name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Complex.arg_of_im_pos | Mathlib.Analysis.SpecialFunctions.Complex.Arg | [
"Norm.norm",
"Real",
"instHDiv",
"Real.instZero",
"Complex.im",
"Real.instDivInvMonoid",
"Complex.instZero",
"Real.instLT",
"Eq.rec",
"Complex.instNorm",
"Complex.arg",
"HDiv.hDiv",
"LT.lt.le",
"Complex.arg_of_im_nonneg_of_ne_zero",
"Complex.re",
"LT.lt.ne'",
"LT.lt",
"DivInvMonoid... | true |
Nat.dfold_zero._proof_7 | Init.Data.Nat.Fold | [
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"Decidable.byContradiction",
"OfNat.ofNat",
"Not",
"Nat.decLe",
"_private.Init.Data.Nat.Fold.0.Nat.dfold_zero._proof_6"
] | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_70 | 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 |
Ideal.comap_map_mk | Mathlib.RingTheory.Ideal.Quotient.Operations | [
"Eq.mpr",
"RingHom.instRingHomClass",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"congrArg",
"Ideal.Quotient.mk",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingHom",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"id",
"Ideal... | true |
prodXSubSMul.eval | Mathlib.Algebra.Polynomial.GroupRingAction | [
"Finset.mem_univ",
"Polynomial.C",
"Polynomial.eval",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MonoidHom.instMonoidHomClass",
"CommRing",
"MonoidHom.instFunLike",
"InvOneClass.toOne",
"Finset.univ",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Polynomial.eval... | true |
QuotientGroup.instSeminormedCommGroup._proof_4 | Mathlib.Analysis.Normed.Group.Quotient | [
"Real.instLE",
"Real",
"SeminormedCommGroup.toPseudoMetricSpace",
"PseudoMetricSpace.dist_triangle",
"QuotientGroup.instHasQuotientSubgroup",
"Subgroup",
"LE.le",
"QuotientGroup.groupSeminorm",
"Real.instAdd",
"HasQuotient.Quotient",
"instHAdd",
"HAdd.hAdd",
"GroupSeminorm.toSeminormedCommGr... | false |
Convexity.ConvexSpace | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"IsStrictOrderedRing",
"PartialOrder",
"Semiring",
"Convexity.ConvexSpace.mk'"
] | true |
Order.IsIntent.eq | Mathlib.Order.Concept | [
"Order.isIntent_iff",
"upperPolar",
"Iff.mp",
"lowerPolar",
"Order.IsIntent",
"Eq",
"Set"
] | true |
_private.Mathlib.Combinatorics.Matroid.Sum.0.Matroid.sum'_isBasis_iff._simp_1_2 | Mathlib.Combinatorics.Matroid.Sum | [
"Equiv.instEquivLike",
"Matroid.mapEquiv",
"Equiv",
"propext",
"Set.image",
"Matroid.mapEquiv_isBasis_iff",
"Equiv.symm",
"Matroid.IsBasis",
"Eq",
"Matroid",
"DFunLike.coe",
"EquivLike.toFunLike",
"Set"
] | false |
Set.InjOn.eq_iff | Mathlib.Data.Set.Function | [
"Membership.mem",
"Eq.rec",
"Iff",
"Iff.intro",
"Set.InjOn",
"Eq",
"Set.instMembership",
"rfl",
"Set"
] | true |
CategoryTheory.Limits.image.fac | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.MonoFactorisation.fac",
"CategoryTheory.Limits.factorThruImage",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.image.ι",
"CategoryTheory.Limits.image",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"C... | true |
DomAddAct.instAddCommMonoidOfAddOpposite | Mathlib.GroupTheory.GroupAction.DomAct.Basic | [
"AddOpposite",
"DomAddAct",
"AddCommMonoid"
] | true |
Dioph._aux_Mathlib_NumberTheory_Dioph___unexpand_Dioph_le_dioph_1 | Mathlib.NumberTheory.Dioph | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
Metric.PiNatEmbed.recOn | Mathlib.Topology.MetricSpace.PiNat | [
"Metric.PiNatEmbed",
"Metric.PiNatEmbed.toPiNat",
"Metric.PiNatEmbed.rec"
] | false |
_private.Mathlib.FieldTheory.RatFunc.Luroth.0.RatFunc.Luroth.generatorIndex.congr_simp | Mathlib.FieldTheory.RatFunc.Luroth | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"IntermediateField",
"OrderBot.toBot",
"Polynomial.algebraOfAlgebra",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Eq.rec",
