name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Std.HashSet.Raw.erase_emptyWithCapacity | Std.Data.HashSet.RawLemmas | [
"_private.Std.Data.HashSet.RawLemmas.0.Std.HashSet.Raw.ext",
"Std.HashSet.Raw.emptyWithCapacity",
"Unit",
"Nat",
"Hashable",
"Std.HashMap.Raw.erase_emptyWithCapacity",
"BEq",
"Eq",
"Std.HashSet.Raw",
"Std.HashSet.Raw.erase"
] | true |
LeftPreLieRing.casesOn | Mathlib.Algebra.NonAssoc.PreLie.Basic | [
"NonUnitalNonAssocRing",
"LeftPreLieRing.rec",
"LeftPreLieRing",
"Eq",
"associator",
"LeftPreLieRing.mk"
] | false |
SSet.prodStdSimplex.nonDegenerate_max_dim_iff._auto_1 | Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Lsp.instToJsonSemanticTokensParams | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SemanticTokensParams",
"Lean.ToJson.mk",
"Lean.ToJson",
"Lean.Lsp.instToJsonSemanticTokensParams.toJson"
] | true |
_private.Mathlib.LinearAlgebra.Projection.0.LinearMap.IsIdempotentElem.comp_eq_right_iff._simp_1_5 | Mathlib.LinearAlgebra.Projection | [
"propext",
"forall_apply_eq_imp_iff",
"Eq"
] | false |
SFinKer.deterministic_id_map | Mathlib.Probability.Kernel.Category.SFinKer | [
"CategoryTheory.ComonObj.comul",
"SFinKer.instMonoidalCategory",
"SFinKer.deterministic_deterministic",
"ProbabilityTheory.IsZeroOrMarkovKernel.isFiniteKernel",
"ProbabilityTheory.Kernel.instIsDeterministicDeterministic",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryT... | true |
Lean.Compiler.LCNF.MonadScope.mk | Lean.Compiler.LCNF.MonadScope | [
"Lean.Compiler.LCNF.Scope",
"Lean.Compiler.LCNF.MonadScope",
"Lean.Compiler.LCNF.MonadScope.mk"
] | true |
Nat.pow_le_pow_left._f | Init.Data.Nat.Basic | [
"instPowNat",
"Nat.le_refl",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.below",
"instNatPowNat",
"Unit",
"HPow.hPow",
"Nat.mul_le_mul",
"Nat",
"Nat.pow",
"_private.Init.Data.Nat.Basic.0.Nat.pow_le_pow_left.match_1_1",
"instHPow",
"OfNat.ofNat",
"Nat.succ"
] | false |
Mathlib.Tactic.Push.instBEqHead.beq | Mathlib.Tactic.Push.Attr | [
"Mathlib.Tactic.Push.Head",
"_private.Mathlib.Tactic.Push.Attr.0.Mathlib.Tactic.Push.instBEqHead.beq.match_1",
"Bool.true",
"BEq.beq",
"Unit",
"Bool",
"Lean.Name",
"Bool.false",
"Lean.Name.instBEq"
] | true |
CategoryTheory.SimplicialObject.cechNerveEquiv._proof_2 | Mathlib.AlgebraicTopology.CechNerve | [
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"CategoryTheory.SimplicialObject.Augmented.toArrow",
"congrArg",
"Quiver.Hom.op",
"CategoryThe... | false |
_private.Lean.Elab.PreDefinition.WF.GuessLex.0.Lean.Elab.WF.GuessLex.withRecApps.loop._unsafe_rec | Lean.Elab.PreDefinition.WF.GuessLex | [
"Pure.pure",
"Lean.instMonadEnvOfMonadLift",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.LocalDeclKind.default",
"Lean.Meta.MatcherApp",
"Bool.not",
"_private.Lean.Elab.PreDefinition.WF.GuessLex.0.Lean.Elab.WF.GuessLex.withRecApps.processApp... | false |
Real.sSup_smul_of_nonneg | Mathlib.Data.Real.Pointwise | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"IsOrderedModule.toPosSMulMono",
"Real.sSup_empty",
"LE.le.eq_or_lt",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHSMul",
"Preorder.toLT",
"Real.instZero",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"Set.smul_set_empty",
"LinearOrder",
... | true |
cfcₙ_complex_eq_real._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.Complex.cot_eq_exp_ratio._simp_1_2 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Lean.Meta.Rewrites.SideConditions.ctorElim | Lean.Meta.Tactic.Rewrites | [
"Lean.Meta.Rewrites.SideConditions",
"Lean.Meta.Rewrites.SideConditions.none",
"Lean.Meta.Rewrites.SideConditions.casesOn",
"Nat",
"Eq.ndrec",
"Lean.Meta.Rewrites.SideConditions.assumption",
