThe... | false |
AlgebraicGeometry.Proj.pullbackAwayιIso._proof_4 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic | [
"Preorder.toLT",
"Nat.le_add_right",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instPreorder",
"LT.lt.trans_le",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat"
] | false |
Representation.IntertwiningMap.mk.congr_simp | Mathlib.RepresentationTheory.Intertwining | [
"Monoid",
"Representation",
"MonoidHom.instFunLike",
"Monoid.toMulOneClass",
"Module.End.instSemiring",
"Eq.rec",
"LinearMap",
"AddCommMonoid",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"LinearMap.comp",
"MulOneClass.toMulOne",
"Representation.IntertwiningMap.mk",
"... | true |
fst_hnot | Mathlib.Order.Heyting.Basic | [
"Prod.instHNot",
"HNot.hnot",
"Prod.fst",
"HNot",
"Prod",
"Eq",
"rfl"
] | true |
groupHomology.IsCycle₂.eq_1 | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"instHSMul",
"Inv",
"HMul.hMul",
"AddCommGroup.toAddCommMonoid",
"SMul",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"Mul",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Pro... | true |
_private.Mathlib.Combinatorics.Additive.VerySmallDoubling.0.Finset.op_smul_eq_iff_mem._simp_1_1 | Mathlib.Combinatorics.Additive.VerySmallDoubling | [
"instHSMul",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"MulOpposite",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"... | false |
Std.Internal.List.isEmpty_filter_not_contains_left | Std.Data.Internal.List.Associative | [
"Bool.not",
"congrArg",
"List.contains",
"Eq.mp",
"Sigma.fst",
"Bool.true",
"List",
"EquivBEq",
"List.isEmpty",
"List.filter",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"BEq",
"Eq",
"Sigma",
"List.isEmpty_iff._simp_1",
"Eq.trans",
"List.nil"
] | true |
Std.DTreeMap.Const.size_insertMany_list_le | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"instForInOfForIn'",
"Ord.mk",
"Ordering",
"inferInstance",
"Std.DTreeMap.inner",
"LE.le",
"Std.DTreeMap.Internal.Impl.Const.size_insertMany_list_le",
"Std.TransCmp",
"instLENat",
"Id",
"Std.DTreeMap.Const.insertMany",
"Membership",
"Std.DTreeMap.size",
"List",
"instHAd... | true |
Action.leftRegularTensorIso._proof_1 | Mathlib.CategoryTheory.Action.Monoidal | [
"MonoidHom.instFunLike",
"Action.trivial",
"DivInvOneMonoid.toInvOneClass",
"CategoryTheory.typesCartesianMonoidalCategory",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Action.leftRegular",
"Group",
"TypeCat.instFunLikeFun",
"Group.toDivisionMonoid"... | false |
_private.Batteries.Data.List.Lemmas.0.List.dropInfix?.go.match_1.eq_1 | Batteries.Data.List.Lemmas | [
"Unit.unit",
"Option.some",
"Option.none",
"List",
"Unit",
"List.dropInfix?.go.match_1",
"Eq.refl",
"Eq",
"Option"
] | true |
PLift.instLawfulApplicative_mathlib | Mathlib.Control.ULift | [
"Applicative.toSeqLeft",
"Pure.pure",
"_private.Mathlib.Control.ULift.0.PLift.instLawfulFunctor_mathlib.match_1",
"LawfulApplicative.mk",
"PLift.instLawfulFunctor_mathlib",
"Monad.toApplicative",
"Function.comp",
"PLift",
"PLift.instMonad_mathlib",
"Seq.seq",
"Applicative.toPure",
"PLift.up",
... | true |
UInt64.lt_iff_toFin_lt | Init.Data.UInt.Lemmas | [
"UInt64.size",
"UInt64",
"Iff.rfl",
"instLTUInt64",
"Iff",
"LT.lt",
"instLTFin",
"Fin",
"UInt64.toFin"
] | true |
_private.Std.Data.DTreeMap.Internal.Balancing.0.Std.DTreeMap.Internal.Impl.balance!_eq_balanceₘ._proof_1_26 | Std.Data.DTreeMap.Internal.Balancing | [
"Lean.Omega.LinearCombo.coordinate_eval_6",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Std.DTreeMap... | false |