"CompleteLattice.toBoundedOrder",
"Algebra.id",
"Ne",
"Bot.bot",
"Field.toSemifiel... | true |
jacobiSym.mul_right' | Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | [
"Int.instCommMonoid",
"Eq.mpr",
"MulOne.toOne",
"jacobiSym.eq_1",
"Nat.Prime",
"Nat.prime_of_mem_primeFactorsList",
"List.prod_append",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Int.instLawfulIdentityHMulOfNat",
"List.Perm.prod_eq",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership... | true |
TopCommRingCat.hasForgetToTopCat | Mathlib.Topology.Category.TopCommRingCat | [
"Continuous",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"TopCommRingCat.instConcreteCategorySubtypeRingHomαContinuousCoe",
"TopCat.instCategory",
"TopCommRingCat.hasForgetToTopCat._proof_1",
"ContinuousMap.mk",
"ContinuousMap",
"TopCommRingCat.instCategory"... | true |
Equiv.Perm.coe_pow._simp_1 | Mathlib.Algebra.Group.End | [
"Equiv.instEquivLike",
"Equiv.Perm.instPowNat",
"Nat.iterate",
"HPow.hPow",
"Equiv.Perm",
"Nat",
"instHPow",
"Eq.symm",
"Eq",
"DFunLike.coe",
"Equiv.Perm.coe_pow",
"EquivLike.toFunLike"
] | false |
CategoryTheory.ShiftMkCore.casesOn | Mathlib.CategoryTheory.Shift.Basic | [
"CategoryTheory.ShiftMkCore.rec",
"CategoryTheory.Functor",
"AddMonoid.toAddSemigroup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.ShiftMkCore",
"C... | false |
_private.Lean.Meta.Tactic.Simp.Types.0.Lean.Meta.Simp.SimpM.run.match_1 | Lean.Meta.Tactic.Simp.Types | [
"Prod.mk",
"Lean.Meta.Simp.State",
"Prod",
"Prod.casesOn"
] | false |
Bundle.ContinuousAlternatingMap.instVectorBundle | Mathlib.Topology.VectorBundle.ContinuousAlternatingMap | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace",
"ContinuousSMul",
"FiberBundle",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"ContinuousAlternatingMap.instNormedSpace",
"PseudoMetricSpace.toUniformSpace",
"AddCommGro... | true |
Batteries.Tactic.PrintPrefixConfig.imported._default | Batteries.Tactic.PrintPrefix | [
"id",
"Bool.true",
"Bool"
] | false |
Qq.unpackParensIdent | Qq.Match | [
"Inhabited.default",
"Lean.Syntax",
"instInhabitedOption",
"Option"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Counting.0.SimpleGraph.triangle_counting'._simp_1_4 | Mathlib.Combinatorics.SimpleGraph.Triangle.Counting | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
Homeomorph.funUnique_apply | Mathlib.Topology.Homeomorph.Lemmas | [
"Inhabited.default",
"Pi.topologicalSpace",
"Unique",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Homeomorph.funUnique",
"Homeomorph",
"Eq.refl",
"Unique.instInhabited",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Finmap.lookup_eq_none | Mathlib.Data.Finmap | [
"AList.mk",
"Finmap.instMembership",
"Membership.mem",
"Finmap.lookup",
"AList.lookup",
"Option.none",
"Iff",
"Finmap.induction_on",
"Finmap.liftOn._proof_2",
"AList",
"Eq",
"AList.toFinmap",
"Not",
"AList.lookup_eq_none",
"AList.perm_lookup",
"Finmap",
"Option",
"DecidableEq",
"... | true |
even_neg._simp_1 | Mathlib.Algebra.Group.Even | [
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionMonoid",
"Even",
"propext",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"Eq",
"even_neg",
... | false |
PowerSeries.constantCoeff_substInvOfIsUnit | Mathlib.RingTheory.PowerSeries.Substitution | [
"CommRing",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"IsUnit",
"RingHom",
"PowerSeries.coeff",
"instOfNatNat",
"MvPowerSeries.instModule",
"PowerSeries.constantCoeff",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
"MvPowerSeries.instSemiring",
... | true |
Lean.Elab.Info.format | Lean.Elab.InfoTree.Main | [
"Lean.Elab.DelabTermInfo.format",
"Pure.pure",
"Lean.Elab.CompletionInfo.format",
"Lean.Elab.PartialTermInfo",
