name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Algebra.SkewMonoidAlgebra.Basic.0.SkewMonoidAlgebra.isScalarTower_self._simp_2 | Mathlib.Algebra.SkewMonoidAlgebra.Basic | [
"instHSMul",
"SMulZeroClass",
"AddMonoid.toAddZeroClass",
"SkewMonoidAlgebra.instZero",
"SkewMonoidAlgebra.instSMulZeroClass",
"AddZeroClass.toAddZero",
"SkewMonoidAlgebra.smul_single",
"AddZero.toZero",
"AddMonoid",
"SkewMonoidAlgebra",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"Eq.symm",
"S... | false |
Multiset.coe_eq_coe | Mathlib.Data.Multiset.Defs | [
"Multiset",
"List.Perm",
"List",
"Multiset.ofList",
"Iff",
"List.isSetoid",
"Eq",
"Quotient.eq"
] | true |
_private.Lean.DocString.Add.0.Lean.makeDocStringVerso._sparseCasesOn_1 | Lean.DocString.Add | [
"Nat.ne_of_beq_eq_false",
"Sum.ctorIdx",
"Nat.shiftRight",
"Sum",
"Nat.hasNotBit",
"instOfNatNat",
"Sum.inl",
"Nat.land",
"Sum.inr",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Sum.rec"
] | false |
_private.Mathlib.Data.List.Triplewise.0.List.triplewise_iff_getElem._proof_1_88 | Mathlib.Data.List.Triplewise | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"of_decide_eq_true",
"Int.Linear.norm_le",
"Lean.Grind.CommRing.Expr.var",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Lean.Grind.Semiring.mul_one",
"Lean.Grind.Order.le_of_eq_2_k",
"Std.IsL... | false |
Valuation.Uniformizer._sizeOf_1 | Mathlib.RingTheory.Valuation.Discrete.Basic | [
"Valuation.Uniformizer.rec",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Valuation.IsUniformizer",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"instSizeOfDefault",
"Membership.mem",
"Subtype",
"Valuation.IsRankOneDiscrete",
"instOfNatNat",
"LinearOrderedCommGroupWithZe... | false |
Equiv.sigmaSigmaSubtype._proof_1 | Mathlib.Logic.Equiv.Basic | [
"Subtype",
"Sigma.fst",
"Sigma.mk",
"Sigma.snd",
"Eq",
"Sigma",
"rfl"
] | false |
Bool.compl_eq_bnot | Mathlib.Order.BooleanAlgebra.Defs | [
"Bool.not",
"Compl.compl",
"Bool.instBooleanAlgebra",
"BooleanAlgebra.toCompl",
"Bool",
"Eq",
"rfl"
] | true |
True | Init.Prelude | [
"True.intro"
] | true |
String.Slice.utf8ByteSize_sliceTo | Init.Data.String.Basic | [
"congrArg",
"String.Slice.Pos.offset",
"HSub.hSub",
"String.Slice.Pos.offset_str",
"String.Slice.utf8ByteSize_eq",
"String.Slice",
"Nat.add_sub_cancel_left",
"instSubNat",
"String.Slice.utf8ByteSize",
"String.Slice.startInclusive",
"String.Pos.Raw",
"String.Pos.Raw.byteIdx_offsetBy",
"String... | true |
LinearMap.compl₂._proof_2 | Mathlib.LinearAlgebra.BilinearMap | [
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"AddZeroClass.toAddZero",
"RingHomCompTriple",
"map_add",
"DistribSMul.toSMulZeroClass",
"LinearMap.semilinearMapClass",
"LinearMap.instAdd",
"LinearMap.module",
"LinearMap",
"AddC... | false |
Lean.CollectFVars.visit | Lean.Util.CollectFVars | [
"Lean.CollectFVars.State",
"Inhabited.default",
"Lean.Expr",
"Pi.instInhabited",
"Lean.CollectFVars.instInhabitedState",
"Lean.CollectFVars.Visitor"
] | true |
Multiset.singleton_ne_zero | Mathlib.Data.Multiset.ZeroCons | [
"PartialOrder.toPreorder",
"Multiset",
"ne_of_gt",
"Ne",
"Multiset.instSingleton",
"Multiset.lt_cons_self",
"Zero.toOfNat0",
"Singleton.singleton",
"OfNat.ofNat",
"Multiset.instPartialOrder",
"Multiset.instZero"
] | true |
IsUniformAddGroup.casesOn | Mathlib.Topology.Algebra.IsUniformGroup.Defs | [
"UniformContinuous",
"UniformSpace",
"instUniformSpaceProd",
"HSub.hSub",
"IsUniformAddGroup.rec",
"IsUniformAddGroup",
"Prod.fst",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"IsUniformAddGroup.mk",
"Prod",
"Prod.snd"
] | false |
GroupExtension.Equiv.ofMonoidHom.eq_1 | Mathlib.GroupTheory.GroupExtension.Basic | [
"Function.invFun",
"MulOne.toOne",
"MonoidHom.instFunLike",
"HMul.hMul",
