name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
eq_of_mul_inv_eq_one | Mathlib.Algebra.Group.Basic | [
"MulOne.toOne",
"DivInvMonoid.toInv",
"HMul.hMul",
"eq_inv_of_mul_eq_one_left",
"Monoid.toMulOneClass",
"congrArg",
"DivisionMonoid",
"Eq.mp",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"DivisionMonoid.toInvolutiveInv",
"DivisionMonoid.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"i... | true |
Std.HashMap.mem_of_mem_filterMap | Std.Data.HashMap.Lemmas | [
"Membership.mem",
"Std.DHashMap.mem_of_mem_filterMap",
"Std.HashMap",
"LawfulHashable",
"EquivBEq",
"Std.HashMap.filterMap",
"Hashable",
"Std.HashMap.inner",
"BEq",
"Std.HashMap.instMembership",
"Option"
] | true |
_private.Mathlib.Data.Num.ZNum.0.PosNum.sub'.match_1.eq_1 | Mathlib.Data.Num.ZNum | [
"PosNum.bit1",
"PosNum.bit0",
"PosNum.sub'.match_1",
"Eq.refl",
"PosNum",
"Eq",
"PosNum.one"
] | true |
OrderType.instAddMonoid._proof_6 | Mathlib.Order.Types.Arithmetic | [
"Eq.mpr",
"congrArg",
"Lex",
"LinearOrder",
"PartialOrder.toPreorder",
"OrderType.type",
"Preorder.toLE",
"OrderIso.sumLexEmpty",
"SemilatticeInf.toPartialOrder",
"OrderIso.type_congr",
"DistribLattice.toLattice",
"Sum",
"id",
"PEmpty",
"instLinearOrderPEmpty",
"instHAdd",
"_private.... | false |
CategoryTheory.ObjectProperty.IsSerreClass.toContainsZero | Mathlib.CategoryTheory.Abelian.SerreClass.Basic | [
"CategoryTheory.ObjectProperty.IsSerreClass",
"CategoryTheory.Abelian",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty.ContainsZero",
"CategoryTheory.ObjectProperty",
"CategoryTheory.Category"
] | true |
Matrix.det_toBlock | Mathlib.LinearAlgebra.Matrix.Block | [
"Int.cast",
"Units.val",
"Eq.mpr",
"instDecidableNot",
"Matrix.fromBlocks",
"CommRing",
"instFintypeSum",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Equiv.instEquivLike",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Finset.univ",
"MonoidHom",
"Monoid.toMu... | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.mul_dvd_of_dvd_ediv.match_1_1 | Init.Data.Int.DivMod.Lemmas | [
"Int.instDiv",
"Dvd.dvd",
"instHDiv",
"HMul.hMul",
"HDiv.hDiv",
"Int",
"Int.instDvd",
"Int.instMul",
"Exists.casesOn",
"Exists.intro",
"Eq",
"instHMul"
] | false |
Option.guard_eq_some' | Mathlib.Data.Option.Basic | [
"guard",
"_private.Mathlib.Data.Option.Basic.0.Option.guard_eq_some'._proof_1_3",
"instAlternativeOption",
"Decidable",
"Option.some",
"Unit",
"Iff",
"Eq",
"Option"
] | true |
MeasureTheory.IsZeroOneMeasure.mk | Mathlib.MeasureTheory.Measure.Typeclasses.ZeroOne | [
"MeasureTheory.IsZeroOneMeasure.mk",
"MeasureTheory.Measure",
"MeasurableSet",
"MeasureTheory.IsZeroOneMeasure",
"MeasurableSpace",
"ENNReal",
"One.toOfNat1",
"Zero.toOfNat0",
"ENNReal.instOne",
"Or",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"MeasureTheory.Measure.instFun... | true |
_private.Mathlib.Analysis.Analytic.ConvergenceRadius.0.constFormalMultilinearSeries.match_1.eq_2 | Mathlib.Analysis.Analytic.ConvergenceRadius | [
"Eq.mpr",
"Unit.unit",
"False",
"congrArg",
"id",
"instOfNatNat",
"dif_neg",
"dite",
"Unit",
"Nat",
"Eq.ndrec_symm",
"Eq.refl",
"congrFun'",
"instDecidableEqNat",
"OfNat.ofNat",
"Eq",
"Not",
"constFormalMultilinearSeries.match_1"
] | true |
_private.Mathlib.MeasureTheory.Order.UpperLower.0.IsLowerSet.null_frontier._simp_1_1 | Mathlib.MeasureTheory.Order.UpperLower | [
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"propext",
"Eq",
"Set.instMembership",
"Not",
"Set.mem_compl_iff",
"Set"
] | false |
Nat.add_one_sqrt_le_of_ne_zero | Mathlib.Data.Nat.Sqrt | [
"Lean.Grind.instIsPreorderNat",
"congrArg",
"Std.instReflLeOfIsPreorder",
"Std.le_refl._simp_1",
"Ne",
"Nat.sqrt",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"Nat.le_induction",
"Nat.pos_of_ne_zero",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"congr",