"Lean.Elab.CommandInfo.format",
"Lean.Elab.FieldRedeclInfo.format",
"Lean.Elab.DocElabInfo.format",
"Lean.Elab.PartialTermInfo.format",
"Monad.toApplicative",
"Lean.Elab.FieldRedeclInfo",... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.bicoloring_of_even._simp_3 | Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions | [
"Decidable",
"decide_eq_decide",
"Iff",
"propext",
"Bool",
"Decidable.decide",
"Eq"
] | false |
Int64.toISize_xor | Init.Data.SInt.Bitwise | [
"BitVec.instXorOp",
"congrArg",
"ISize.toBitVec_inj",
"Int64.toBitVec_xor",
"BitVec",
"Int64",
"instOfNatNat",
"System.Platform.numBits",
"instXorOpISize",
"ISize.toBitVec_xor",
"instXorOpInt64",
"Nat",
"congr",
"BitVec.signExtend_xor",
"True",
"HXor.hXor",
"ISize.toBitVec",
"eq_se... | true |
CategoryTheory.Limits.coprod.inl_snd_assoc | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.coprod.inl_snd",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.HasBinaryCoproduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.coprod.snd",
"Eq.mp",
"id",
"CategoryTheory.Li... | true |
_private.Mathlib.Algebra.Module.Submodule.Invariant.0.Module.End.invtSubmodule_inf_invtSubmodule_le_invtSubmodule_add.match_1_1 | Mathlib.Algebra.Module.Submodule.Invariant | [
"Sublattice",
"Submodule",
"Submodule.completeLattice",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"AddCommMonoid",
"And.casesOn",
"SetLike.coe",
"And.intro",
"Sublattice.instInf",
"Semiring",
"Sublattice.instSetLike",
"ConditionallyCompleteLattice.toLattice",
"Mod... | false |
_private.Mathlib.FieldTheory.Galois.Infinite.0.InfiniteGalois.restrict_fixedField._simp_1_6 | Mathlib.FieldTheory.Galois.Infinite | [
"Set.mem_inter_iff",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
Bool.not_eq_eq_eq_not | Init.SimpLemmas | [
"False",
"Bool.not_false",
"Bool.not",
"congrArg",
"False.elim",
"noConfusion_of_Nat",
"iff_self",
"Bool.ctorIdx",
"Bool.true",
"Iff",
"Bool.casesOn",
"congr",
"True",
"eq_self",
"Bool",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"congrFun'",
"Eq.symm",
"Bool.false",
"eq_false'",... | true |
MeasureTheory.OuterMeasure.map._proof_1 | Mathlib.MeasureTheory.OuterMeasure.Operations | [
"Eq.mpr",
"ENNReal.instAddCommMonoid",
"congrArg",
"MeasureTheory.OuterMeasure",
"id",
"LE.le",
"MeasureTheory.measure_iUnion_le",
"Set.preimage",
"tsum",
"MeasureTheory.OuterMeasure.instFunLikeSetENNReal",
"Nat",
"ENNReal.instLE",
"ENNReal",
"ENNReal.instTopologicalSpace",
"congrFun'",
... | false |
_private.Lean.Elab.Do.Control.0.Lean.Elab.Do.ControlStack.exceptT.stM | Lean.Elab.Do.Control | [
"Pure.pure",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT.instMonad",
"Lean.mkApp2",
"Lean.Expr",
"Lean.Level",
"Applicative.toPure",
"Lean.Elab.Do.MonadInfo.u",
"Lean.mkConst",
"List.cons",
"Lean.Elab.Do.ReturnCont.resultType",
"Lean.Elab.Do.MonadInfo",
"Lean.Elab.Term.TermElabM",
"Lean.... | true |
MeasureTheory.Measure.restrict_apply_self | Mathlib.MeasureTheory.Measure.Restrict | [
"MeasureTheory.Measure",
"MeasureTheory.Measure.restrict",
"MeasurableSpace",
"Set.Subset.rfl",
"ENNReal",
"Eq",
"DFunLike.coe",
"MeasureTheory.Measure.restrict_eq_self",
"MeasureTheory.Measure.instFunLike",
"Set"
] | true |
AlgebraicTopology.DoldKan.degeneraciesVanish_iff_QInfty_f_comp | Mathlib.AlgebraicTopology.DoldKan.Degeneracies | [
"AlgebraicTopology.DoldKan.PInfty_f_add_QInfty_f",
"AlgebraicTopology.DoldKan.σ_comp_PInfty_assoc",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"Opposite",
"instDecidableTrue",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Finset.univ",
"Nat.instOne",
"HomologicalComplex.Hom.f",
... | true |
Array.filter_empty | Init.Data.Array.Lemmas | [
"instOfNatNat",
"List.toArray",