Matrix.isNilpotent_iff | Mathlib.RingTheory.Finiteness.Nilpotent | [
"Eq.mpr",
"Pi.Function.module",
"Algebra.to_smulCommClass",
"Module.End.instMonoid",
"Semiring.toModule",
"Pi.addCommMonoid",
"Matrix.module",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"AddMonoid.toAddZeroClass",
"Function.smulCommClass",
"LinearMap.instFunLike",
"Matrix.toLin'",
... | true |
Algebra.SubmersivePresentation.free_cotangent | Mathlib.RingTheory.Smooth.StandardSmoothCotangent | [
"CommRing",
"Algebra.Extension.instModuleCotangent",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Algebra.SubmersivePresentation.toPreSubmersivePresentation",
"Finite",
"Algebra.SubmersivePresentation.basisCotangent",
"Algebra",
"Algebra.PreSubmersivePresentation.toPresentation",
"A... | true |
deriv_pos_left_of_sign_deriv | Mathlib.Analysis.Calculus.DerivativeTest | [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"sub_pos",
"AddGroup.toSubtractionMonoid",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Semiring.toModule",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Real.denselyNormedField",
"Real.instZero",
"SignType.instOne",
"congrArg",
"Compl.... | true |
Module.forall_dual_apply_eq_zero_iff | Mathlib.LinearAlgebra.Dual.Lemmas | [
"Mathlib.Tactic.Push.not_forall_eq",
"Eq.mpr",
"Semiring.toModule",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Module.Projective",
"RingHom",
"Exists",
"AddZeroClass.toAddZero",
"map_zero",
"id",
"LinearMap.semilinea... | true |
UniformSpaceCat.completionFunctor._proof_4 | Mathlib.Topology.Category.UniformSpace | [
"UniformSpaceCat.carrier",
"UniformSpace.Completion.uniformSpace",
"UniformSpace.Completion.t0Space",
"UniformSpaceCat.str",
"T0Space",
"UniformSpaceCat",
"UniformSpace.toTopologicalSpace",
"UniformSpace.Completion"
] | false |
ext_nat' | Mathlib.Algebra.Group.Nat.Hom | [
"Eq.mpr",
"Nat.recAux",
"congrArg",
"DFunLike.ext",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"map_zero",
"map_add",
"id",
"AddMonoidHomClass",
"instOfNatNat",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"AddMonoidHomClass.toAddHomClass... | true |
_private.Mathlib.Analysis.Distribution.SchwartzSpace.Basic.0.SchwartzMap.seminormAux_nonneg.match_1_1 | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | [
"Norm.norm",
"Real.instLE",
"Real",
"HMul.hMul",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"ContinuousMultilinearMap.hasOpNorm'",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"Membership.me... | false |
summable_pow_mul_jacobiTheta₂_term_bound | Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Filter.tendsto_atTop_add_const_right",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Real.instIsOrderedRing",
"Int.cast",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRi... | true |
SSet.horn.ι_ι_assoc | Mathlib.AlgebraicTopology.SimplicialSet.Horn | [
"SSet.Subcomplex.toSSet",
"CategoryTheory.Category.assoc",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.CosimplicialObject.δ",
"SSet.horn.ι",
"Eq.mp",
"id",
"Ne",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"in... | true |
Lean.Parser.Command.mixfix._regBuiltin.Lean.Parser.Command.postfix.formatter_23 | Lean.Parser.Syntax | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Lean.Parser.Command.postfix.formatter",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
instNontrivialSubtypeMemSubmoduleValSetIsotypicComponents | Mathlib.RingTheory.SimpleModule.Isotypic | [