"LT.lt",
"True",
"Nat.sq... | true |
_private.Mathlib.NumberTheory.MulChar.Lemmas.0.MulChar.equiv_rootsOfUnity._simp_1 | Mathlib.NumberTheory.MulChar.Lemmas | [
"mem_rootsOfUnity",
"Membership.mem",
"Units",
"Subgroup",
"Units.instGroup",
"rootsOfUnity",
"Units.instOne",
"Monoid.toPow",
"HPow.hPow",
"CommMonoid.toMonoid",
"Nat",
"propext",
"One.toOfNat1",
"instHPow",
"OfNat.ofNat",
"Eq",
"CommMonoid",
"Units.instMonoid",
"SetLike.instMem... | false |
RingAut.instGroup._proof_9 | Mathlib.Algebra.Ring.Aut | [
"Mul.mk",
"RingEquiv.refl",
"One.mk",
"HMul.hMul",
"Mul",
"RingAut",
"One.toOfNat1",
"RingEquiv.trans",
"OfNat.ofNat",
"Eq",
"Add",
"rfl",
"instHMul"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._simp_1_1 | Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | [
"Finset.subset_empty",
"Finset",
"HasSubset.Subset",
"Finset.instEmptyCollection",
"propext",
"Finset.instHasSubset",
"EmptyCollection.emptyCollection",
"Eq.symm",
"Eq"
] | false |
MeasureTheory.OuterMeasure.trim.eq_1 | Mathlib.MeasureTheory.OuterMeasure.Induced | [
"MeasurableSet",
"MeasureTheory.OuterMeasure.empty",
"MeasurableSet.empty",
"MeasureTheory.inducedOuterMeasure",
"MeasureTheory.OuterMeasure",
"MeasurableSpace",
"MeasureTheory.OuterMeasure.instFunLikeSetENNReal",
"ENNReal",
"Eq.refl",
"MeasureTheory.OuterMeasure.trim",
"Eq",
"DFunLike.coe",
... | true |
Std.IterM.Equiv.toList_eq | Std.Data.Iterators.Lemmas.Consumers.Monadic.Collect | [
"congrArg",
"Monad.toApplicative",
"Std.Iterators.Finite",
"Std.IterM.toListRev",
"LawfulMonad",
"Std.Iterator",
"Std.IterM.Equiv",
"List",
"Std.IterM.Equiv.toListRev_eq",
"congr",
"True",
"eq_self",
"List.reverse",
"of_eq_true",
"Applicative.toFunctor",
"Std.IterM",
"Std.IterM.toLis... | true |
ZNum.addMonoidWithOne._proof_1 | Mathlib.Data.Num.ZNum | [
"Eq.mpr",
"congrArg",
"instZeroZNum",
"id",
"Num.ofNat'_zero",
"instOfNatNat",
"Num.toZNum",
"ZNum",
"Num",
"instZeroNum",
"Nat",
"Zero.toOfNat0",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Num.ofNat'"
] | false |
Aesop.RuleStats.rule | Aesop.Stats.Basic | [
"Aesop.DisplayRuleName",
"Aesop.RuleStats"
] | true |
_private.Init.Data.SInt.Lemmas.0.ISize.ofInt_eq_iff_bmod_eq_toInt._simp_1_1 | Init.Data.SInt.Lemmas | [
"ISize.toInt_inj",
"Int",
"propext",
"Eq.symm",
"ISize",
"Eq",
"ISize.toInt"
] | false |
Classical.not_imp._simp_3 | Mathlib.Tactic.Push | [
"And",
"Classical.not_imp",
"propext",
"Eq.symm",
"Eq",
"Not"
] | false |
CompleteLatticeHom.instFunLike._proof_1 | Mathlib.Order.Hom.CompleteLattice | [
"sInfHom.mk",
"sInfHom.toFun",
"Eq.rec",
"sInfHom.casesOn",
"InfSet",
"CompleteLatticeHom.tosInfHom",
"CompleteLattice.toCompleteSemilatticeInf",
"sInfHom",
"CompleteLatticeHom.casesOn",
"Eq.ndrec",
"CompleteSemilatticeSup.toSupSet",
"Eq.refl",
"Set.image",
"CompleteLatticeHom",
"Complet... | false |
infClosed_univ._simp_1 | Mathlib.Order.SupClosed | [
"infClosed_univ",
"Set.univ",
"SemilatticeInf",
"True",
"eq_true",
"InfClosed",
"Eq"
] | false |
HVertexOperator.ext | Mathlib.Algebra.Vertex.HVertexOperator | [
"HahnModule.instBaseModule",
"CommRing",
"HVertexOperator",
"LinearMap.ext",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddCommGroup.toAddGroup",
"HahnModule",
"AddZeroClass.toAddZero",
"P... | true |
Std.Http.instInhabitedVersion.default | Std.Internal.Http.Data.Version | [
"Std.Http.Version.v10",
"Std.Http.Version"
] | true |
Frm.Hom.hom | Mathlib.Order.Category.Frm | [
"Frm.Hom",
"FrameHom",
"CategoryTheory.ConcreteCategory.hom",
"Frm.str",
"Order.Frame.toCompleteLattice",
"Frm.instConcreteCategoryFrameHomCarrier",
"Frm.carrier",
"FrameHom.instFunLike",
"Frm",
"Frm.instCategory"
] | true |
Finset.Ioo_eq_empty_iff | Mathlib.Order.Interval.Finset.Basic | [
"Eq.mpr",
"Finset.coe_eq_empty",
"Preorder.toLT",
"congrArg",
"Finset",