"GroupExtension.Equiv.ofMonoidHom",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"GroupExtension.Equiv.ofMonoidHom._proof_2",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",... | true |
Turing.PartrecToTM2.codeSupp'.match_1 | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.Cont'",
"namedPattern",
"Turing.ToPartrec.Code.succ",
"Turing.ToPartrec.Code.tail",
"Turing.ToPartrec.Code.casesOn",
"Turing.ToPartrec.Code.comp",
"Turing.ToPartrec.Code.case",
"Eq.refl",
"Turing.ToPartrec.Code.zero'",
"Eq",
"Turing.ToPartrec.Code.fix",
"Turing.ToPartrec.C... | false |
Lean.Lsp.ReferenceContext | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.ReferenceContext.mk"
] | true |
_private.Init.Data.Int.Gcd.0.Int.gcd_le_right._proof_1_1 | Init.Data.Int.Gcd | [
"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",
"Int.decLe",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Int... | false |
Std.HashSet.isEmpty_eq_size_eq_zero | Std.Data.HashSet.Lemmas | [
"Std.HashSet.size",
"Std.HashSet",
"instOfNatNat",
"instBEqOfDecidableEq",
"BEq.beq",
"Unit",
"Std.HashSet.inner",
"Nat",
"Bool",
"Std.HashSet.isEmpty",
"Hashable",
"instDecidableEqNat",
"OfNat.ofNat",
"Std.HashMap.isEmpty_eq_size_eq_zero",
"BEq",
"Eq"
] | true |
Tilt.instField._aux_8 | Mathlib.RingTheory.Perfection | [
"Tilt",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"CommRing",
"Nat.Prime",
"Semiring.toModule",
"Tilt._proof_1",
"CommSemiring.toSemiring",
"OreLocalization",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra",
"nonZeroDivisors",
"Field.toDivisionRing",
"Fact",
"infe... | false |
_private.Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory.0.MeasureTheory.exists_lt_lowerSemicontinuous_integral_lt._simp_1_7 | Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | [
"False",
"eq_false",
"EReal.coe_ennreal_ne_bot",
"EReal",
"Bot.bot",
"ENNReal.toEReal",
"ENNReal",
"Eq",
"instBotEReal"
] | false |
Std.IterM.DefaultConsumers.forIn_eq | Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop | [
"Std.IteratorLoop.forIn",
"Std.IterM.DefaultConsumers.forIn'",
"id",
"Subtype",
"Std.IterM.IsPlausibleIndirectOutput",
"ForInStep",
"Std.Iterator",
"Std.IterM",
"Std.IteratorLoop.defaultImplementation",
"Monad",
"Eq",
"rfl"
] | true |
Nat.gcd_self | Init.Data.Nat.Gcd | [
"Nat.gcd",
"Nat.mod_self",
"Nat.gcd_zero_right",
"congrArg",
"Nat.gcd_succ",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"Nat.casesAuxOn",
"instHAdd",
"HMod.hMod",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Nat.gcd_zero_left",
"Eq.ndrec",
"instAddNat",
"Eq.refl",
"c... | true |
Subgroup.IsComplement.toRightFun.eq_1 | Mathlib.GroupTheory.Complement | [
"Equiv.instEquivLike",
"Group",
"Subgroup.IsComplement.toRightFun",
"Quotient.mk''",
"Function.comp",
"Set.Elem",
"Equiv",
"Subgroup",
"SetLike.coe",
"Quotient",
"Eq.refl",
"Subgroup.IsComplement",
"Subgroup.IsComplement.rightQuotientEquiv",
"Eq",
"DFunLike.coe",
"QuotientGroup.rightRe... | true |
_private.Mathlib.Geometry.Manifold.HasGroupoid.0.restr_mem_maximalAtlas_aux1 | Mathlib.Geometry.Manifold.HasGroupoid | [
"StructureGroupoid.mem_of_eqOnSource",
"Eq.mpr",
"OpenPartialHomeomorph.restr_inter_source",
"OpenPartialHomeomorph.open_source",
"congrArg",
"OpenPartialHomeomorph.EqOnSource.trans'",
"OpenPartialHomeomorph.trans",
"Membership.mem",
"OpenPartialHomeomorph.isOpen_image_iff_of_subset_source",
"Stru... | true |
Lean.Meta.SynthInstance.State.generatorStack._default | Lean.Meta.SynthInstance | [
"id",
"List.toArray",
"Array",
"Lean.Meta.SynthInstance.GeneratorNode",
"List.nil"
] | false |
BitVec.toFin_ofFnLEAux | Batteries.Data.BitVec.Lemmas | [
"instPowNat",
"BitVec.ofFnLEAux",
"congrArg",
"Nat.instNeZeroHPow",
"BitVec.toNat_ofFnLEAux",
"Fin.ofNat",
"BitVec.toFin",
"Nat.instMod",
"Nat.ofBits",
"instHMod",
"instOfNatNat",
"Fin.ext",
"Fin.val",
"instNatPowNat",
"HMod.hMod",
"HPow.hPow",