"Nontrivial",
"Iff.mpr",
"Submodule",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"Membership.mem",
"AddCommGroup",
"Set.Elem",
"Subtype",
"Ne",
"Submodule.instPartialOrder",
"Bot.bot",
"LT.lt.ne'",
"Submodule.instBot",
"Submodule.nontrivial_iff_ne_bot",
"Submodule.setLi... | true |
Aesop.RuleTerm.const | Aesop.RuleTac.RuleTerm | [
"Aesop.RuleTerm.const",
"Lean.Name",
"Aesop.RuleTerm"
] | true |
MulAction.aestabilizer.congr_simp | Mathlib.MeasureTheory.Group.AEStabilizer | [
"MeasureTheory.Measure",
"Group",
"Eq.rec",
"MulAction.aestabilizer",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"MeasurableSpace",
"MulAction",
"Monoid.toSemigroup",
"Eq.ndrec",
"Eq.refl",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
"MeasureTheory.... | true |
MulEquiv.withOneCongr.eq_1 | Mathlib.Algebra.Group.WithOne.Basic | [
"WithOne",
"MulEquiv.toMulHom",
"MulEquiv.withOneCongr",
"MonoidHom.instFunLike",
"MonoidHom",
"MulEquiv.withOneCongr._proof_3",
"Mul",
"WithOne.mapMulHom",
"Equiv.mk",
"WithOne.instMulOneClass",
"MulOneClass.toMulOne",
"MulEquiv.withOneCongr._proof_1",
"MulEquiv.withOneCongr._proof_2",
"M... | true |
CategoryTheory.Functor.fromLeftDerivedZero._proof_1 | Mathlib.CategoryTheory.Abelian.LeftDerived | [
"HomologicalComplex.homologyFunctor",
"CategoryTheory.ProjectiveResolution.π",
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsL... | false |
finFunctionFinEquiv._proof_4 | Mathlib.Algebra.BigOperators.Fin | [
"Nat.instMonoid",
"instDecidableEqFin",
"Pi.instFintype",
"Preorder.toLE",
"Fintype.card",
"LE.le",
"Fin.fintype",
"Monoid.toPow",
"HPow.hPow",
"Nat.instPreorder",
"Nat",
"instHPow",
"finFunctionFinEquiv._proof_1",
"le_of_eq",
"Fin"
] | false |
Set.infs_singleton | Mathlib.Data.Set.Sups | [
"Set.instSingletonSet",
"HasInfs.infs",
"SemilatticeInf.toMin",
"SemilatticeInf",
"Set.hasInfs",
"Set.image",
"Singleton.singleton",
"Set.image2_singleton_right",
"Eq",
"Min.min",
"Set"
] | true |
AddMonoid.Coprod.inr._proof_1 | Mathlib.GroupTheory.Coprod.Basic | [
"AddCon.instFunLikeForallProp",
"Iff.mpr",
"AddCon",
"FreeAddMonoid.of",
"AddMonoid.toAddZeroClass",
"AddMonoid.Coprod.mk",
"setOf",
"FreeAddMonoid.instAddCancelMonoid",
"AddCancelMonoid.toAddRightCancelMonoid",
"Membership.mem",
"AddZeroClass.toAddZero",
"Sum",
"AddMonoid.coprodCon",
"Sum... | false |
_private.Init.Data.Dyadic.Basic.0.Dyadic.add.match_3.eq_3 | Init.Data.Dyadic.Basic | [
"Dyadic.add.match_3",
"Dyadic",
"instHMod",
"Int",
"HMod.hMod",
"instOfNat",
"Dyadic.zero",
"Int.instMod",
"Eq.refl",
"Dyadic.ofOdd",
"OfNat.ofNat",
"Eq"
] | true |
Option.filter_some_neg | Init.Data.Option.Lemmas | [
"Eq.mpr",
"congrArg",
"Option.some",
"id",
"instDecidableEqBool",
"Bool.true",
"Option.none",
"Option.filter",
"Bool.not_eq_true",
"Bool",
"Eq.refl",
"Bool.false",
"Eq",
"if_neg",
"Not",
"Option",
"Option.filter_some",
"ite"
] | true |
Lean.Grind.CommRing.SPolResult.noConfusion | Lean.Meta.Tactic.Grind.Arith.CommRing.Poly | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.SPolResult.noConfusionType",
"Int",
"Lean.Grind.CommRing.SPolResult",
"Eq.ndrec",
"Eq.refl",
"Lean.Grind.CommRing.SPolResult.casesOn",
"Eq",
"Lean.Grind.CommRing.Mon"
] | false |
Lean.IR.Checker.CheckerContext | Lean.Compiler.IR.Checker | [
"Lean.IR.Checker.CheckerContext.mk"
] | true |
_private.Init.Data.Array.Subarray.0.Subarray.findSomeRevM?._proof_1 | Init.Data.Array.Subarray | [
"Subarray",
"Nat.le_refl",
"LE.le",
"instLENat",