"Iff.rfl",
"id",
"Finset.coe_Ioo",
"Finset.instEmptyCollection",
"Iff",
"SetLike.coe",
"Finset.instSetLike",
"LT.lt",
"propext",
"Set.instEmptyCollection",
"LocallyFiniteOrder",
"DenselyOrdered",
"Set.Ioo_eq_em... | true |
_private.Mathlib.LinearAlgebra.Projection.0.LinearMap.IsIdempotentElem.commute_iff_of_isUnit._simp_1_1 | Mathlib.LinearAlgebra.Projection | [
"Units.val",
"MulEquiv.instEquivLike",
"Module.End.instMonoid",
"LinearMap.GeneralLinearGroup.generalLinearEquiv_to_linearMap",
"Monoid.toMulOneClass",
"LinearMap.GeneralLinearGroup",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"LinearMap",
"AddCommMonoid",
"Group.toDivInvMonoid",
"MulOneClass.to... | false |
WeakDual.coeFn_continuous | Mathlib.Topology.Algebra.Module.Spaces.WeakDual | [
"Continuous",
"instSMulOfMul",
"Pi.topologicalSpace",
"CommSemiring.toSemiring",
"Distrib.toAdd",
"ContinuousConstSMul",
"AddCommMonoid",
"instDistribOfSemiring",
"CommSemiring",
"TopologicalSpace",
"Distrib.toMul",
"instTopologicalSpaceWeakDual",
"WeakDual",
"continuous_induced_dom",
"i... | true |
Complex.instAlgebraOfReal.match_1 | Mathlib.LinearAlgebra.Complex.Module | [
"Real",
"Complex.casesOn",
"Complex",
"Complex.mk"
] | false |
UInt32.lt_iff_toFin_lt | Init.Data.UInt.Lemmas | [
"UInt32.size",
"Iff.rfl",
"Iff",
"instLTUInt32",
"LT.lt",
"instLTFin",
"UInt32",
"UInt32.toFin",
"Fin"
] | true |
instInvNonemptyInterval.eq_1 | Mathlib.Algebra.Order.Interval.Basic | [
"Inv",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IsOrderedMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"DivisionMonoid.toDivInvOneMonoid",
"PartialOrder",
"Prod.mk",
"instInvNonemptyInterval",
"CommGroup",
"CommGroup.toDivisionCommMonoid",
"Prod.fst",
... | true |
ContT.instMonadLiftOfMonad | Mathlib.Control.Monad.Cont | [
"MonadLift",
"ContT.mk",
"Monad.toBind",
"Bind.bind",
"MonadLift.mk",
"Monad",
"ContT"
] | true |
_private.Mathlib.Topology.Order.0.continuous_Prop._simp_1_2 | Mathlib.Topology.Order | [
"Filter.Eventually",
"tendsto_nhds_Prop",
"nhds",
"Filter.Tendsto",
"sierpinskiSpace",
"propext",
"Eq",
"Filter"
] | false |
Derivation.liftKaehlerDifferential_comp | Mathlib.RingTheory.Kaehler.Basic | [
"Derivation",
"Subtype.coe_mk",
"Derivation.liftKaehlerDifferential",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Derivation.ext",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"map_sub",
... | true |
PrimeSpectrum.isBasis_basic_opens | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"Set.range_comp",
"Eq.mpr",
"PrimeSpectrum.basicOpen",
"congrArg",
"HEq.refl",
"TopologicalSpace.Opens",
"Function.comp",
"Eq.casesOn",
"id",
"TopologicalSpace.Opens.instSetLike",
"PrimeSpectrum.isTopologicalBasis_basic_opens",
"TopologicalSpace.Opens.IsBasis",
"CommSemiring",
"Topological... | true |
SimplexCategory.σ₀Iter._proof_2 | Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter | [
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"Fin.val",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"SimplexCategory.mk",
"Nat",
"LT.lt",
"_private.Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter.0.SimplexCategory.σ₀Iter._proof_1",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Eq",
... | false |
PowerSeries.hasSubst_substInv | Mathlib.RingTheory.PowerSeries.Substitution | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"LinearMap.instFunLike",
"PowerSeries.HasSubst",
"PowerSeries.substInv",
"PowerSeries.coeff",
"instOfNatNat",
"MvPowerSeries.instModule",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
"instDis... | true |
Nat.four_pow_le_two_mul_self_mul_centralBinom | Mathlib.Data.Nat.Choose.Central | [
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"Semigroup.toMul",
"Trans.trans",
"Nat.choose",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"instReflLe",