"Nat.instNeZeroSucc",
"Nat",
"True"... | true |
_private.Mathlib.Topology.Constructions.0.inducing_sigma.match_1_2 | Mathlib.Topology.Constructions | [
"Sigma.mk",
"Sigma.casesOn",
"Sigma"
] | false |
Finset.compls.eq_1 | Mathlib.Data.Finset.Sups | [
"BooleanAlgebra",
"Compl.compl",
"Finset",
"Finset.compls",
"Finset.map",
"Function.Embedding.mk",
"BooleanAlgebra.toCompl",
"compl_injective",
"Eq.refl",
"Eq"
] | true |
one_le_pow₀ | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"Nat.zero_le",
"MulOne.toOne",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"Preorder.toLE",
"Eq.rec",
"ZeroLEOneClass",
"instOfNatNat",
"LE.le",
"pow_zero",
"MulZeroOneClass.toMulOneClass",
"Monoid.toPow",
"MulOneClass.toMulOne",
"MonoidWithZero",
"PosMulMono",
"MonoidWithZero.toMulZ... | true |
CategoryTheory.LocallyDiscrete.eqToHom_toLoc | Mathlib.CategoryTheory.Bicategory.LocallyDiscrete | [
"CategoryTheory.LocallyDiscrete.categoryStruct",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"Eq.rec",
"CategoryTheory.LocallyDiscrete",
"Quiver.Hom.toLoc",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct... | true |
_private.Mathlib.Algebra.Homology.ExactSequence.0.CategoryTheory.ComposableArrows.exact₂_iff._proof_1_10 | Mathlib.Algebra.Homology.ExactSequence | [
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"Classical.byContradiction",
"HSub.hSub",
"Eq.mp",
"Nat.ToInt.natCast_ofNat",
"id",
"Lean.RArray",
"instSubNat",
"instOfNatNat",
"Int",
"Nat.ToInt.of_diseq",
"LE.le",
"Int.Linear.Poly.num",
"instLENat",
... | false |
isClosed_coinduced | Mathlib.Topology.Order | [
"congrArg",
"Compl.compl",
"Set.instCompl",
"TopologicalSpace.coinduced",
"iff_self",
"IsClosed",
"TopologicalSpace",
"Iff",
"Set.preimage",
"isOpen_coinduced",
"congr",
"True",
"propext",
"of_eq_true",
"IsOpen",
"Eq.trans",
"_private.Mathlib.Topology.Order.0.isClosed_coinduced._simp... | true |
Finite.exists_max | Mathlib.Data.Fintype.Lattice | [
"Finset.univ",
"congrArg",
"Finset",
"LinearOrder",
"Finite",
"PartialOrder.toPreorder",
"instInhabitedTrue",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Finset.univ_nonempty",
"SemilatticeInf.toPartialOrder",
"Eq.mp",
"DistribLattice.toLattice",
"Finset.exists_max_image",
"LE.le",
... | true |
CategoryTheory.NatTrans.IsMonoidal.casesOn | Mathlib.CategoryTheory.Monoidal.NaturalTransformation | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.NatTrans.IsMonoidal.rec",
"CategoryTheory.Functor.LaxMonoidal.μ",
"CategoryTheory.NatTrans.I... | false |
Lean.Grind.CommRing.Expr.denoteSAsRing.eq_2 | Init.Grind.Ring.CommSemiringAdapter | [
"Lean.Grind.Ring.OfSemiring.ofSemiring",
"Lean.Grind.CommRing.Expr.natCast",
"Lean.Grind.Semiring.ofNat",
"Nat",
"Lean.Grind.Semiring",
"Lean.Grind.Ring.OfSemiring.Q",
"Lean.Grind.CommRing.Context",
"Eq.refl",
"Lean.Grind.Ring.toSemiring",
"Lean.Grind.CommRing.Expr.denoteSAsRing",
"OfNat.ofNat",... | true |
SymmetricPower.instAddCommGroup._aux_6 | Mathlib.LinearAlgebra.TensorPower.Symmetric | [
"CommRing",
"instHSMul",
"addConGen",
"SymmetricPower.Rel",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"SymmetricPower",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Int",
"PiTensorProduct.instAddCommMonoid",
"PiTensorPro... | false |
Std.DTreeMap.Raw.isSome_getKey?_iff_mem._simp_1 | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.instMembership",
"Membership.mem",
"Ordering",
"Std.DTreeMap.Raw.getKey?",
"Std.TransCmp",
"Bool.true",
"propext",
"Bool",
"Option.isSome",
"Eq",
"Std.DTreeMap.Raw.isSome_getKey?_iff_mem",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] | false |
Lean.Elab.Term.SavedContext.recOn | Lean.Elab.Term.TermElabM | [
"Lean.Elab.Term.SavedContext.mk",
"Array",
"Lean.Elab.Term.FixedTermElabRef",
"List",
"Lean.Elab.MacroStack",
"Lean.Elab.Term.SavedContext",