"Std.Slice.Internal.SubarrayData",
"Nat",
"Std.Slice.size",
"Subarray.instSliceSizeSubarrayData"
] | false |
AddSubmonoid.op_bot | Mathlib.Algebra.Group.Submonoid.MulOpposite | [
"AddSubmonoid.instCompleteLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"AddOpposite",
"AddSubmonoid",
"AddSubmonoid.op",
"Bot.bot",
"AddZeroClass",
"BoundedOrder.toOrderBot",
"AddSubmonoid.opEquiv",
"AddSubmonoid.instBot",
"Eq",
"OrderIso.map_bot"... | true |
Set.preimage_diff | Mathlib.Data.Set.Image | [
"SDiff.sdiff",
"Set.preimage",
"Eq",
"rfl",
"Set.instSDiff",
"Set"
] | true |
_private.Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension.0.IsOpen.exists_contDiff_support_eq._simp_1_9 | Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
_private.Mathlib.Probability.Distributions.Gaussian.Real.0.ProbabilityTheory.integrable_gaussianPDFReal._simp_1_10 | Mathlib.Probability.Distributions.Gaussian.Real | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
SetLike.instSMulCommClassSubtypeMem_1 | Mathlib.GroupTheory.GroupAction.SubMulAction | [
"SetLike",
"Monoid",
"instHSMul",
"instSMulOfMul",
"Monoid.toMulOneClass",
"IsScalarTower",
"SMul",
"SMulMemClass",
"Membership.mem",
"MulOne.toMul",
"Subtype",
"IsScalarTower.left",
"MulOneClass.toMulOne",
"SetLike.smul'",
"MulAction",
"Monoid.toSemigroup",
"HSMul.hSMul",
"Semigro... | true |
_private.Lean.Linter.UnusedVariables.0.Lean.Linter.UnusedVariables.collectReferences._sparseCasesOn_23 | Lean.Linter.UnusedVariables | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
SupHom.coe_bot | Mathlib.Order.Hom.Lattice | [
"SupHom.instFunLike",
"SemilatticeSup.toMax",
"Max",
"Pi.instBotForall",
"Bot.bot",
"Bot",
"SupHom.instBot",
"SupHom",
"Eq",
"SemilatticeSup",
"DFunLike.coe",
"rfl"
] | true |
_private.Mathlib.MeasureTheory.Measure.Sub.0.MeasureTheory.Measure.restrict_sub_eq_restrict_sub_restrict._simp_1_1 | Mathlib.MeasureTheory.Measure.Sub | [
"LE.le",
"OrderTop",
"LE",
"OrderTop.toTop",
"le_top",
"True",
"eq_true",
"Top.top",
"Eq"
] | false |
Vector.mapFinIdx_eq_ofFn._proof_1 | Init.Data.Vector.MapIdx | [
"Std.IsLinearPreorder.toIsPreorder",
"Std.instReflLeOfIsPreorder",
"Std.le_refl._simp_1",
"LE.le",
"instLENat",
"Fin.val",
"Nat",
"LT.lt",
"Fin.val_lt_of_le",
"of_eq_true",
"instLTNat",
"Fin",
"Nat.instIsLinearOrder",
"Std.IsLinearOrder.toIsLinearPreorder"
] | false |
CoheytingHom.cancel_right._simp_1 | Mathlib.Order.Heyting.Hom | [
"CoheytingHom.comp",
"CoheytingHom",
"CoheytingAlgebra",
"CoheytingHom.cancel_right",
"CoheytingHom.instFunLike",
"propext",
"Eq",
"DFunLike.coe",
"Function.Surjective"
] | false |
_private.Mathlib.AlgebraicTopology.SimplexCategory.Basic.0.SimplexCategory.mkOfSucc_subinterval_eq.match_1_1 | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"Unit.unit",
"False",
"Fin.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Fin.mk",
"Fin.instOfNat",
"instOfNatNat",
"Nat.le.step",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat.le",
"Nat.instNeZeroSucc",
"Nat",
"LT.lt",
"Eq.ndrec",
"Nat.ctorIdx",
"instAddNat",
"Nat.zero",... | false |
CategoryTheory.Limits.ColimitPresentation.ctorIdx | Mathlib.CategoryTheory.Limits.Presentation | [
"Nat",
"CategoryTheory.Limits.ColimitPresentation",
"CategoryTheory.Category"
] | false |
Lean.Elab.Term.StructInst.StructInstView.fields | Lean.Elab.StructInst | [
"Array",
"Lean.Elab.Term.StructInst.StructInstView",
"Lean.Elab.Term.StructInst.FieldView"
] | true |
_private.Init.Data.Array.Lemmas.0.Array.all_eq'._simp_1_1 | Init.Data.Array.Lemmas | [