"PULift.down",
"Eq",
"Lean.Meta.Rewrites.SideConditions.ctorIdx",
"Lean.Meta.Rewrites.SideConditions.solveB... | false |
ConvexOn.convex_le | Mathlib.Analysis.Convex.Function | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Trans.trans",
"DistribMulAction.toDistribSMul",
"SMul",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"add_le_add",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
... | true |
_private.Std.Internal.Http.Data.URI.Basic.0.Std.Http.URI.Path.normalize.loop._unsafe_rec | Std.Internal.Http.Data.URI.Basic | [
"String",
"Std.Http.URI.EncodedString.instToString",
"instDecidableEqBool",
"ToString.toString",
"instBEqOfDecidableEq",
"List.cons",
"Bool.true",
"List",
"BEq.beq",
"Unit",
"Std.Http.Internal.Char.isPChar",
"instDecidableEqString",
"List.reverse",
"Std.Http.URI.EncodedSegment",
"_privat... | false |
Vector.foldr_add_const | Init.Data.Vector.Lemmas | [
"HMul.hMul",
"Vector",
"congrArg",
"Vector.casesOn",
"Eq.rec",
"Vector.foldr",
"instMulNat",
"Array",
"instHAdd",
"Nat.add_left_cancel_iff._simp_1",
"HAdd.hAdd",
"Vector.mk",
"Nat",
"Array.foldr_add_const",
"True",
"eq_self",
"of_eq_true",
"instAddNat",
"Eq.refl",
"congrFun'",
... | true |
sSupHom.symm_dual_comp | Mathlib.Order.Hom.CompleteLattice | [
"Equiv.instEquivLike",
"sSupHom.dual",
"Equiv",
"SupSet",
"sInfHom.comp",
"OrderDual.infSet",
"sInfHom",
"sSupHom",
"OrderDual",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"sSupHom.comp",
"rfl",
"EquivLike.toFunLike"
] | true |
AddLocalization.r_eq_r' | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"AddMemClass.toAddCommSemigroup",
"AddCon.instFunLikeForallProp",
"AddCon",
"Eq.mpr",
"AddSubmonoidClass.toAddMemClass",
"AddSubmonoid.instAddSubmonoidClass",
"AddMonoid.toAddSemigroup",
"AddCon.add",
"congrArg",
"Prod.instAdd",
"HEq.refl",
"add_assoc",
"Prod.instAddZeroClass",
"AddMonoid.... | true |
Nat.instNeZeroSucc | Init.Data.Nat.Basic | [
"NeZero.mk",
"Zero.ofOfNat0",
"instOfNatNat",
"instHAdd",
"Nat.succ_ne_zero",
"HAdd.hAdd",
"Nat",
"instAddNat",
"NeZero",
"OfNat.ofNat"
] | true |
Lean.Meta.Grind.Arith.Cutsat.resolveConflict | Lean.Meta.Tactic.Grind.Arith.Cutsat.Search | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.Meta.Grind.GrindM",
"Std.TreeSet",
"Lean.Meta.Grind.Arith.Cutsat.Search.State",
"Lean.MessageData",
"Lean.Meta.Grind.Arith.Cutsat.CooperSplitPred.numCases",
"Unit.unit",
"Lean.Meta.Grind.Goal",
"Std.TreeSet.toList",
"Lean.Meta.Grind.Arith.Colle... | true |
ProbabilityTheory.exponentialPDF | Mathlib.Probability.Distributions.Exponential | [
"Real",
"ENNReal.ofReal",
"ENNReal",
"ProbabilityTheory.exponentialPDFReal"
] | true |
Nat.primeFactors_pow | Mathlib.Data.Nat.PrimeFin | [
"Eq.mpr",
"False",
"congrArg",
"Nat.primeFactors_pow_succ",
"Finset",
"Nat.instMonoid",
"False.elim",
"Eq.mp",
"not_true_eq_false",
"id",
"Ne",
"instOfNatNat",
"Monoid.toPow",
"Nat.casesAuxOn",
"instHAdd",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"True",
"eq_self",
"Eq.ndrec",
"ins... | true |
Fin2.noConfusionType | Mathlib.Data.Fin.Fin2 | [
"Fin2.casesOn",
"Nat",
"HEq",
"Eq",
"Fin2"
] | false |
_private.Mathlib.CategoryTheory.Types.Basic.0.TypeCat.Hom.mk.sizeOf_spec | Mathlib.CategoryTheory.Types.Basic | [
"TypeCat.Fun._sizeOf_inst",
"TypeCat.Hom",
"_private.Mathlib.CategoryTheory.Types.Basic.0.TypeCat.Hom.mk",
"instOfNatNat",
"instHAdd",
"TypeCat.Fun",
"HAdd.hAdd",
"Nat",
"TypeCat.Hom._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"Eq"
] | true |
Lean.Meta.Origin.decl.noConfusion | Lean.Meta.Tactic.Simp.SimpTheorems | [
"Lean.Meta.Origin.decl",
"id",
"Bool.true",
"Bool",
"Lean.Name",
"optParam",
"Lean.Meta.Origin",
"Bool.false",
"Eq",