"congrArg",
"Nat.instMonoid",
"False.elim",
"AddMonoid.toAddZeroClass",
"mul_assoc",
"Nat.instZeroLEOneClass",
"Nat.instMulOneClass",
"Nat... | true |
_private.Mathlib.GroupTheory.GroupAction.MultipleTransitivity.0.SubMulAction.ofStabilizer.isMultiplyPretransitive._simp_1_1 | Mathlib.GroupTheory.GroupAction.MultipleTransitivity | [
"DivInvMonoid.toInv",
"instHSMul",
"inv_smul_eq_iff",
"Group",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"Inv.inv",
"MulAction",
"propext",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq"
] | false |
WithBot.natCast_eq_map_iff | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"WithBot.some",
"WithBot",
"Exists",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"WithBot.some_eq_map_iff",
"And",
"Iff",
"WithBot.natCast",
"Nat",
"WithBot.map",
"Eq",
"AddMonoidWithOne"
] | true |
Algebra.Generators.Hom.equivAlgHom | Mathlib.RingTheory.Extension.Generators | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.Generators.Ring",
"MvPolynomial.aeval",
"Algebra.algebraMap",
"Algebra.Generators.Hom.equivAlgHom._proof_2",
"Algebra.Generators.Hom.toAlgHom",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"A... | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_373 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Instances___unexpand_spectrum_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances | [
"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 |
dist_edist | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"Eq.mpr",
"Real",
"ENNReal.ofReal",
"congrArg",
"dist_nonneg",
"id",
"ENNReal.toReal_ofReal",
"PseudoMetricSpace",
"ENNReal.toReal",
"edist_dist",
"PseudoMetricSpace.toEDist",
"ENNReal",
"Eq.refl",
"Dist.dist",
"PseudoMetricSpace.toDist",
"EDist.edist",
"Eq"
] | true |
RKHS.ctorIdx | Mathlib.Analysis.InnerProductSpace.Reproducing | [
"outParam",
"RCLike",
"Nat",
"RKHS",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"InnerProductSpace",
"NormedAddCommGroup"
] | false |
_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.AnalyzeResult.rec | Lean.Elab.Extra | [
"Lean.Expr",
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.AnalyzeResult.mk",
"Bool",
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.AnalyzeResult",
"Option"
] | false |
Urysohns.CU.approx_le_approx_of_U_sub_C | Mathlib.Topology.UrysohnsLemma | [
"Urysohns.CU.C",
"Urysohns.CU.approx_of_mem_C",
"Real.instLE",
"Real",
"Trans.trans",
"Real.instZero",
"Urysohns.CU.approx_nonneg",
"Classical.propDecidable",
"Membership.mem",
"HasSubset.Subset",
"LE.le",
"Urysohns.CU.approx",
"dite",
"Urysohns.CU.approx_le_one",
"instTransEq",
"Real.... | true |
Lean.Meta.Grind.Arith.Linear.RingEqCnstr.toExprProof | Lean.Meta.Tactic.Grind.Arith.Linear.Proof | [
"Lean.Meta.Grind.GrindM",
"Inhabited.default",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.Linear.LinearM.Context",
"instInhabitedOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.Context",
"ReaderT.instMonad",
"Lean.Meta.Grind.Context",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.Real... | true |
Lean.getPPMatch | Lean.PrettyPrinter.Delaborator.Options | [
"Bool.not",
"Lean.pp.match",
"Lean.KVMap.instValueBool",
"Lean.Options.get",
"Bool",
"Lean.getPPAll",
"Lean.Options",
"Lean.Option.name"
] | true |
AddCommute.all | Mathlib.Algebra.Group.Commute.Defs | [
"AddCommMagma",
"add_comm",
"AddCommute",
"AddCommMagma.toAdd"
] | true |
CategoryTheory.Pseudofunctor.CoGrothendieck.comp_const | Mathlib.CategoryTheory.FiberedCategory.Grothendieck | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Cat.str",
"CategoryTheory.Pseudofunctor.C... | true |
Lean.Compiler.LCNF.Ownedness.borrow | Lean.Compiler.LCNF.PropagateBorrow | [
"Lean.Compiler.LCNF.Ownedness",
"Lean.Compiler.LCNF.Ownedness.borrow"
] | true |