"Bool",
"Lean.Name",
"Lean.Elab.Term.SavedContext.rec",
"Lean.Options",
"Lean.OpenDecl",
"Option"
] | false |
MonotoneOn.slope_nonneg | Mathlib.LinearAlgebra.AffineSpace.Slope | [
"Iff.mpr",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Eq.rec",
"AddZeroClass.toA... | true |
_private.Mathlib.RingTheory.Coalgebra.CoassocSimps.0.CoassocSimps.«term_⊗ₘ_» | Mathlib.RingTheory.Coalgebra.CoassocSimps | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Name.anonymous",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
IsSolvableByRad | Mathlib.FieldTheory.AbelRuffini | [
"IsSolvableByRad.mul",
"Algebra",
"IsSolvableByRad.inv",
"Field.toSemifield",
"IsSolvableByRad.rad",
"Semifield.toDivisionSemiring",
"IsSolvableByRad.base",
"DivisionSemiring.toSemiring",
"Semifield.toCommSemiring",
"IsSolvableByRad.neg",
"Field",
"IsSolvableByRad.add"
] | true |
ge_of_tendsto | Mathlib.Topology.Order.OrderClosed | [
"Set.Ici",
"ClosedIciTopology",
"Filter.NeBot",
"Filter.Eventually",
"Preorder.toLE",
"nhds",
"IsClosed.mem_of_tendsto",
"LE.le",
"TopologicalSpace",
"Filter.Tendsto",
"Filter",
"isClosed_Ici",
"Preorder"
] | true |
UniformCauchySeqOnFilter.eq_1 | Mathlib.Topology.UniformSpace.UniformConvergence | [
"Filter.instMembership",
"UniformSpace",
"SProd.sprod",
"Filter.Eventually",
"uniformity",
"Membership.mem",
"Prod.mk",
"Prod.fst",
"Eq.refl",
"Prod",
"Filter.instSProd",
"UniformCauchySeqOnFilter",
"Eq",
"Set.instMembership",
"Prod.snd",
"Filter",
"Set"
] | true |
CategoryTheory.ExactFunctor.whiskeringRight_obj_map | Mathlib.CategoryTheory.Limits.ExactFunctor | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.exactFunctor",
"CategoryTheory.ExactFunctor.forget",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.ObjectProperty.... | true |
HasFTaylorSeriesUpTo.hasFDerivAt | Mathlib.Analysis.Calculus.ContDiff.FTaylorSeries | [
"LinearIsometryEquiv.instEquivLike",
"Iff.mpr",
"HasFDerivAt",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"hasFTaylorSeriesUpToOn_univ_iff",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"congrArg",
"CommSemiring.toSemiring",
"FormalMu... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.mem_of_getKey?_eq_some._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
FirstOrder.Language.StrongHomClass.realize_formula._simp_1 | Mathlib.ModelTheory.Semantics | [
"FirstOrder.Language.StrongHomClass",
"Function.comp",
"FirstOrder.Language.Structure",
"FirstOrder.Language.StrongHomClass.realize_formula",
"EquivLike",
"FirstOrder.Language.Formula",
"propext",
"FirstOrder.Language",
"Eq",
"DFunLike.coe",
"FirstOrder.Language.Formula.Realize",
"EquivLike.to... | false |
_private.Mathlib.SetTheory.Ordinal.Topology.0.Ordinal.mem_closure_tfae._simp_1_2 | Mathlib.SetTheory.Ordinal.Topology | [
"iSup",
"Membership.mem",
"Set.Elem",
"SupSet",
"Eq.symm",
"Subtype.val",
"Eq",
"Set.instMembership",
"SupSet.sSup",
"sSup_eq_iSup'",
"Set"
] | false |
Aesop.RuleTac.ForwardM.instInhabitedState | Aesop.RuleTac.Forward | [
"Aesop.RuleTac.ForwardM.instInhabitedState.default",
"Inhabited",
"Aesop.RuleTac.ForwardM.State",
"Inhabited.mk"
] | true |
Lean.Parser.Command.mixfix._regBuiltin.Lean.Parser.Command.mixfix.formatter_41 | Lean.Parser.Syntax | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin",
"Lean.Parser.Command.mixfix.formatter"
] | false |
CliffordAlgebra.map_comp_ι | Mathlib.LinearAlgebra.CliffordAlgebra.Basic | [
"AlgHom.toLinearMap",
"CliffordAlgebra.ι",
"CommRing",
"Semiring.toModule",
"CliffordAlgebra.ι._proof_2",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"CliffordAlgebra.ι_comp_lift",
"instAlgebraCliffordAlgebra",
"QuadraticForm",
"AddCom... | true |
TopCat.of.sizeOf_spec | Mathlib.Topology.Category.TopCat.Basic | [
"instSizeOfDefault",
"instOfNatNat",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"Nat",