"Lean.Meta.Origin.noConfusion"
] | false |
Std.Tactic.BVDecide.BVExpr.bitblast.blastUdiv.BlastUdivOutput.mk | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Udiv | [
"Std.Sat.AIG.Decl",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastUdiv.BlastUdivOutput",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastUdiv.BlastUdivOutput.mk",
"LE.le",
"instLENat",
"Std.Sat.AIG",
"Nat",
"Hashable",
"Std.Sat.AIG.RefVec",
"Array.size",
"Std.Sat.AIG.decls",
"DecidableEq"
] | true |
_private.Mathlib.NumberTheory.NumberField.House.0.NumberField.house.supOfBasis | Mathlib.NumberTheory.NumberField.House | [
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Finset.univ",
"Algebra.algebraMap",
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"Real.instSemilatticeSup",
"NumberField.RingOfIntegers.instAlgebra_1",
"_private.Mathlib.NumberTheory.N... | true |
String.Slice.trimAscii | Init.Data.String.Slice | [
"String.Slice",
"String.Slice.trimAsciiEnd",
"String.Slice.trimAsciiStart"
] | true |
PSet.Lift.match_1 | Mathlib.SetTheory.ZFC.PSet | [
"ULift.casesOn",
"ULift",
"ULift.up"
] | false |
lowerSemicontinuousWithinAt_sum | Mathlib.Topology.Semicontinuity.Basic | [
"Eq.mpr",
"False",
"OrderTopology",
"Finset.mem_insert_self",
"eq_false",
"congrArg",
"Finset",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"LowerSemicontinuousWithinAt.add",
"Classical.propDecidable",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"AddZeroC... | true |
Lean.Syntax.instReprPreresolved | Init.Meta.Defs | [
"Repr.mk",
"Lean.Syntax.Preresolved",
"Lean.Syntax.instReprPreresolved.repr",
"Repr"
] | true |
ModularGroup.coe_S | Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.of",
"instDecidableEqFin",
"AddGroupWithOne.toAddMonoidWithOne",
"Equiv",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Fin.fintype",
"AddMonoidWithOne.toOne",
"ModularGroup.S",
"Int.instCommRing",
"instOfNat",
"Nat",
"Matrix.vecEmpty",
"One.toOfN... | true |
_private.Mathlib.MeasureTheory.Covering.Besicovitch.0.Mathlib.Meta.Positivity.evalBesicovitchSatelliteConfigR._proof_1 | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"PLift",
"Lean.Expr.sort",
"Lean.Level",
"PLift.down",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Level.instOfNat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"List.nil"
] | false |
CategoryTheory.Functor.natTransEquiv._proof_5 | Mathlib.CategoryTheory.Functor.FunctorHom | [
"Eq.mpr",
"CategoryTheory.Functor.HomObj.ofNatTrans",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.coyoneda",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"CategoryTheory.Functor.HomObj.mk",
"con... | false |
Unitary.coe_neg._simp_1 | Mathlib.Algebra.Star.Unitary | [
"NegZeroClass.toNeg",
"Ring.toNonAssocRing",
"Unitary.instNegSubtypeMemSubmonoidUnitary",
"Monoid.toMulOneClass",
"unitary",
"Membership.mem",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCo... | false |
IsDiscreteValuationRing.remainder.eq_1 | Mathlib.RingTheory.DiscreteValuationRing.Basic | [
"CommRing",
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"semigroupDvd",
"Classical.propDecidable",
"SemigroupWithZero.toSemigroup",
"NonUnitalSemiring.toSemigroupWithZero",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"CommRing.toCommSemiring",
"NonUnitalCommRing.toNonU... | true |
_private.Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic.0.CategoryTheory.Abelian.Ext.comp_assoc._proof_1_1 | Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"congrArg",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"Nat.ToInt.add_congr",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"NatCast.natCast",
"I... | false |