"Array",
"Array.filter",
"Nat",
"Bool",
"OfNat.ofNat",
"Eq",
"Array.size",
"rfl",
"List.nil"
] | true |
_private.Plausible.Gen.0.Plausible.Gen.permutationOf._proof_7 | Plausible.Gen | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",... | false |
_private.Mathlib.Analysis.Normed.Unbundled.SpectralNorm.0.spectralNorm.spectralMulAlgNorm_eq_of_mem_roots._simp_1_3 | Mathlib.Analysis.Normed.Unbundled.SpectralNorm | [
"Polynomial.eval",
"Polynomial.IsRoot",
"Polynomial.IsRoot.def",
"Polynomial",
"propext",
"Semiring",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero",
"instMulZeroClassOfSemiring"
] | false |
HurwitzZeta.hasSum_int_oddKernel | Mathlib.NumberTheory.LSeries.HurwitzZetaOdd | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"HasSum.congr_fun",
"add_mul",
"Int.cast",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"HasSum.add",
"Mat... | true |
_private.Lean.Meta.Tactic.Grind.Theorems.0.Lean.Meta.Grind.Theorems.eraseDecl.match_1 | Lean.Meta.Tactic.Grind.Theorems | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Meta.Tactic.Grind.Theorems.0.Lean.Meta.Grind.Theorems.insert._sparseCasesOn_1",
"Array",
"Lean.Name",
"Option"
] | false |
CategoryTheory.PreZeroHypercover.pullbackCoverOfLeftIsoPullback₁._proof_3 | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.Limits.pullbackSymmetry",
"CategoryTheory.Limits.limit.π",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.PreZeroHypercover.pullbackCoverOfLeft._proof_1",
"CategoryTheory.Functor",
"CategoryTheory.PreZeroHy... | false |
Algebra.Extension.noConfusion | Mathlib.RingTheory.Extension.Basic | [
"CommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"HEq.refl",
"IsScalarTower",
"Algebra.Extension.noConfusionType",
"Algebra",
"RingHom",
"Algebra.toSMul",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Algebra.Extension",
"Se... | false |
Lean.Omega.Fin.lt_of_not_le | Init.Omega.Int | [
"LE.le",
"instLEFin",
"Nat",
"LT.lt",
"instLTFin",
"Lean.Omega.Fin.not_le",
"Iff.mp",
"Fin",
"Not"
] | true |
CategoryTheory.Limits.coproductIsCoproduct'._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.Products | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.Sigma.ι",
"id",
"CategoryTheory.Limits.HasCoproduct",
"CategoryTh... | false |
_private.Aesop.Tree.ExtractProof.0.Aesop.extractProofGoal.match_3 | Aesop.Tree.ExtractProof | [
"Option.ctorIdx",
"Aesop.RappRef",
"Option.some",
"Lean.MVarId",
"_private.Aesop.Tree.ExtractProof.0.Aesop.copyExprMVar._sparseCasesOn_3",
"Nat.hasNotBit",
"Prod.mk",
"Array",
"Prod",
"Prod.casesOn",
"Lean.Environment",
"Option"
] | false |
QuotientGroup.fintypeQuotientRightRel | Mathlib.GroupTheory.Coset.Card | [
"Group",
"QuotientGroup.instHasQuotientSubgroup",
"Subgroup",
"QuotientGroup.quotientRightRelEquivQuotientLeftRel",
"Fintype.ofEquiv",
"HasQuotient.Quotient",
"Fintype",
"Quotient",
"Equiv.symm",
"QuotientGroup.rightRel"
] | true |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.Reify.0.Lean.Meta.Grind.Arith.Linear.reify?.isOfNatZero | Lean.Meta.Tactic.Grind.Arith.Linear.Reify | [
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Arith.Linear.instMonadGetStructLinearM",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.Linear.LinearM.Context",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.State",
"Lean.Meta.isDefEqD",
"instMonadLiftT",
"Lean.Meta.Sym.Context",
"ReaderT.instMonad",... | true |
Lean.Omega.IntList.mul_get | Init.Omega.IntList | [
"Eq.mpr",
"HMul.hMul",
"_private.Init.Omega.IntList.0.List.getElem?_zipWith",
"congrArg",
"Option.casesOn",
"Option.getD",
"List.instGetElem?NatLtLength",
"Option.some",
"id",
"Int",
"Lean.Omega.IntList.instMul",
"_private.Init.Omega.IntList.0.List.getElem?_zipWith.match_1",