WithBotTop.coe_lt_coe | Mathlib.Order.WithBotTop | [
"WithBotTop.coe",
"Eq.mpr",
"WithBot.instLT",
"congrArg",
"id",
"WithTop.some",
"WithTop.coe_lt_coe",
"Iff",
"WithBot.coe_lt_coe",
"WithTop.instLT",
"LT.lt",
"propext",
"Eq.symm",
"Eq",
"WithBotTop",
"LT",
"WithTop"
] | true |
Set.Ico_subset_Iio_self | Mathlib.Order.Interval.Set.Basic | [
"Preorder.toLT",
"Preorder.toLE",
"HasSubset.Subset",
"LE.le",
"Set.Ico",
"And.right",
"LT.lt",
"Set.Iio",
"Preorder",
"Set.instHasSubset",
"Set"
] | true |
TopCat.toSSetObj₀Equiv._proof_3 | Mathlib.AlgebraicTopology.SimplicialSet.TopAdj | [
"Inhabited.default",
"Real.partialOrder",
"Real",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Pi.topologicalSpace",
"ContinuousMap.mk",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"TopCat.toSSetObj₀Equiv._proof_1",
"Membership.mem",
"Real.semiring",
"Set.Elem",
"... | false |
Representation.finsuppTensorLeft_symm_apply_single | Mathlib.RepresentationTheory.Equiv | [
"Monoid",
"Representation.Equiv.symm",
"Representation",
"Finsupp.module",
"congrArg",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"TensorProduct.finsuppLeft_symm_apply_single",
"AddZeroClass.toAddZero",
"Algebra.id",
"Representation.tprod",
"Represe... | true |
_private.Lean.Server.Watchdog.0.Lean.Server.Watchdog.handleRequest.match_6 | Lean.Server.Watchdog | [
"Option.ctorIdx",
"Option.some",
"Lean.Lsp.WaitForILeansParams.casesOn",
"Nat.hasNotBit",
"Lean.Lsp.DocumentUri",
"_private.Lean.Server.Watchdog.0.Lean.Server.Watchdog.RequestQueueMap.erase._sparseCasesOn_1",
"Nat",
"Lean.Lsp.WaitForILeansParams.mk",
"Lean.Lsp.WaitForILeansParams",
"Option"
] | false |
Subring.mem_mk | Mathlib.Algebra.Ring.Subring.Defs | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Subsemiring.instSetLike",
"Subring.instSetLike",
"AddGroupWithOne.toAddGroup",
"Iff.rfl",
"Submonoid.toSubsemigroup",
"Membership.mem",
"MulOne.toMul",
"SubtractionMonoid.toSubNegZeroMonoid",
"NonAssocSemiring.toMulZeroOneClass",
"NonAssoc... | true |
CategoryTheory.Functor.isPointwiseLeftKanExtensionAtOfIsoOfIsLocalization._proof_3 | Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.LeftExtension.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Cos... | false |
_private.Lean.Meta.MkIffOfInductiveProp.0.Lean.Meta.nCasesSum._sunfold | Lean.Meta.MkIffOfInductiveProp | [
"Pure.pure",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.CasesSubgoal",
"Lean.Meta.CasesSubgoal.toInductionSubgoal",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.throwError",
"Lean.MVarId",
"Lean.MonadQuotation.toMon... | false |
Hyperreal.not_infinitePos_add_infiniteNeg | Mathlib.Analysis.Real.Hyperreal | [
"Hyperreal.instField",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Hyperreal.InfinitePos",
"Eq.rec",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"add_comm",
"Field.toSemifield",
"Field.toCommRing",
"instDistribOfSemiring",
"NonUni... | true |
Finset.sup'_inf_distrib_left | Mathlib.Data.Finset.Lattice.Fold | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Finset.cons",
"congrArg",
"Finset",
"Finset.cons_nonempty",
"Membership.mem",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"id",
"SemilatticeInf.toMin",
"Finset.Nonempty.cons_induction",
"DistribLattice",
"inf_sup_left",
"Finset.instSetLike",... | true |
_private.Batteries.Data.RBMap.WF.0.Batteries.RBNode.balance2.match_1.splitter._sparseCasesOn_2 | Batteries.Data.RBMap.WF | [
"Batteries.RBNode",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"Batteries.RBNode.nil",
"instOfNatNat",
"Batteries.RBNode.ctorIdx",
"Nat.land",
"Batteries.RBNode.rec",
"Batteries.RBColor",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Batteries.RBNode.node"
] | false |
Subfield.instCompleteLattice._proof_4 | Mathlib.Algebra.Field.Subfield.Basic | [
"Lattice.toSemilatticeSup",