_private.Mathlib.Topology.UniformSpace.UniformApproximation.0.uniformContinuous_of_uniform_approx_of_uniformContinuous._simp_1_1 | Mathlib.Topology.UniformSpace.UniformApproximation | [
"UniformContinuous",
"UniformSpace",
"Set.univ",
"uniformContinuousOn_univ",
"propext",
"UniformContinuousOn",
"Eq"
] | false |
CategoryTheory.yonedaCommRing_map_app_apply | Mathlib.CategoryTheory.Monoidal.Cartesian.Ring | [
"CategoryTheory.Functor",
"CategoryTheory.yonedaCommRingObj",
"Opposite",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"CategoryTheory.Functor.category",
"CommRingCat.instConcreteCa... | true |
StochHom | Mathlib.Probability.Kernel.Category.Stoch | [
"CategoryTheory.MorphismProperty",
"SFinKer.Hom.hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SFinKer",
"SFinKer.str",
"ProbabilityTheory.IsMarkovKernel",
"SFinKer.carrier",
"CategoryTheory.Category.toCategoryStruct",
"SFinKer.instLargeCategory"
] | true |
Std.IterM.step_uLift.match_1 | Init.Data.Iterators.Lemmas.Combinators.Monadic.ULift | [
"Std.IterStep",
"Subtype.casesOn",
"Std.IterM.IsPlausibleStep",
"Std.IterStep.skip",
"Std.Iterator",
"Subtype.mk",
"Std.IterStep.yield",
"Std.IterM.Step",
"Std.IterStep.done",
"Std.IterM",
"Std.IterStep.casesOn"
] | false |
Matroid.contract_finitary | Mathlib.Combinatorics.Matroid.Minor.Contract | [
"Iff.mpr",
"Matroid.IsBasis'.contract_eq_contract_delete",
"Eq.mpr",
"instDecidableNot",
"ChainCompletePartialOrder.instOfCompleteLattice",
"instDecidableTrue",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Set.Finite.inter_of_left",
"congrArg",
"Matroid.E",
"Set.disjoint_left",
"False.e... | true |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.mk.noConfusion | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.w._autoParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.fst",
"... | false |
CategoryTheory.Limits.snd_opProdIsoCoprod_hom | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products | [
"Eq.mpr",
"CategoryTheory.Limits.opProdIsoCoprod",
"CategoryTheory.op_comp",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.coprod.desc",
"CategoryTheory.Limits... | true |
Lean.PrettyPrinter.Formatter.State.isUngrouped._default | Lean.PrettyPrinter.Formatter | [
"id",
"Bool",
"Bool.false"
] | false |
_private.Mathlib.ModelTheory.Syntax.0.FirstOrder.Language.Term.constantsVarsEquiv._simp_2 | Mathlib.ModelTheory.Syntax | [
"True",
"propext",
"Subsingleton",
"Eq",
"eq_iff_true_of_subsingleton"
] | false |
Polynomial.monomial_sub | Mathlib.Algebra.Polynomial.Basic | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Semiring.toModule",
"Polynomial.instNeg",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"sub_eq_add_neg",
"HSub.hSub",
"AddZeroClass.toAddZero",
"map_add",
"Polynomial.monomial",
"id",
"LinearMap.semilinear... | true |
SimpleGraph.Walk.IsPath.ne_of_mem_support_of_append | Mathlib.Combinatorics.SimpleGraph.Paths | [
"Eq.mpr",
"SimpleGraph.Walk.nil_iff_support_eq",
"False",
"eq_false",
"congrArg",
"False.elim",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Membership.mem",
"Eq.mp",
"id",
"Or.resolve_left",
"Ne",
"List.not_mem_nil._simp_1",
"List.tail",
"List.cons",
"SimpleGraph",
"SimpleGrap... | true |
Lean.Meta.Simp.Config.mk.noConfusion | Init.MetaTypes | [
"Lean.Meta.Simp.Config",
"id",
"Lean.Meta.Simp.Config.noConfusion",
"Lean.Meta.EtaStructMode",
"Nat",
"Bool",
"Eq",
"Lean.Meta.Simp.Config.mk",
"Option"
] | false |
_private.Init.Data.String.Lemmas.Pattern.Find.Basic.0.String.Slice.Pattern.Model.find?_eq_none_iff._simp_1_3 | Init.Data.String.Lemmas.Pattern.Find.Basic | [
"And",
"propext",
"not_and",
"Eq",
"Not"
] | false |