"Array.all",
"Array.all_eq_true'",
"Array.instMembership",
"Membership.mem",
"instOfNatNat",
"Array",
"Bool.true",
"Nat",
"propext",
"Bool",
"OfNat.ofNat",
"Eq",
"Array.size"
] | false |
_private.Mathlib.RingTheory.Flat.Basic.0.IsReduced.tensorProduct_of_flat_of_forall_fg._simp_1_1 | Mathlib.RingTheory.Flat.Basic | [
"Pow",
"isReduced_iff",
"Nat",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"IsNilpotent",
"Eq",
"IsReduced",
"Zero"
] | false |
_private.Mathlib.RingTheory.Support.0.Module.mem_support_iff_of_span_eq_top._simp_1_4 | Mathlib.RingTheory.Support | [
"Submodule",
"CommRing",
"instHSMul",
"Semiring.toModule",
"IsScalarTower.right",
"LocalizedModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"LocalizedModule.mem_ker_mkLinearMap_iff",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"Membership.mem",
"Exists",
"AddZeroClas... | false |
Vector.getElem_attach | Init.Data.Vector.Attach | [
"Vector.instMembership",
"Vector.attach",
"Vector",
"Vector.instGetElemNatLt",
"Membership.mem",
"Subtype",
"Subtype.mk",
"GetElem.getElem",
"Nat",
"LT.lt",
"Vector.getElem_mem",
"Vector.getElem_attachWith",
"instLTNat",
"Eq",
"Vector.attach._proof_1"
] | true |
CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app | Mathlib.CategoryTheory.Functor.KanExtension.Basic | [
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"Equiv",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"CategoryTheory.Functor.IsRightKanExtension",
"CategoryTheory.Categ... | true |
DifferentiableOn.csinh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | [
"NormedCommRing.toSeminormedCommRing",
"Complex.sinh",
"Semiring.toModule",
"NormedSpace",
"NormedSpace.toModule",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Complex.instDenselyNormedField",
"Field.toSemifield",
"Complex.addCommGrou... | true |
Set.mem_pi | Mathlib.Data.Set.Operations | [
"Iff.rfl",
"Membership.mem",
"Iff",
"Set.pi",
"Set.instMembership",
"Set"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKeyD_modify_self._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
Lean.Meta.Grind.Order.ToPropagate._sizeOf_1 | Lean.Meta.Tactic.Grind.Order.Types | [
"Lean.Meta.Grind.Order.Cnstr._sizeOf_inst",
"Lean.Expr",
"instOfNatNat",
"instHAdd",
"Lean.Meta.Grind.Order.NodeId",
"Lean.Meta.Grind.Order.Weight",
"HAdd.hAdd",
"Nat",
"Lean.Meta.Grind.Order.ToPropagate",
"SizeOf.sizeOf",
"instAddNat",
"instSizeOfNat",
"Lean.Meta.Grind.Order.Weight._sizeOf_... | false |
IsLocalization.cardinalMk | Mathlib.RingTheory.Localization.Cardinality | [
"CommRing",
"IsLocalization.lift_cardinalMk",
"IsLocalization",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Cardinal.lift",
"Algebra",
"Preorder.toLE",
"Cardinal.mk",
"nonZeroDivisors",
"Eq.mp",
"LE.le",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOn... | true |
CategoryTheory.ShortComplex.Exact.exact_up_to_refinements | Mathlib.CategoryTheory.Abelian.Refinements | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Abelian",
"Exists",
"Eq.mp",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"Catego... | true |
Subalgebra.LinearDisjoint.isDomain_of_injective | Mathlib.RingTheory.LinearDisjoint | [
"Subalgebra.instSetLike",
"IsDomain",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"Subalgebra.instModuleSubtypeMem._proof_1",
"Algebra.toSMul",
"Membership.mem",
"Algebra.toModule",
"Algebra.id",
"Subtype",
"AlgEquiv.toMulEquiv",
"Algebra.TensorProduct.leftAlgebra",
... | true |