"completeLatticeOfInf",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Subfield.instPartialOrder",
"CompleteLattice.toSupSet",
"CompleteLattice.isLUB_sSup",
"IsLUB",
"DivisionRing",
"Subfield",
"SemilatticeSup.toPartialOrder",
"Subfield.... | false |
Aesop.DisplayRuleName.ctorElimType | Aesop.Rule.Name | [
"cond",
"Aesop.RuleName",
"Nat.ble",
"Aesop.DisplayRuleName",
"PULift",
"Aesop.DisplayRuleName.ruleName",
"Nat",
"Aesop.DisplayRuleName.normUnfold",
"Aesop.DisplayRuleName.normSimp"
] | false |
Lean.Server.instRpcEncodableWithRpcRefOfTypeName.rpcDecode | Lean.Server.Rpc.Basic | [
"Lean.Lsp.RpcWireFormat.refFieldName",
"TypeName",
"Lean.Json",
"instMonadReaderOfReaderTOfMonad",
"Lean.Server.WithRpcRef",
"ReaderT",
"String",
"instMonadLiftT",
"Lean.instFromJsonUSize",
"MonadReader.read",
"ReaderT.instMonad",
"Lean.Json.getObjValAs?",
"liftM",
"ExceptT.instMonadLift",... | true |
OrderIso.ofCmpEqCmp._proof_4 | Mathlib.Order.Hom.Basic | [
"Eq.symm",
"Eq"
] | false |
ContinuousWithinAt.cexp | Mathlib.Analysis.SpecialFunctions.Exp | [
"NormedCommRing.toSeminormedCommRing",
"ContinuousWithinAt",
"nhdsWithin",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace",
"Complex.exp",
"SeminormedCommRing.toSeminormedRing",
"Filter.Tendsto.cexp",
"SeminormedRing.toPseudoMetricSpace",
"NormedField.toNormedCo... | true |
_private.Mathlib.RingTheory.PowerSeries.WellKnown.0.PowerSeries.invOneSubPow.match_1.eq_2 | Mathlib.RingTheory.PowerSeries.WellKnown | [
"instOfNatNat",
"Unit",
"Nat",
"PowerSeries.invOneSubPow.match_1",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
SimpleGraph.Walk.support_append | Mathlib.Combinatorics.SimpleGraph.Walk.Operations | [
"congrArg",
"HEq.refl",
"SimpleGraph.Adj",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"SimpleGraph.Walk.casesOn",
"List.tail",
"List.append_nil",
"List.cons",
"SimpleGraph",
"SimpleGraph.Walk.cons",
"instHAppendOfAppend",
"List",
"SimpleGraph.Walk.nil",
"SimpleGraph.Walk.rec",
"co... | true |
_private.Mathlib.Data.List.Induction.0.List.bidirectionalRec_cons_append._proof_1_23 | Mathlib.Data.List.Induction | [
"List.getLast",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"Lean.Grind.nestedProof",
"Lean.Grind.Order.lt_eq_true_of_lt_k",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
"Lean.Grind.Order.le_of_eq_2_k",
"Std.IsLinearPreorder.toIsPreorder",
"Lean.Grind.Order.lt_le_trans_k",
"_private.Math... | false |
Std.HashMap.Raw.getKey!_union_of_not_mem_left | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.WF.out",
"Membership.mem",
"Std.HashMap.Raw.WF",
"LawfulHashable",
"Std.HashMap.Raw",
"EquivBEq",
"Inhabited",
"Std.HashMap.Raw.inner",
"Std.HashMap.Raw.instMembershipOfBEqOfHashable",
"Hashable",
"Std.DHashMap.Raw.getKey!_union_of_not_mem_left",
"Union.union",
"BEq",
"Eq"... | true |
_private.Mathlib.Logic.Function.Basic.0.Function.Bijective.existsUnique_iff.match_1_3 | Mathlib.Logic.Function.Basic | [
"And.casesOn",
"And",
"Exists.casesOn",
"ExistsUnique",
"And.intro",
"Exists.intro",
"Eq"
] | false |
PSet.mem_image | Mathlib.SetTheory.ZFC.PSet | [
"_private.Mathlib.SetTheory.ZFC.PSet.0.PSet.mem_image.match_1_3",
"PSet.instMembership",
"_private.Mathlib.SetTheory.ZFC.PSet.0.PSet.mem_image.match_1_5",
"PSet.Func",
"Membership.mem",
"Exists",
"PSet.Mem.mk",
"PSet.mk",
"PSet",
"_private.Mathlib.SetTheory.ZFC.PSet.0.PSet.mem_image.match_1_1",
... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_split_helper._simp_1_12 | Mathlib.Combinatorics.SimpleGraph.Triangle.Counting | [
"Finset",
"SimpleGraph.Adj",
"DecidableRel",
"Membership.mem",
"Prod.fst",
"SimpleGraph",
"And",
"SimpleGraph.mem_interedges_iff",
"Finset.instSetLike",
"propext",
"Prod",
"Eq",
"Prod.snd",
"SetLike.instMembership",
"SimpleGraph.interedges"
] | false |