"TopCat._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"TopCat",
"OfNat.ofNat",
"Eq",
"TopCat.of"
] | true |
_private.Mathlib.Geometry.Euclidean.Incenter.0.Affine.Simplex.touchpointWeights_singleton_pos._simp_1_1 | Mathlib.Geometry.Euclidean.Incenter | [
"Preorder.toLT",
"SignType.instOne",
"PartialOrder.toPreorder",
"SignType.instLinearOrder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"OrderHom.instFunLike",
"LT.lt",
"propext",
"SignType",
"One.toOfNat1",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"SignTy... | false |
instCommutativeInt8HAnd | Init.Data.SInt.Bitwise | [
"Std.Commutative",
"Int8.and_comm",
"Int8",
"HAnd.hAnd",
"Std.Commutative.mk",
"instHAndOfAndOp",
"instAndOpInt8"
] | true |
_private.Lean.Meta.Constructions.NoConfusion.0.Lean.mkNoConfusionType._sparseCasesOn_1 | Lean.Meta.Constructions.NoConfusion | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
Int.dvd_mul_gcd_iff_dvd_mul | Init.Data.Int.Gcd | [
"Nat.gcd",
"Int.gcd",
"Dvd.dvd",
"HMul.hMul",
"Int.natAbs_mul",
"congrArg",
"_private.Init.Data.Int.Gcd.0.Int.dvd_mul_gcd_iff_dvd_mul._simp_1_1",
"instMulNat",
"Int",
"Nat.cast",
"_private.Init.Data.Int.Gcd.0.Int.dvd_mul_gcd_iff_dvd_mul._simp_1_2",
"Int.instDvd",
"Int.instMul",
"iff_self",... | true |
Turing.TM1.Stmt.brecOn | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Turing.TM1.Stmt.brecOn.go",
"Turing.TM1.Stmt.below",
"Turing.TM1.Stmt"
] | false |
Finset.exists_ne_map_eq_of_card_image_lt | Mathlib.Data.Finset.Card | [
"Finset.exists_ne_map_eq_of_card_lt_of_maps_to",
"Finset",
"Membership.mem",
"Exists",
"Set.mapsTo_image",
"Eq.rec",
"Finset.coe_image",
"Ne",
"And",
"SetLike.coe",
"Finset.instSetLike",
"Set.MapsTo",
"Nat",
"LT.lt",
"Finset.card",
"Set.image",
"instLTNat",
"Eq.symm",
"Eq",
"Fi... | true |
_private.Std.Do.PostCond.0.Std.Do.ExceptConds.entails.match_1.eq_3 | Std.Do.PostCond | [
"Std.Do.ExceptConds.entails.match_1",
"Std.Do.PostShape.except",
"Std.Do.PostShape.arg",
"Std.Do.PostShape",
"Std.Do.PostShape.pure",
"Eq.refl",
"Eq",
"Std.Do.ExceptConds"
] | true |
_private.Mathlib.Topology.MetricSpace.Pseudo.Defs.0.Metric.dense_iff_iUnion_ball._simp_1_1 | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Set.univ",
"Set.eq_univ_iff_forall",
"Membership.mem",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.Enriched.FunctorCategory.isLimitConeFunctorEnrichedHom._proof_1 | Mathlib.CategoryTheory.Enriched.FunctorCategory | [
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom",
"CategoryTheory.Limits.Cone",
"Opposite",
"CategoryTheory.EnrichedOrdinaryCategory",
"CategoryTheory.Enriche... | false |
_private.Mathlib.Topology.Order.IsLUB.0.ConditionallyCompleteLinearOrder.isCompact_Icc.match_1_6 | Mathlib.Topology.Order.IsLUB | [
"Preorder.toLT",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"LT.lt",
"Exists.intro",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"ConditionallyComple... | false |
MulAction.IsPreprimitive.isQuasiPreprimitive | Mathlib.GroupTheory.GroupAction.Primitive | [
"Set.ext",
"Eq.mpr",
"MulAction.isPretransitive_iff_orbit_eq_univ",
"instHSMul",
"congrArg",
"Set.univ",
"Iff.rfl",
"MulAction.IsBlock.orbit_of_normal",
"Group",
"MulAction.IsPretransitive",
"Membership.mem",
"Exists",
"Subgroup.instMulAction",
"MulAction.IsQuasiPreprimitive.mk",
"Eq.mp"... | true |
Lean.Meta.ExprConfigCacheKey.expr | Lean.Meta.Basic | [
"Lean.Expr",
"Lean.Meta.ExprConfigCacheKey"
] | true |
_private.Mathlib.Analysis.Complex.Convex.0.Complex.rectangle_eq_convexHull._simp_1_2 | Mathlib.Analysis.Complex.Convex | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"segment_eq_uIcc",
"LinearOrder",
"IsStrictOrderedRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"segment",
"Field.toSemifie... | false |
Batteries.RBNode.forM.eq_def | Batteries.Data.RBMap.Lemmas | [