preNormEDS'_odd | Mathlib.NumberTheory.EllipticDivisibilitySequence | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"preNormEDS'.eq_6",
"CommRing",
"instHDiv",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"Nat.mul_div_cancel_left",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMon... | true |
Subring.range_fst | Mathlib.Algebra.Ring.Subring.Basic | [
"Prod.fst_surjective",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Zero.instNonempty",
"NonAssocRing",
"Subsemiring",
"NonAssocRing.toNonUnitalNonAssocRing",
"RingHom.rangeS_top_of_surjective",
"Subsemiring.instTop",
"Prod.instNonAssocSemiring"... | true |
CategoryTheory.Functor.Initial.limitConeOfComp | Mathlib.CategoryTheory.Limits.Final | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.Initial.isLimitExtendConeEquiv",
"CategoryTheory.Limits.Cone",
"Equiv.instEquivLike",
"CategoryTheory.Functor.Initial",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.LimitCone",
"Equiv",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Func... | true |
RingEquiv.sumArrowEquivProdArrow._proof_1 | Mathlib.Algebra.Ring.Equiv | [
"HMul.hMul",
"Sum",
"Equiv.toFun",
"NonAssocSemiring",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalNonAssocSemiring.toDistrib",
"Pi.instMul",
"Prod",
"Eq",
"rfl",
"instHMul",
"Equiv.sumArrowEquivProdArrow"
] | false |
HomotopicalAlgebra.PrepathObject.RightHomotopy.fullSubcategoryEquiv._proof_3 | Mathlib.AlgebraicTopology.ModelCategory.RightHomotopy | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ObjectProperty.ι",
"HomotopicalAlgebra.PrepathObject.p₀",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"HomotopicalAlgebra.PrepathObject.RightHomotopy",
"HomotopicalAlgebra.PrepathObject.P",
"CategoryTheory.ObjectProperty.... | false |
RingCat.instCreatesLimitSemiRingCatForget₂RingHomCarrierCarrier._proof_2 | Mathlib.Algebra.Category.Ring.Limits | [
"RingCat.limitRing",
"Eq.mpr",
"RingCat.ofHom",
"CategoryTheory.Limits.Cone.π",
"SemiRingCat.instConcreteCategoryRingHomCarrier",
"RingCat.of",
"CategoryTheory.NatTrans.naturality_apply",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Types.Small.limitCone",
"CategoryTheory.CategoryStruct.toQuiv... | false |
IsNilpotent.exp_mul_exp_neg_self | Mathlib.RingTheory.Nilpotent.Exp | [
"add_neg_cancel",
"NegZeroClass.toNeg",
"HMul.hMul",
"IsNilpotent.neg",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"IsNilpotent.exp_add_of_commute",
"AddMonoid.toAddZeroClass",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"AddZeroClass.toAddZero",
"Distrib.toAdd",
"No... | true |
_private.Init.Data.Vector.Range.0.Vector.range'_eq_append_iff._simp_1_1 | Init.Data.Vector.Range | [
"Vector",
"Array",
"Nat",
"propext",
"Eq.symm",
"Eq",
"Vector.toArray",
"Vector.toArray_inj"
] | false |
MeasureTheory.Integrable.of_fst_of_snd_prodLp | Mathlib.MeasureTheory.SpecificCodomains.WithLp | [
"MeasureTheory.integrable_prodLp_iff",
"Iff.mpr",
"WithLp",
"MeasureTheory.Measure",
"WithLp.instProdTopologicalSpace",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Integrable",
"Fact",
"SeminormedAddGroup.toContinuousENorm",
"WithLp.snd",
"LE.le",
"MeasurableSpace",
"SeminormedAddComm... | true |
CategoryTheory.Limits.FormalCoproduct.recOn | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.Limits.FormalCoproduct.rec",
"CategoryTheory.Limits.FormalCoproduct.mk"
] | false |
Prod.continuousAdd | Mathlib.Topology.Algebra.Monoid | [
"Prod.instAdd",
"Continuous.snd",
"continuous_id'",
"instTopologicalSpaceProd",
"Prod.fst",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"Continuous.fun_add",
"Continuous.fst",
"ContinuousAdd",
"Prod",
"Prod.snd",
"ContinuousAdd.mk",
"Add",
"Continuous.prodMk"
] | true |
Array.range'_one | Init.Data.Array.Range | [