Std.Internal.IndexMultiMap.instDecidableMem | Std.Internal.Http.Internal.IndexMultiMap | [
"Std.Internal.IndexMultiMap.indexes",
"Bool.decEq",
"Std.Internal.IndexMultiMap.instMembership",
"Decidable",
"Membership.mem",
"Array",
"Bool.true",
"Std.DHashMap.contains",
"Nat",
"Hashable",
"Std.Internal.IndexMultiMap",
"Std.HashMap.inner",
"BEq"
] | true |
CategoryTheory.SimplicialThickening.instSimplicialCategory._proof_10 | Mathlib.AlgebraicTopology.SimplicialNerve | [
"CategoryTheory.Functor",
"CategoryTheory.SimplicialThickening",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"Equiv.trans",
"LinearOrder",
"CategoryTheory.EnrichedCategory.mk",
"PartialOrder.toPreorde... | false |
EckmannHilton.addCommMonoid.eq_1 | Mathlib.GroupTheory.EckmannHilton | [
"EckmannHilton.addCommMonoid",
"EckmannHilton.addCommMonoid._proof_3",
"AddMonoid.mk",
"AddZeroClass.toAddZero",
"AddZeroClass.zero_add",
"EckmannHilton.addCommMonoid._proof_1",
"EckmannHilton.addCommMonoid._proof_4",
"AddSemigroup.mk",
"EckmannHilton.addCommMonoid._proof_2",
"AddCommMonoid",
"n... | true |
Turing.Tape.ctorIdx | Mathlib.Computability.TuringMachine.Tape | [
"Turing.Tape",
"Nat",
"Inhabited"
] | false |
Real.artanh_eq_zero_iff | Mathlib.Analysis.SpecialFunctions.Artanh | [
"Real.instLE",
"Real",
"Real.instZero",
"LE.le",
"Real.instOne",
"Iff",
"Real.instNeg",
"_private.Mathlib.Analysis.SpecialFunctions.Artanh.0.Real.artanh_eq_zero_iff._proof_1_2",
"One.toOfNat1",
"Zero.toOfNat0",
"Real.artanh",
"Or",
"OfNat.ofNat",
"Eq",
"Neg.neg"
] | true |
BitVec.srem_self | Init.Data.BitVec.Lemmas | [
"BitVec.neg_zero",
"congrArg",
"BitVec",
"instHMod",
"instOfNatNat",
"BitVec.ofNat",
"BitVec.instNeg",
"BitVec.srem",
"Bool.true",
"HMod.hMod",
"Unit",
"Bool.casesOn",
"Nat",
"congr",
"True",
"BitVec.sdiv_eq.match_1",
"eq_self",
"BitVec.srem_eq",
"Bool",
"of_eq_true",
"Eq.ndr... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Basic.0.SimpleGraph.Walk.mem_darts_iff_infix_support._proof_1_7 | Mathlib.Combinatorics.SimpleGraph.Walk.Basic | [
"Lean.RArray.leaf",
"False",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"List.length_cons",
"SimpleGraph.Walk.length",
"Classical.byContradiction",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"SimpleGraph.Walk.length_... | false |
OmegaCompletePartialOrder.Chain.map_id | Mathlib.Order.OmegaCompletePartialOrder | [
"OrderHom.id",
"funext",
"OmegaCompletePartialOrder.Chain",
"Nat",
"eq_self",
"OmegaCompletePartialOrder.Chain.ext",
"OmegaCompletePartialOrder.Chain.instFunLikeNat",
"of_eq_true",
"OmegaCompletePartialOrder.Chain.map",
"Eq",
"DFunLike.coe",
"Preorder"
] | true |
Complex.cpow_ofNat_inv_pow | Mathlib.Analysis.SpecialFunctions.Pow.Complex | [
"Nat.instMulZeroClass",
"Nat.AtLeastTwo.toNeZero",
"Complex.instPow",
"instOfNatNat",
"Complex.instNatCast",
"Monoid.toPow",
"Inv.inv",
"HPow.hPow",
"Nat",
"Semiring.toMonoid",
"Complex.cpow_nat_inv_pow",
"instHPow",
"Complex",
"OfNat.ofNat",
"Eq",
"instOfNatAtLeastTwo",
"Complex.ins... | true |
Lean.Grind.not_ite | Init.Grind.Norm | [
"eq_false",
"congrArg",
"Decidable",
"ite_cond_eq_true",
"dite",
"congr",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"ite_cond_eq_false",
"Eq",
"Not",
"Eq.trans",
"ite"
] | true |
PosPart.casesOn | Mathlib.Algebra.Notation | [
"PosPart",
"PosPart.rec",
"PosPart.mk"
] | false |
_private.Mathlib.CategoryTheory.Triangulated.Opposite.OpOp.0.CategoryTheory.Pretriangulated.Opposite.instCommShiftOppositeUnopUnopInt._simp_3 | Mathlib.CategoryTheory.Triangulated.Opposite.OpOp | [
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"Quiver.Hom.unop",
"CategoryTheory.unop_comp",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.CategoryStruct",
"Eq.symm",
"Eq",
"Opposite.unop"
] | false |
_private.Lean.Elab.Tactic.Grind.BuiltinTactic.0.Lean.Elab.Tactic.Grind.evalCasesNext | Lean.Elab.Tactic.Grind.BuiltinTactic | [