"Pure.pure",
"Batteries.RBNode",
"Eq.mpr",
"_private.Batteries.Data.RBMap.Lemmas.0.Batteries.RBNode.fold.match_1.splitter",
"Batteries.RBNode.fold.match_1",
"Batteries.RBNode.below",
"congrArg",
"Batteries.RBNode.brecOn.eq",
"Monad.toApplicative",
"Batteries.RBNode.brecOn.go",
"id",
"Batteries... | true |
_private.Mathlib.RingTheory.QuasiFinite.Weakly.0.Algebra.WeaklyQuasiFiniteAt.of_quasiFiniteAt_residueField._simp_1_1 | Mathlib.RingTheory.QuasiFinite.Weakly | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"RingHom",
"Algebra.toSMul",
"CommSemiring",
"RingHom.comp",
"IsScalarTower.algebraMap_eq",
"Semiring",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq"
] | false |
IsAtom.uniqueFinpartition._proof_1 | Mathlib.Order.Partition.Finpartition | [
"Eq.mpr",
"Lattice",
"Finset.mem_singleton",
"Finpartition.ext",
"Preorder.toLT",
"congrArg",
"Finset",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Finset.ext",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"id",
"Or.resolve_left",
"Ne",
"IsAtom.... | false |
SSet.horn₂₁.isPushout | Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | [
"SSet.Subcomplex.toSSet",
"Opposite",
"Lattice.BicartSq.le₁₂",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finset",
"instDecidableEqFin",
"CategoryTheory.Functor.category",
"CategoryTheory.CosimplicialObject.δ",
"Lattice.BicartSq.le₂₄",
"CategoryTheory.IsPusho... | true |
MulChar.val_neg_one_eq_one_of_odd_order | Mathlib.NumberTheory.MulChar.Basic | [
"Eq.mpr",
"NegZeroClass.toNeg",
"MulOne.toOne",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"MulChar.one_apply_coe",
"Monoid.toMulOneClass",
"MulChar.hasOne",
"congrArg",
"Odd",
"AddGroupWithOne.toAddMonoidWithOne",
"Units.instNeg",
"Units",... | true |
Lean.OLeanLevel.casesOn | Lean.Environment | [
"Lean.OLeanLevel.exported",
"Lean.OLeanLevel.rec",
"Lean.OLeanLevel.private",
"Lean.OLeanLevel.server",
"Lean.OLeanLevel"
] | false |
CalcPanel.rpc._rpc_wrapped | Mathlib.Tactic.Widget.Calc | [
"Lean.Server.wrapRpcProcedure",
"CalcParams",
"Lean.Server.RpcProcedure",
"ProofWidgets.Html",
"instRpcEncodableCalcParams",
"ProofWidgets.instRpcEncodableHtml",
"Lean.Name.mkStr2",
"CalcPanel.rpc"
] | false |
FirstOrder.Language.Substructure.closure._proof_1 | Mathlib.ModelTheory.Substructures | [
"Iff.mpr",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Set.Subset.trans",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"FirstOrder.Language.Substructure.instSetLike",
"FirstOrder.Language.Substructure.instInfSet",
"HasSubset.Subset",
"LE.le",
"ChainCompletePar... | false |
CategoryTheory.Presieve.CoverByImageStructure.mk._flat_ctor | Mathlib.CategoryTheory.Sites.DenseSubsite.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Presieve.CoverByImageStructure",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"autoParam",
"CategoryTheory.Presieve.CoverByImageStructure.fac._autoParam",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryT... | false |
FirstOrder.Field.FieldAxiom.addAssoc.elim | Mathlib.ModelTheory.Algebra.Field.Basic | [
"PULift.up",
"FirstOrder.Field.FieldAxiom.ctorIdx",
"FirstOrder.Field.FieldAxiom",
"Nat",
"FirstOrder.Field.FieldAxiom.addAssoc",
"FirstOrder.Field.FieldAxiom.ctorElim",
"Eq.symm",
"Eq"
] | false |
isNoetherian_mk | Mathlib.RingTheory.Noetherian.Defs | [
"isNoetherian_iff'",
"Iff.mpr",
"Submodule",
"Preorder.toLT",
"WellFoundedGT",
"PartialOrder.toPreorder",
"Submodule.instPartialOrder",
"AddCommMonoid",
"IsNoetherian",
"Semiring",
"Module"
] | true |
GenLoop.Homotopic | Mathlib.Topology.Homotopy.HomotopyGroup | [
"Real",
"Pi.topologicalSpace",
"ContinuousMap",
"ContinuousMap.HomotopicRel",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Cube.boundary",
"Set.Elem",
"GenLoop",
"TopologicalSpace",
"Real.pseudoMetricSpace",