"Int.instMul",
... | true |
Lean.Elab.MonadAutoImplicits.casesOn | Lean.Elab.InfoTree.Types | [
"Lean.Elab.MonadAutoImplicits",
"Lean.Elab.MonadAutoImplicits.rec",
"Lean.Expr",
"Array",
"Lean.Elab.MonadAutoImplicits.mk"
] | false |
Batteries.RBNode.foldr_reverse | Batteries.Data.RBMap.Lemmas | [
"Batteries.RBNode",
"Eq.mpr",
"congrArg",
"flip",
"id",
"Batteries.RBNode.foldl",
"Batteries.RBNode.foldl_reverse",
"Batteries.RBNode.foldr",
"Batteries.RBNode.reverse_reverse",
"Batteries.RBNode.reverse",
"Eq.refl",
"congrFun'",
"Eq.symm",
"Eq",
"Eq.trans"
] | true |
lift_nhds_left | Mathlib.Topology.UniformSpace.Defs | [
"UniformSpace",
"Eq.mpr",
"SetRel",
"congrArg",
"uniformity",
"PartialOrder.toPreorder",
"Monotone",
"Function.comp",
"nhds",
"CompleteLattice.toConditionallyCompleteLattice",
"id",
"Prod.mk",
"Filter.comap_lift_eq2",
"UniformSpace.ball",
"Set.preimage",
"Filter.lift",
"eq_self",
"... | true |
Option.get!_none | Init.Data.Option.Lemmas | [
"Inhabited.default",
"Option.get!",
"Option.none",
"Inhabited",
"Eq",
"rfl"
] | true |
_private.Mathlib.Data.Set.Prod.0.Set.pi_inter_distrib._proof_1_1 | Mathlib.Data.Set.Prod | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"Set.ext",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Set.mem_inter_iff",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"Membership.m... | false |
sub_lt_comm | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"AddCommGroup.toAddCommMonoid",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"sub_lt_iff_lt_add'",
"SubNegMonoid.toSub",
"instHAdd",
"Iff",
"AddLeftStrictMono",
"instHSub",
"AddGroup.toS... | true |
SimpleGraph.Walk.take_add_eq | Mathlib.Combinatorics.SimpleGraph.Walk.Operations | [
"HEq.trans",
"heq_eqRec_iff_heq._simp_1",
"heq_eq_eq",
"SimpleGraph.Walk",
"Eq.rec",
"SimpleGraph",
"instHAdd",
"SimpleGraph.Walk.copy",
"HAdd.hAdd",
"SimpleGraph.Walk.take",
"SimpleGraph.Walk.take_add_heq",
"SimpleGraph.Walk.drop_getVert",
"Nat",
"True",
"eq_self",
"of_eq_true",
"eq... | true |
PadicInt.withValIntegersRingEquiv | Mathlib.NumberTheory.Padics.WithVal | [
"Int.instAddCommGroup",
"NormedCommRing.toNormedRing",
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"Nat.Prime",
"NormedRing.toRing",
"Subring.instSetLike",
"PadicInt",
"Valued.integer",
"CommSemiring.toSemiring",
"instCommRingPadic",
"Int.instLinearOrder",
"Rat",
"PartialOrder.t... | true |
DiscreteTiling.PlacedTile.coe_nonempty_iff | Mathlib.Combinatorics.Tiling.Tile | [
"Quotient.out_eq'",
"Eq.mpr",
"instHSMul",
"DiscreteTiling.Protoset.tiles",
"Quotient.liftOn'_mk''",
"Quotient.liftOn'",
"Subgroup.map",
"congrArg",
"Subgroup.subtype",
"Group",
"DiscreteTiling.PlacedTile.mk",
"Quotient.mk''",
"Membership.mem",
"QuotientGroup.leftRel",
"DiscreteTiling.Pl... | true |
Std.PRange.Least?.recOn | Init.Data.Range.Polymorphic.UpwardEnumerable | [
"Std.PRange.Least?.mk",
"Std.PRange.Least?.rec",
"Std.PRange.Least?",
"Option"
] | false |
ContinuousMap.Homotopy.casesOn | Mathlib.Topology.Homotopy.Basic | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"Membership.mem",
"Real.semiring",
"Set.Elem",
"Prod.mk",
"TopologicalSpace",
"ContinuousMap.Homotopy",
"One.toOfNat1",
"Zero.toOfNa... | false |
AddHomClass.toAddHom.eq_1 | Mathlib.Algebra.Group.Hom.Defs | [
"AddHom",
"AddHomClass.map_add",
"AddHomClass.toAddHom",
"AddHomClass",
"Eq.refl",
"AddHom.mk",
"Eq",
"DFunLike.coe",
"Add",
"FunLike"
] | true |
TopologicalSpace.NonemptyCompacts.coe_map | Mathlib.Topology.Sets.Compacts | [
"TopologicalSpace.NonemptyCompacts.instSetLike",
"Continuous",
"TopologicalSpace.NonemptyCompacts",
"TopologicalSpace",
"SetLike.coe",
"Set.image",
"TopologicalSpace.NonemptyCompacts.map",
"Eq",
"rfl",
"Set"
] | true |