"HMul.hMul",
"Nat.le_refl",
"Array.push",
"congrArg",
"HSub.hSub",
"Fin.mk",
"instSubNat",
"instMulNat",
"instOfNatNat",
"Fin.val",
"List.toArray",
"List.cons",
"Array",
"Nat.sub_self",
"instHAppendOfAppend",
"List",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Array.range'",
"Nat",... | true |
Module.Basis.equivFun_apply | Mathlib.LinearAlgebra.Basis.Defs | [
"Finsupp.instFunLike",
"Pi.Function.module",
"Semiring.toModule",
"Pi.addCommMonoid",
"Finsupp.module",
"Finite",
"Module.Basis.repr",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Module.Basis",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"R... | true |
_private.Init.Data.List.ToArray.0.List.zipWith_toArray._simp_1_2 | Init.Data.List.ToArray | [
"LawfulMonad",
"List",
"List.zipWithM'",
"List.zipWithM",
"Eq.symm",
"Monad",
"Eq",
"List.zipWithM'_eq_zipWithM"
] | false |
ContinuousMulEquiv.toHomeomorph_eq_coe | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"ContinuousMulEquiv.instHomeomorphClass",
"ContinuousMulEquiv.instEquivLike",
"Mul",
"HomeomorphClass.toHomeomorph",
"TopologicalSpace",
"Homeomorph",
"ContinuousMulEquiv.toHomeomorph",
"ContinuousMulEquiv",
"Eq",
"rfl"
] | true |
Finset.univ_disjSum_univ | Mathlib.Data.Fintype.Sum | [
"instFintypeSum",
"Finset.univ",
"Finset",
"Sum",
"Fintype",
"Finset.disjSum",
"Eq",
"rfl"
] | true |
QuadraticAlgebra.norm_zero | Mathlib.Algebra.QuadraticAlgebra.Basic | [
"QuadraticAlgebra.re",
"CommRing",
"MonoidHom.instFunLike",
"HMul.hMul",
"QuadraticAlgebra",
"MonoidHom",
"sub_self",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"AddZeroClass.toAddZero"... | true |
_private.Mathlib.SetTheory.Cardinal.UnivLE.0.univLE_iff_cardinal_le._simp_1_1 | Mathlib.SetTheory.Cardinal.UnivLE | [
"UnivLE",
"univLE_iff",
"propext",
"Eq",
"Small"
] | false |
ContinuousOn.add_const | Mathlib.Topology.Algebra.Monoid.Defs | [
"Membership.mem",
"SeparatelyContinuousAdd",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"ContinuousWithinAt.add_const",
"ContinuousOn",
"Set.instMembership",
"Add",
"Set"
] | true |
atTop_isCountablyGenerated_of_archimedean | Mathlib.Order.Filter.AtTopBot.Archimedean | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Set.Ici",
"IsOrderedRing",
"PartialOrder.toPreorder",
"PartialOrder",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"atTop_hasCountableBasis_of_archimedean",
"Nat.cast",
"Filter.atTop",
"NonUnitalNonAssocSemiring.toAddCommMon... | true |
Std.HashMap.not_mem_emptyWithCapacity | Std.Data.HashMap.Lemmas | [
"Membership.mem",
"Std.HashMap",
"Std.DHashMap.not_mem_emptyWithCapacity",
"Nat",
"Hashable",
"Std.HashMap.emptyWithCapacity",
"BEq",
"Not",
"Std.HashMap.instMembership"
] | true |
Lean.Meta.Tactic.Cbv.instHashableCbvSimprocPhase | Lean.Meta.Tactic.Cbv.CbvSimproc | [
"Lean.Meta.Tactic.Cbv.instHashableCbvSimprocPhase.hash",
"Lean.Meta.Tactic.Cbv.CbvSimprocPhase",
"Hashable.mk",
"Hashable"
] | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_220 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.instEquivLike",
"Finset",
"Lean.Grind.Nat.lt_eq",
"Equiv",
"Insert.insert",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"Finset.instInsert",
"List.cons",
"List.idxOfNth",
"instHAdd",
"HAdd.hAdd",
"Equiv.Perm",
"Nat",
"List.filter",
"LT.lt",
"Eq.substr",
... | false |
CategoryTheory.Comma.rightIso_inv | Mathlib.CategoryTheory.Comma.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.rightIso",
"CategoryTheory.Iso",
"CategoryTheory.Comma",
"CategoryTheory.commaCategory",
"CategoryTheory.CommaMorphism.right",
"Eq.refl",
"CategoryTheory.Category... | true |