Lean.PrettyPrinter.delabCore | Lean.PrettyPrinter.Delaborator.Basic | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.instantiateMVars",
"Lean.MonadError.mk",
"Unit.unit",
"Option.instBEq",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Options.getInPattern",
"Lean.Syntax.missing",
"Lean.Meta.erasePatternRefAnnotations",
"Bool.not",
"_private.Lean.PrettyPrint... | true |
Std.ExtTreeMap.contains_insertIfNew_self | Std.Data.ExtTreeMap.Lemmas | [
"Ordering",
"Std.TransCmp",
"Std.ExtDTreeMap.contains_insertIfNew_self",
"Bool.true",
"Std.ExtTreeMap",
"Std.ExtTreeMap.inner",
"Bool",
"Std.ExtTreeMap.insertIfNew",
"Std.ExtTreeMap.contains",
"Eq"
] | true |
SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding.match_1 | Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | [
"Unit.unit",
"False",
"Fin.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Fin.mk",
"Fin.instOfNat",
"instOfNatNat",
"Nat.le.step",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat.le",
"Nat.instNeZeroSucc",
"Nat",
"LT.lt",
"Eq.ndrec",
"Nat.ctorIdx",
"instAddNat",
"Nat.zero",... | false |
FreeAddMagma.map_of | Mathlib.Algebra.Free | [
"AddHom",
"FreeAddMagma.of",
"AddHom.funLike",
"FreeAddMagma.instAdd",
"FreeAddMagma.map",
"Eq",
"DFunLike.coe",
"FreeAddMagma",
"rfl"
] | true |
SSet.Homotopy.toSimplicialObjectHomotopy._proof_12 | Mathlib.AlgebraicTopology.SimplicialSet.Homotopy | [
"SSet.yonedaEquiv",
"SSet.Subcomplex.toSSet",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"SSet.RelativeMorphism",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"CompleteLattice.toLattice",
"Fin.succ",
"c... | false |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.addStructField | Lean.Elab.StructInst | [
"Pure.pure",
"Lean.instMonadEnvOfMonadLift",
"Array.mkEmpty",
"Lean.PersistentArrayNode.node",
"Lean.Meta.instMonadLCtxMetaM",
"Lean.findField?",
"instMonadReaderOfReaderTOfMonad",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Meta.State",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.Ex... | true |
CategoryTheory.Limits.CoproductsFromFiniteFiltered.isColimitFiniteSubproductsCocone._proof_2 | Mathlib.CategoryTheory.Limits.Constructions.Filtered | [
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.HasColimitsOfShape",
"Finset",
"PartialOrder.toPreorder",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.HasFiniteCoproducts",
"Preorder.smallCategory",
"Finset.partialOrder",
"CategoryTheory.Limits.CoproductsF... | false |
Lean.Expr.getAppFn'._unsafe_rec | Lean.Expr | [
"Lean.Expr.getAppFn'._unsafe_rec",
"Lean.Expr",
"Lean.MData",
"_private.Lean.Expr.0.Lean.Expr.getAppFn'.match_1"
] | false |
Std.TreeSet.diff | Std.Data.TreeSet.Basic | [
"Std.TreeSet",
"Std.TreeMap.diff",
"Ordering",
"Std.TreeSet.inner",
"Std.TreeSet.mk",
"Unit"
] | true |
OrderDual.instAddMonoid.eq_1 | Mathlib.Algebra.Order.Group.Synonym | [
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddMonoid.nsmul_zero",
"AddMonoid.mk",
"AddZeroClass.toAddZero",
"OrderDual.instAddSemigroup",
"AddZero.toZero",
"OrderDual.instAddMonoid._proof_1",
"AddMonoid.nsmul_succ",
"OrderDual.instAddMonoid",
"AddMonoid",
"OrderDual.instAddMonoid... | true |
_private.Mathlib.RingTheory.Coalgebra.TensorProduct.0.Coalgebra._aux_Mathlib_RingTheory_Coalgebra_TensorProduct___unexpand_TensorProduct_map_1 | Mathlib.RingTheory.Coalgebra.TensorProduct | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk... | false |
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