_private.Mathlib.Analysis.InnerProductSpace.GramMatrix.0.Matrix.posSemidef_opNorm_smul_gram_sub_gram._proof_1_3 | Mathlib.Analysis.InnerProductSpace.GramMatrix | [
"NormedCommRing.toNormedRing",
"Finsupp.instFunLike",
"InnerProductSpace.toNormedSpace",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedRing.toRing",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Lean.... | false |
Std.PreorderPackage.ofLE._proof_3 | Init.Data.Order.PackageFactories | [
"Std.Packages.PreorderOfLEArgs.le_trans",
"Std.IsPreorder",
"Std.Packages.PreorderOfLEArgs.le_refl",
"Std.IsPreorder.mk",
"Std.Packages.PreorderOfLEArgs.le",
"Std.Packages.PreorderOfLEArgs"
] | false |
_private.Mathlib.Analysis.Convex.Function.0.strictConvexOn_iff_div._simp_1_1 | Mathlib.Analysis.Convex.Function | [
"Preorder.toLT",
"One",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"ZeroLEOneClass",
"zero_lt_one",
"LT.lt",
"True",
"eq_true",
"One.toOfNat1",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
Subring.mem_mk'._simp_1 | Mathlib.Algebra.Ring.Subring.Defs | [
"Subring.instSetLike",
"AddGroupWithOne.toAddGroup",
"Membership.mem",
"NonAssocSemiring.toMulZeroOneClass",
"NonAssocRing",
"MulZeroOneClass.toMulOneClass",
"AddSubgroup",
"NonAssocRing.toAddCommGroupWithOne",
"SetLike.coe",
"Subring",
"AddSubgroup.instSetLike",
"Subring.mk'",
"propext",
... | false |
instPartialOrderGroupCone | Mathlib.Algebra.Order.Group.Cone | [
"PartialOrder.ofSetLike",
"GroupCone.instSetLike",
"PartialOrder",
"CommGroup",
"GroupCone"
] | true |
CategoryTheory.Abelian.SpectralObject.cokernelSequenceCycles_f | Mathlib.Algebra.Homology.SpectralObject.Cycles | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Abelian",
"CategoryTheory.ComposableArrows",
"Preorder.smallCategory",
"instOfNat... | true |
IsLowerSet.null_frontier | Mathlib.MeasureTheory.Order.UpperLower | [
"instWeaklyLocallyCompactSpaceOfLocallyCompactSpace",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"frontier_compl",
"NormedCommRing.toSeminormedCommRing",
"frontier",
"locallyCompact_of_proper",
"False",
"Real.instLE",
"Real",
"Set.Ioi",
"MeasureTheory.Measure",
"instHDiv",
"instIsAddHaar... | true |
_private.Aesop.RuleSet.0.Aesop.BaseRuleSet.merge.match_1 | Aesop.RuleSet | [
"Unit.unit",
"Aesop.RuleName",
"Option.casesOn",
"Option.some",
"Aesop.RuleName.instBEq",
"Option.none",
"Unit",
"Aesop.UnorderedArraySet",
"Option"
] | false |
MulEquiv.symmEquiv_apply_apply | Mathlib.Algebra.Group.Equiv.Defs | [
"MulEquiv.instEquivLike",
"Equiv.instEquivLike",
"Mul",
"Equiv",
"MulEquiv.symmEquiv",
"MulEquiv",
"Eq.refl",
"MulEquiv.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
CategoryTheory.Oplax.OplaxTrans.naturality_comp_assoc | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Oplax.OplaxTrans.naturality_comp",
"CategoryTheory.OplaxFunctor.mapComp",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"Eq.mp",
"CategoryTheory.Bicategory.whiskerRight",
"id",
"... | true |
MeasureTheory.measureUnivNNReal | Mathlib.MeasureTheory.Measure.Typeclasses.Finite | [
"MeasureTheory.Measure",
"Set.univ",
"NNReal",
"ENNReal.toNNReal",
"MeasurableSpace",
"ENNReal",
"DFunLike.coe",
"MeasureTheory.Measure.instFunLike",
"Set"
] | true |
Lean.Server.Watchdog.handleDidChange | Lean.Server.Watchdog | [
"Pure.pure",
"Unit.unit",
"Lean.Server.DocumentMeta.uri",
"Lean.Server.DocumentMeta.mk",
"Lean.Lsp.VersionedTextDocumentIdentifier.version?",
"Lean.Server.Watchdog.ServerM",
"String",
"Lean.JsonRpc.Notification.mk",
"Lean.FileMap",
"Lean.Server.Watchdog.FileWorker.state",
"IO",
"Option.getD",
... | true |
isPRadical_iff | Mathlib.FieldTheory.IsPerfectClosure | [
"RingHom.instRingHomClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingHom",