Real.sqrtTwoAddSeries.match_1 | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Subsemiring.mk.inj | Mathlib.Algebra.Ring.Subsemiring.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddZeroClass",
"Submonoid.toSubsemigroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subsemiring.mk.noConfusion",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Subsemiring",
"MulZeroOne... | true |
Lean.Parser.Command.GrindCnstr.notDefEq.parenthesizer | Lean.Meta.Tactic.Grind.Parser | [
"Lean.Parser.optional.parenthesizer",
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Name.mkStr5",
"Lean.Parser.ident.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.atomic.parenthesizer",
"Lean.PrettyPrinter... | true |
AddCommMonCat.equivalence_unitIso | Mathlib.Algebra.Category.MonCat.Basic | [
"AddCommMonCat.equivalence",
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"AddCommMonCat.instCategory",
"CategoryTheory.Functor.category",
"AddCommMonCat",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso.refl",
"CategoryTheory.Iso",
"CommMonCat",
"Eq.refl",
"Eq",
"CommMon... | true |
MeasureTheory.integral_one_sub_of_ae_eq_zero_or_one | Mathlib.Probability.Distributions.TwoValued | [
"MeasureTheory.ae",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"ContinuousSub.measurableSub₂",
"Real",
"Trans.trans",
"MeasureTheory.Measure",
"AEMeasurable",
"Real.instZero",
"Real.instRCLike",
"congrArg",
"Real.instSub",
"Filter.Eventually",
"setOf",
... | true |
Semiquot.ext | Mathlib.Data.Semiquot | [
"Membership.mem",
"Semiquot.ext_s",
"Semiquot.s",
"Iff",
"Semiquot.instMembership",
"Iff.trans",
"Set.ext_iff",
"Semiquot",
"Eq",
"Set"
] | true |
AddMonoidHom.fiberEquivKerOfSurjective | Mathlib.GroupTheory.Coset.Basic | [
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Eq.rec",
"AddZeroClass.toAddZero",
"Set.Elem",
"Set.instSingletonSet",
"Equiv",
"Subtype",
"AddSubgroup",
"AddGroup",
"AddMonoidHom.fiberEquivKerOfSurjective._proof_1",
"AddGroup.toSubNegMonoid",
"Set.preimage",
"AddSubgroup.instSetLike",
"E... | true |
List.cyclicPermutations_eq_singleton_iff._simp_1 | Mathlib.Data.List.Rotate | [
"List.cyclicPermutations",
"List.cyclicPermutations_eq_singleton_iff",
"List.cons",
"List",
"propext",
"Eq",
"List.nil"
] | false |
Std.Tactic.BVDecide.BVExpr.bitblast.denote_blastNot | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Not | [
"Std.Sat.AIG.RefVec.denote_map",
"Std.Sat.AIG.RefVec.get",
"Std.Sat.AIG.RefVec.LawfulMapOperator.instMkNotCached",
"Bool.not",
"Std.Sat.AIG.mkNotCached",
"congrArg",
"Std.Sat.AIG.RefVec.map",
"Std.Sat.AIG.RefVecEntry.vec",
"Std.Sat.AIG.instLawfulOperatorRefMkNotCached",
"Std.Sat.AIG.RefVec.MapTarg... | true |
_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.emitMainFnIfNeeded.match_1 | Lean.Compiler.LCNF.EmitC | [
"Option.ctorIdx",
"Option.some",
"Lean.Compiler.LCNF.Decl",
"Nat.hasNotBit",
"Lean.Compiler.LCNF.Purity.impure",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.instEmitToStringName._sparseCasesOn_1",
"Option"
] | false |
Int.dvd_self_sub_tmod | Init.Data.Int.DivMod.Lemmas | [
"Int.tmod",
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"HSub.hSub",
"Int.neg_sub",
"id",
"Int.instNegInt",
"Int",
"Int.instDvd",
"Int.dvd_neg",
"instHSub",
"Iff.mp",
"Int.dvd_tmod_sub_self",
"Int.instSub",
"Eq",
"Neg.neg"
] | true |
GenContFract.le_of_succ_succ_get?_contsAux_b | Mathlib.Algebra.ContinuedFractions.Computation.Approximations | [
"GenContFract.s",
"GenContFract.contsAux",
"GenContFract.Pair.b",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"CommRing.toNonUnitalCommRing",
"GenContFract.Pair.a",
"congrArg",
"_private.Mathlib.Algebra.ContinuedFractions.Computation.Ap... | true |
Mathlib.Meta.NormNum.IsRat.den_nz | Mathlib.Tactic.NormNum.Result | [