"Lean.Syntax",
"Bool.true",
"Lean.Elab.Tactic.Grind.GrindTactic",
"Lean.Elab.Tactic.Grind.liftAction",
"Lean.Meta.Grind.Action.splitNext",
"Bool.false"
] | true |
_private.Mathlib.Topology.Sets.Closeds.0.TopologicalSpace.Closeds.isAtom_iff._simp_1_4 | Mathlib.Topology.Sets.Closeds | [
"Membership.mem",
"Iff",
"propext",
"Set.ext_iff",
"Eq",
"Set.instMembership",
"Set"
] | false |
Lean.Lsp.TextDocumentRegistrationOptions | Lean.Data.Lsp.Basic | [
"Lean.Lsp.TextDocumentRegistrationOptions.mk"
] | true |
Std.DTreeMap.minKey | Std.Data.DTreeMap.Basic | [
"Std.DTreeMap",
"Std.DTreeMap.isEmpty",
"Ordering",
"Std.DTreeMap.inner",
"Std.DTreeMap.Internal.Impl.minKey",
"Bool",
"Bool.false",
"Eq"
] | true |
Array.scanr_extract | Batteries.Data.Array.Scan | [
"Pure.pure",
"Eq.mpr",
"congrArg",
"Monad.toApplicative",
"id",
"instOfNatNat",
"Id.run",
"Id",
"Applicative.toPure",
"Array.extract",
"Array",
"Nat",
"Array.scanrM",
"Eq.refl",
"Id.instMonad",
"Array.scanr",
"OfNat.ofNat",
"Eq",
"Array.size",
"Array.scanrM_extract",
"Id.inst... | true |
MeasureTheory.Measure.MutuallySingular.compProd_of_right' | Mathlib.Probability.Kernel.Composition.AbsolutelyContinuous | [
"MeasureTheory.ae",
"Eq.mpr",
"ProbabilityTheory.IsFiniteKernel",
"MeasureTheory.Measure",
"congrArg",
"Filter.Eventually",
"MeasurableSpace.CountableOrCountablyGenerated",
"ProbabilityTheory.Kernel.instFunLike",
"id",
"MeasurableSpace",
"MeasureTheory.Measure.MutuallySingular.compProd_of_right"... | true |
_private.Mathlib.Geometry.Euclidean.Circumcenter.0.Affine.Simplex.circumcenter_eq_centroid._simp_1_1 | Mathlib.Geometry.Euclidean.Circumcenter | [
"instHSMul",
"AddGroupWithOne.toAddGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"sub_smul",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"SubNegMonoid.toSub",
"AddZero... | false |
Fin.add_one_le_iff._simp_1 | Init.Data.Fin.Lemmas | [
"instNeZeroNatHAdd_1",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
"instLEFin",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Fin.last",
"propext",
"instAddNat",
"Fin.instAdd",
"OfNat.ofNat",
"Fin",
"Eq",
"Fin.add_one_le_iff"
] | false |
_private.Lean.Elab.Tactic.Do.ProofMode.MGoal.0.Lean.Elab.Tactic.Do.ProofMode.parseMGoal?.match_1 | Lean.Elab.Tactic.Do.ProofMode.MGoal | [
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"Prod.mk",
"_private.Lean.Elab.Tactic.Do.ProofMode.MGoal.0.Lean.Elab.Tactic.Do.ProofMode.SPred.mkAnd._sparseCasesOn_1",
"Prod",
"Prod.casesOn",
"Option"
] | false |
Lean.Meta.DefEq.isInstLTNat | Lean.Meta.NatInstTesters | [
"Pure.pure",
"Lean.Nat.mkInstLT",
"Lean.Meta.State",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"Applicative.toPure",
"Bool.true",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"Bool",
"Monad.toBind",
"Bind.bind",
"Le... | true |
Real.arcsin_sin | Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse | [
"Real.instLE",
"Real",
"instHDiv",
"Real.pi",
"Real.arcsin",
"Real.instDivInvMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"Preorder.toLE",
"HDiv.hDiv",
"instOfNatNat",
"LE.le",
"Nat.instNeZeroSucc",
"Nat",
"And.intro",
"Real.instNeg",
"DivInvMonoid.toDiv",
"Real.arcsin_sin'",
"OfNat.ofN... | true |
_private.Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction.0.BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic._simp_1_1 | Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction | [
"Real",
"BoxIntegral.Box.Icc",
"Membership.mem",
"BoxIntegral.TaggedPrepartition.instMembershipBox",
"LE.le",
"BoxIntegral.TaggedPrepartition.single",
"Set.instLE",
"propext",
"BoxIntegral.Box.instLE",
"OrderEmbedding",
"BoxIntegral.TaggedPrepartition.mem_single",
"Eq",
"Set.instMembership",... | false |
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