"Exists",
"Submodule.instPartialOrder",
"pNilradical",
"LE.le",
"IsPRadical.casesOn",
"Ideal",
"Monoid.toPow",
"And.casesOn",
"CommSemiri... | true |
Filter.Tendsto.nonpos_add_atBot | Mathlib.Order.Filter.AtTopBot.Monoid | [
"AddMonoid.toAddZeroClass",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"Pi.instZero",
"Filter.Eventually.of_forall",
"LE.le",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"Filter.Tendsto",
"Filter.atBot",
"AddZero.toAdd",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"Of... | true |
MeasureTheory.eLpNorm_conj | Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity | [
"Norm.norm",
"_private.Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity.0.MeasureTheory.eLpNorm_conj._simp_1_1",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.Measure",
"RCLike.norm_conj",
"congrArg",
"CommSemiring.toSemiring",
"Pi.starRing'",
"PseudoMetricSpace.toUniformSpac... | true |
Std.Internal.IO.Process.ResourceUsageStats.casesOn | Std.Internal.Async.Process | [
"UInt64",
"Std.Internal.IO.Process.ResourceUsageStats.mk",
"Std.Time.Millisecond.Offset",
"Std.Internal.IO.Process.ResourceUsageStats",
"Std.Internal.IO.Process.ResourceUsageStats.rec"
] | false |
String.Pos.toSlice_nextn | Init.Data.String.Lemmas.Basic | [
"String.Pos.nextn_toSlice",
"String.toSlice",
"String",
"String.Pos.toSlice",
"Nat",
"String.Pos",
"String.Slice.Pos",
"String.Slice.Pos.nextn",
"Eq.symm",
"Eq",
"String.Pos.nextn"
] | true |
_private.Mathlib.RingTheory.SimpleModule.Isotypic.0.Submodule.le_linearEquiv_of_sSup_eq_top.match_1_3 | Mathlib.RingTheory.SimpleModule.Isotypic | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"Submodule.completeLattice",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"Subtype",
"Ne",
"Submodule.mo... | false |
IsNilpotent.charpoly_eq_X_pow_finrank | Mathlib.LinearAlgebra.Eigenspace.Zero | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"AlgEquiv.instEquivLike",
"IsDomain",
"CommRing",
"IsDomain.to_noZeroDivisors",
"Module.End.instMonoid",
"Semiring.toModule",
"instSMulOfMul",
"Matrix.module",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"sub_eq_zero",
"A... | true |
Lean.Meta.DefEqCacheKind.toCtorIdx | Lean.Meta.ExprDefEq | [
"Nat",
"Lean.Meta.DefEqCacheKind.ctorIdx",
"Lean.Meta.DefEqCacheKind"
] | false |
Std.TreeSet.get?_erase | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"instDecidableEqOrdering",
"Ordering",
"Std.TreeSet.inner",
"Ordering.eq",
"Std.TransCmp",
"Option.none",
"Unit",
"Std.TreeSet.get?",
"Std.TreeSet.erase",
"Eq",
"Std.TreeMap.getKey?_erase",
"Option",
"ite"
] | true |
Std.Internal.IndexMultiMap.getAll? | Std.Internal.Http.Internal.IndexMultiMap | [
"Std.Internal.IndexMultiMap.instMembership",
"Option.some",
"Membership.mem",
"Std.Internal.IndexMultiMap.instDecidableMem",
"dite",
"Std.Internal.IndexMultiMap.getAll",
"Array",
"Option.none",
"Hashable",
"Std.Internal.IndexMultiMap",
"BEq",
"Not",
"Option"
] | true |
Subsemiring.instCompleteLattice._proof_2 | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"Subsemiring.instSetLike",
"Membership.mem",
"Subsemiring",
"And",
"NonAssocSemiring",
"SetLike.coe",
"And.left",
"Set.instMembership",
"Set"
] | false |
BitVec.toInt_neg_of_msb_true | Init.Data.BitVec.Lemmas | [
"_private.Init.Data.BitVec.Lemmas.0.BitVec.toInt_neg_of_msb_true._proof_1_2",
"instPowNat",
"HMul.hMul",
"HSub.hSub",
"BitVec.msb_eq_true_iff_two_mul_ge",
"BitVec",
"GE.ge",
"id",
"instMulNat",
"instOfNatNat",
"Int",
"BitVec.toNat",
"instLENat",
"Nat.cast",
"instNatPowNat",
"Int.instLT... | true |
CategoryTheory.Limits.HasZeroObject.instMono | Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects | [
"CategoryTheory.Limits.HasZeroObject.to_zero_ext",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Mono.mk",
"CategoryTheory.Limits.HasZeroObject",
"CategoryTheory.CategoryStruct.comp",
"Zero.toOfNat0",
"CategoryTheory.Category.toCategoryStruct",
"OfN... | true |
Qq.getLevelQ | Mathlib.Util.Qq | [
"Pure.pure",
"Lean.Meta.State",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Expr.sort",
"Lean.Level",
"Lean.Meta.getLevel",
"Applicative.toPure",
"Qq.Quoted",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"Monad.toBind",
"Bind.bind",
"... | true |
_private.Mathlib.RingTheory.Jacobson.Ideal.0.Ideal.jacobson_eq_top_iff.match_1_3 | Mathlib.RingTheory.Jacobson.Ideal | [
"Semiring.toModule",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"And.casesOn",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"And",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"And.intro",
"Ideal.IsMaximal",
"... | false |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.0.Nat.NatOffset.ctorElim | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat | [
"_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.0.Nat.NatOffset.casesOn",
"_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.0.Nat.NatOffset",
"Lean.Expr",
"_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.0.Nat.NatOffset.const",
"_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Nat.0.Nat.NatOffset.off... | false |
CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse_assoc | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Equivalence.counitInv_app_tensor_comp_functor_map_δ_inverse",
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functo... | true |
_private.Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue.0.MeasureTheory.Measure.add_sub_of_mutuallySingular._abel_1_1 | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | [
"MeasureTheory.Measure",
"Compl.compl",
"AddMonoid.toAddZeroClass",
"Mathlib.Tactic.Abel.subst_into_add",
"Mathlib.Tactic.Abel.term",
"HSub.hSub",
"MeasureTheory.Measure.instSub",
"MeasureTheory.Measure.restrict",
"instOfNatNat",
"MeasureTheory.Measure.instZero",
"zero_add",
"Set.instCompl",
... | false |
Std.DTreeMap.Raw.min?_keys | Std.Data.DTreeMap.Raw.Lemmas | [
"List.min?",
"Std.LawfulOrderMin",
"Std.LawfulOrderLeftLeaningMin",
"Ord.mk",
"Std.DTreeMap.Raw.minKey?",
"Ordering",
"Std.DTreeMap.Raw.keys",
"Std.TransCmp",
"LE",
"Min",
"Std.DTreeMap.Raw.WF.out",
"Std.LawfulEqCmp",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Internal.Impl.min?_keys",
"Std... | true |
UpperSet.instAddCommMonoid._proof_1 | Mathlib.Algebra.Order.UpperLower | [
"UpperSet",
"AddCommGroup.toAddCommMonoid",
"Preorder.toLE",
"AddCommGroup",
"AddCommSemigroup.toAddSemigroup",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"UpperSet.addCommSemigroup",
"Eq",
"IsOrderedAddMonoid",
"Preorder",
"AddCommSemigroup.add_comm"
] | false |
_private.Mathlib.Topology.UniformSpace.Closeds.0.UniformSpace.hausdorff.uniformContinuous_prod.match_1_1 | Mathlib.Topology.UniformSpace.Closeds | [
"Filter.instMembership",
"UniformSpace",
"uniformity",
"Membership.mem",
"Prod.mk",
"Prod.fst",
"And.casesOn",
"And",
"And.intro",
"Prod",
"Prod.snd",
"Filter",
"Set"
] | false |
IntermediateField.subsingleton_of_rank_adjoin_eq_one | Mathlib.FieldTheory.IntermediateField.Adjoin.Basic | [
"IntermediateField.instPartialOrder",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"Cardinal.instOne",
"CommRing.toNonUnitalCommRing",
"Cardinal",
"IntermediateField",
"IntermediateField.toField",
"Algebra",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"Algebra.toMo... | true |
Aesop.GoalWithMVars.ctorIdx | Aesop.Script.GoalWithMVars | [
"Aesop.GoalWithMVars",
"Nat"
] | false |
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