"Int.cast",
"Invertible.ne_zero",
"HMul.hMul",
"AddGroupWithOne.toAddMonoidWithOne",
"Invertible.invOf",
"_private.Mathlib.Tactic.NormNum.Result.0.Mathlib.Meta.NormNum.IsRat.den_nz.match_1_1",
"DivisionRing.toDivisionSemiring",
"AddMonoidWithOne.toNatCast",
"Ne",
"DivisionRing.toRing",
"Int",
... | true |
isClosedMap_smul_left | Mathlib.Topology.Algebra.Module.FiniteDimension | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"CompleteSpace",
"ContinuousSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Topology.IsClosedEmbedding.isClosedMap",
"PseudoMetricSpace.toUniformSpace",
"Classical.pr... | true |
_private.Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic.0.inv_nonpos._simp_1_1 | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"not_lt",
"LT.lt",
"propext",
"Eq.symm",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
Mathlib.Tactic.Abel.term_eq | Mathlib.Tactic.Abel | [
"instHSMul",
"Mathlib.Tactic.Abel.term",
"AddMonoid.toNSMul",
"AddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"Nat",
"HSMul.hSMul",
"AddCommMonoid.toAddMonoid",
"AddCommSemigroup.toAddCommMagma",
"AddCommMonoid.toAddCommSemigroup",
"Eq",
"rfl",
"AddCommMagma.toAdd"
] | true |
Mathlib.Tactic.Sat.buildReify.match_1 | Mathlib.Tactic.Sat.FromLRAT | [
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
mdifferentiableAt_iff_target_of_mem_source | Mathlib.Geometry.Manifold.MFDeriv.Basic | [
"Eq.mpr",
"ContinuousWithinAt",
"extChartAt",
"instAddMonoidWithOneENat",
"chartedSpaceSelf",
"NormedSpace",
"chartAt",
"mdifferentiableWithinAt_univ",
"congrArg",
"ContinuousAt",
"continuousWithinAt_univ",
"Set.univ",
"Iff.rfl",
"PseudoMetricSpace.toUniformSpace",
"MDifferentiableAt",
... | true |
IsPurelyInseparable.HasExponent | Mathlib.FieldTheory.PurelyInseparable.Exponent | [
"CommRing",
"Algebra",
"IsPurelyInseparable.HasExponent.mk",
"CommRing.toCommSemiring",
"Ring.toSemiring",
"Ring"
] | true |
Lean.Compiler.LCNF.FixedParams.State.visited | Lean.Compiler.LCNF.FixedParams | [
"instHashableProd",
"Lean.Compiler.LCNF.FixedParams.AbsValue",
"Lean.Compiler.LCNF.FixedParams.instBEqAbsValue",
"Std.HashSet",
"Array.instBEq",
"Lean.Compiler.LCNF.FixedParams.State",
"Array",
"Lean.Compiler.LCNF.FixedParams.instHashableAbsValue",
"instBEqProd",
"Lean.Name",
"Prod",
"Lean.Nam... | true |
_private.Mathlib.Data.Seq.Computation.0.Computation.Corec.f.match_1.splitter | Mathlib.Data.Seq.Computation | [
"Sum",
"Computation.Corec.f.match_1",
"Sum.inl",
"Sum.inr"
] | true |
MeasureTheory.stoppedProcess_eq_of_mem_finset | Mathlib.Probability.Process.Stopping | [
"not_le",
"Iff.mpr",
"Eq.mpr",
"False",
"Preorder.toLT",
"Finset.sum_eq_single_of_mem",
"Lattice.toSemilatticeSup",
"Pi.addCommMonoid",
"WithTop.instPreorder",
"congrArg",
"Set.indicator",
"Finset",
"LinearOrder",
"False.elim",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"... | true |
String.Slice.Pos.prev_eq_posLT._proof_1 | Init.Data.String.Lemmas.FindPos | [
"Eq.mpr",
"String.instLTRaw",
"congrArg",
"String.Slice.Pos.offset",
"String.Pos.Raw.eq_zero_iff._simp_1",
"_private.Init.Data.String.Lemmas.FindPos.0.String.Slice.posGT_eq_next._simp_1",
"String.Slice",
"Eq.mp",
"id",
"Ne",
"instOfNatNat",
"String.Slice.startPos",
"String.Pos.Raw",
"Nat",... | false |
IntermediateField.extendRight.instIsScalarTowerSubtypeMem_1 | Mathlib.FieldTheory.IntermediateField.ExtendRight | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"Module.Free.instFaithfulSMulOfNontrivial",
"IntermediateField",
"IsScalarTower",
"IntermediateField.toField",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"Al... | true |
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