"instTopologicalSpaceSubtype",
"Subtype.val",
"UniformSpace.toTopologica... | true |
TopologicalSpace.IsSeparable.of_separableSpace | Mathlib.Topology.Bases | [
"Iff.mpr",
"Set.subset_univ",
"Set.univ",
"TopologicalSpace.IsSeparable",
"TopologicalSpace",
"TopologicalSpace.IsSeparable.mono",
"TopologicalSpace.isSeparable_univ_iff",
"TopologicalSpace.SeparableSpace",
"Set"
] | true |
Lean.Lsp.ResolvableCompletionItemData._sizeOf_inst | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.ResolvableCompletionItemData._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Lsp.ResolvableCompletionItemData"
] | false |
QuadraticModuleCat.cliffordAlgebra_map | Mathlib.LinearAlgebra.CliffordAlgebra.CategoryTheory | [
"CommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgCat.instCategory",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"QuadraticModuleCat.cliffordAlgebra",
"AlgCat",
"QuadraticModuleCat.toModuleCat",
"QuadraticModuleCat",
"CliffordAlgebra.map",
"QuadraticModuleCat.form",
... | true |
List.length_permutationsAux | Mathlib.Data.List.Permutation | [
"List.permutationsAux_nil",
"Eq.mpr",
"Nat.mul_succ",
"HMul.hMul",
"Nat.succ_eq_add_one",
"congrArg",
"Nat.factorial_succ",
"List.length_foldr_permutationsAux2'",
"Membership.mem",
"List.permutationsAux_cons",
"Eq.mp",
"id",
"List.permutations",
"instMulNat",
"instOfNatNat",
"Nat.mul_c... | true |
Lean.Server.LspResponse.mk.noConfusion | Lean.Server.Requests | [
"Lean.Server.LspResponse.mk",
"id",
"Lean.Server.LspResponse",
"heq_of_eq",
"Lean.Server.LspResponse.noConfusion",
"Bool",
"Eq.refl",
"HEq",
"Eq"
] | false |
Asymptotics.IsBigOWith.comp_tendsto | Mathlib.Analysis.Asymptotics.Defs | [
"Norm.norm",
"Real.instLE",
"Real",
"HMul.hMul",
"Asymptotics.IsBigOWith",
"setOf",
"Function.comp",
"Norm",
"LE.le",
"Filter.Tendsto",
"Real.instMul",
"Asymptotics.IsBigOWith.bound",
"Asymptotics.IsBigOWith.of_bound",
"Filter",
"instHMul"
] | true |
Std.DTreeMap.Equiv.maxEntry_eq | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.Equiv.isEmpty_eq",
"Std.DTreeMap.isEmpty",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.Internal.Impl.Equiv.maxEntry_eq",
"Std.DTreeMap.Equiv.inner",
"Std.DTreeMap.maxEntry",
"Std.DTreeMap.wf",
"Bool",
"Std.DTreeMap.Equiv",
"Eq.sym... | true |
Mathlib.Tactic.Ring.Common.evalAtom | Mathlib.Tactic.Ring.Common | [
"Qq.QuotedDefEq",
"Pure.pure",
"Mathlib.Tactic.Ring.Common.Result.mk",
"_private.Mathlib.Tactic.Ring.Common.0.Mathlib.Tactic.Ring.Common.evalAddOverlap._proof_1",
"instMonadReaderOfReaderTOfMonad",
"ReaderT",
"Lean.Meta.Simp.Result.expr",
"Lean.Meta.State",
"Lean.Expr.const",
"Lean.Name.mkStr5",
... | true |
_private.Lean.Parser.Tactic.Doc.0.Lean.Parser.Tactic.Doc.initFn.match_3._@.Lean.Parser.Tactic.Doc.710499956._hygCtx._hyg.2 | Lean.Parser.Tactic.Doc | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.Name",
"_private.Lean.Parser.Tactic.Doc.0.Lean.Parser.Tactic.Doc.isTactic._sparseCasesOn_1",
"Option"
] | false |
Polynomial.instNormalizationMonoid._proof_5 | Mathlib.Algebra.Polynomial.FieldDivision | [
"Units.val",
"Eq.mpr",
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Polynomial.instOne",
"CommRing",
"Polynomial.C_1",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"NormalizationMonoid",
"NormalizationMonoid.normUnit_coe_units",... | false |
mdifferentiableAt_atlas | Mathlib.Geometry.Manifold.MFDeriv.Atlas | [
"Eq.mpr",
"WithTop.charZero",
"instCharZeroENat",
"extChartAt",
"instAddMonoidWithOneENat",
"chartedSpaceSelf",
"NormedSpace",
"chartAt",
"mdifferentiableAt_iff",
"contDiffGroupoid",
"OpenPartialHomeomorph.open_source",
"congrArg",
"CommSemiring.toSemiring",
"and_self",
"ContinuousAt",
... | true |
AlgebraicGeometry.Scheme.Modules.instHasLimits | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"CategoryTheory.Limits.HasLimits",
"_private.Mathlib.AlgebraicGeometry.Modules.Sheaf.0.AlgebraicGeometry.Scheme.Modules.instHasLimits._proof_1",
"AlgebraicGeometry.Scheme.Modules"
] | true |
MeasureTheory.OuterMeasure.comap | Mathlib.MeasureTheory.OuterMeasure.Operations | [
"MeasureTheory.OuterMeasure.map._proof_2",
"MeasureTheory.OuterMeasure.mk",
"Semiring.toModule",
"IsScalarTower.right",
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"CommSemiring.toSemiring",
"Disjoint",
"CompleteLattice.toConditionallyCompleteLattice",
"MeasureTheory.Outer... | true |
StarAlgEquiv.isometry | Mathlib.Analysis.CStarAlgebra.Spectrum | [
"StarAlgEquiv.norm_map",
"MonoidHom.instFunLike",
"NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"AddMonoidHomClass.isometry_of_norm",
"outParam",
"MonoidHom",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"NormedSpace.toModule... | true |
Rep.instModuleHom._proof_1 | Mathlib.RepresentationTheory.Rep.Basic | [
"Monoid",
"Rep.V",
"instHSMul",
"Representation.IntertwiningMap.instAddCommMonoid",
"Rep.add_hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"AddMonoid.toAddZeroClass",
"Rep.... | false |
Std.ExtDTreeMap.minEntry! | Std.Data.ExtDTreeMap.Basic | [
"Std.DTreeMap.minEntry!",
"Std.DTreeMap",
"Ordering",
"Std.DTreeMap.Equiv.minEntry!_eq",
"Std.TransCmp",
"Std.ExtDTreeMap",
"Inhabited",
"Std.DTreeMap.Equiv",
"Sigma",
"Std.ExtDTreeMap.lift"
] | true |
Ideal.exists_mem_pow_notMem_pow_succ | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"CommRing",
"Semiring.toModule",
"IsScalarTower.right",
"SetLike.exists_of_lt",
"CommSemiring.toSemiring",
"Membership.mem",
"Exists",
"Algebra.id",
"Nat.lt_succ_self",
"Ne",
"Submodule.instPartialOrder",
"instOfNatNat",
"Bot.bot",
"Submodule.instTop",
"Ideal",
"NonUnitalNonAssocSemiri... | true |
Set.Ico_subset_Ico_left | Mathlib.Order.Interval.Set.Basic | [
"le_rfl",
"Preorder.toLE",
"HasSubset.Subset",
"LE.le",
"Set.Ico_subset_Ico",
"Set.Ico",
"Preorder",
"Set.instHasSubset",
"Set"
] | true |
StarOrderedRing.nonneg_iff_spectrum_nonneg | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"spectrum",
"Ring.toNonAssocRing",
"cfc_nonneg_iff",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"cfc",
"IsTopologicalSemiring",
"ContinuousStar",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"Algebra",
"Preorder.toLE",
"Membership.mem",... | true |
ConvexCone.map.match_1 | Mathlib.Geometry.Convex.Cone.Basic | [
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"ConvexCone.instSetLike",
"Membership.mem",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"LinearMap",
"AddCommMonoid",
"And.casesOn",
"AddZero.toZero",
"And",
"Exists.casesOn"... | false |
_private.Std.Data.DHashMap.Internal.WF.0.Std.DHashMap.Internal.AssocList.forInStep.go.eq_2 | Std.Data.DHashMap.Internal.WF | [
"Pure.pure",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.forInStep.go.match_1",
"Monad.toApplicative",
"ForInStep.done",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.forInStep.go",
"Applicative.toPure",
"ForInStep",
"... | true |
MatrixEquivTensor.toFunBilinear | Mathlib.RingTheory.MatrixAlgebra | [
"AlgHom.toLinearMap",
"MatrixEquivTensor.toFunBilinear._proof_4",
"MatrixEquivTensor.toFunBilinear._proof_2",
"Semiring.toModule",
"Matrix.module",
"CommSemiring.toSemiring",
"MatrixEquivTensor.toFunBilinear._proof_3",
"Matrix",
"Module.End.instSemiring",
"Algebra",
"Algebra.toSMul",
"Algebra.... | true |
ENNReal.ofNat_lt_ofReal | Mathlib.Data.ENNReal.Real | [
"Real",
"Preorder.toLT",
"ENNReal.ofReal",
"PartialOrder.toPreorder",
"Real.instLT",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Iff",
"ENNReal.natCast_lt_ofReal",
"Nat",
"LT.lt",
"ENNReal",
"ENNReal.instPartialOrder",
"OfNat.ofNat",
"instOfNatAtLeastTwo",
... | true |
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