name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
MvPolynomial.eval₂_zero'_apply | Mathlib.Algebra.MvPolynomial.Eval | [
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"RingHom",
"MvPolynomial.eval₂",
"MvPolynomial.eval₂_zero_apply",
"CommSemiring",
"RingHom.instFunLike",
"Nat",
"MvPolynomial",
"Zero.toOfNat0",
"AddMonoidAlgebra... | true |
DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk | Mathlib.RingTheory.Ideal.Quotient.Operations | [
"CommRing",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"RingEquiv.instEquivLike",
"RingHom",
"SemilatticeSup.toMax",
"Algebra.id",
"Distrib.toAdd",
"Ideal.map",
"DoubleQuot.quotQuotMk",
"Ideal",
"instDistribOfSemiring",
"IdemSemiring.toSemilatticeSup",
"HasQuotient.Quotient",
"Ideal... | true |
Submodule.subtypeₗᵢ_toLinearMap | Mathlib.Analysis.Normed.Operator.LinearIsometry | [
"Submodule",
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"Membership.mem",
"Subtype",
"Submodule.module",
"LinearMap",
"SeminormedAddCommGroup.toAddCommGroup",
"LinearIsometry.toLinearMap",
"Submodule.setLike",
"Submodule.subtype",
"Submodule.seminormedAddCommGroup",
"Module",
... | true |
ZFSet.Definable₁._proof_1 | Mathlib.SetTheory.ZFC.Basic | [
"Zero.ofOfNat0",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"NeZero",
"OfNat.ofNat"
] | false |
CategoryTheory.MorphismProperty.instHasOfPostcompPropertyIsomorphismsOfRespectsIso | Mathlib.CategoryTheory.MorphismProperty.Composition | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.HasOfPostcompProperty.mk",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.isomorphisms",
"CategoryTheory.MorphismProperty.HasOfPostcompProperty",
"CategoryTheory.Morphi... | true |
Finset.le_sum_of_subadditive | Mathlib.Algebra.Order.BigOperators.Group.Finset | [
"Multiset.sum",
"Multiset.map",
"instReflLe",
"congrArg",
"Finset",
"Std.le_refl",
"AddMonoid.toAddZeroClass",
"Preorder.toLE",
"Function.comp",
"Membership.mem",
"AddZeroClass.toAddZero",
"Multiset",
"LE.le",
"Finset.val",
"AddCommMonoid",
"AddZero.toZero",
"Multiset.instMembership"... | true |
IntermediateField.fixedField.algebra._proof_10 | Mathlib.FieldTheory.Galois.Basic | [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"RingHom.mk",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField.fixedField.algebra._proof_9",
"CommSemiring.toSemirin... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.get?_inter._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
ArchimedeanClass.mk_eq_zero_of_archimedean | Mathlib.Algebra.Order.Ring.Archimedean | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"ArchimedeanClass.mk_eq_mk_of_archimedean",
"CommSemiring.toSemiring",
"NeZero.charZero_one",
"LinearOrder",
"AddGroupWithOne.toAddMonoidWithOne",
"IsStrictOrderedRing",
"SemilatticeInf.toPartialOrder",
... | true |
Lean.Compiler.LCNF.Closure.Context.mk.injEq | Lean.Compiler.LCNF.Closure | [
"Eq.propIntro",
"Lean.Compiler.LCNF.Closure.Context",
"Lean.injEq_helper",
"Lean.FVarId",
"And",
"Lean.Compiler.LCNF.Closure.Context.mk.inj",
"Bool",
"Eq.ndrec",
"Lean.Compiler.LCNF.Closure.Context.mk",
"Eq.refl",
"Eq"
] | true |
Lean.Parser.Term.termUnless._regBuiltin.Lean.Parser.Term.termUnless.docString_3 | Lean.Parser.Do | [
"Lean.addBuiltinDocString",
"IO",
"Unit",
"Lean.Name.mkStr4"
] | false |
Set.inv_prod | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Prod.instInv",
"Set.instSProd",
"Inv",
"SProd.sprod",
"Inv.inv",
"Set.inv",
"Prod",
"Eq",
"rfl",
"Set"
] | true |
FP.Float.recOn | Mathlib.Data.FP.Basic | [
"FP.Float.nan",
"Int",
"FP.FloatCfg",
"FP.Float",
"FP.Float.inf",
"Nat",
"FP.ValidFinite",
"Bool",
"FP.Float.finite",
"FP.Float.rec"
] | false |
Lean.Lsp.TextDocumentEdit.noConfusion | Lean.Data.Lsp.Basic | [
"Lean.Lsp.TextDocumentEdit.casesOn",
"Lean.Lsp.TextEditBatch",
"Lean.Lsp.VersionedTextDocumentIdentifier",
"Lean.Lsp.TextDocumentEdit",
"Eq.ndrec",
"Eq.refl",
"Lean.Lsp.TextDocumentEdit.noConfusionType",
"Eq"
] | false |
HasFPowerSeriesWithinAt.comp_sub | Mathlib.Analysis.Analytic.Basic | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"HasFPowerSeriesWithinOnBall",
"NormedSpace.toModule",
"AddMonoid.t... | true |
_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.casesOn | Lean.Meta.Tactic.Grind.Types | [
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.eq",
"Lean.Meta.Grind.ParentSet",
"Lean.Expr",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.nil",
"Nat",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPr... | false |
NonemptyChain.ext | Mathlib.Order.BourbakiWitt | [
"HEq.refl",
"_private.Mathlib.Order.BourbakiWitt.0.NonemptyChain.ext.match_1",
"Eq.casesOn",
"LE.le",
"LE",
"Set.Nonempty",
"IsChain",
"NonemptyChain.carrier",
"Eq.ndrec",
"Eq.refl",
"HEq",
"NonemptyChain.mk",
"Eq.symm",
"Eq",
"NonemptyChain",
"Set"
] | true |
Nat.mapsTo_digitsAppend | Mathlib.Data.Nat.Digits.Lemmas | [
"Eq.mpr",
"congrArg",
"Nat.instMonoid",
"Nat.digitsAppend",
"setOf",
"Nat.lt_of_mem_digitsAppend",
"Membership.mem",
"id",
"instOfNatNat",
"Nat.length_digitsAppend",
"Monoid.toPow",
"List",
"And",
"HPow.hPow",
"List.instMembership",
"Set.MapsTo",
"Nat",
"And.intro",
"LT.lt",
"E... | true |
Icc_mem_nhdsGE | Mathlib.Topology.Order.OrderClosed | [
"Filter.instMembership",
"Eq.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"le_rfl",
"Set.Ici",
"ClosedIciTopology",
"congrArg",
"LinearOrder",
"nhdsWithin",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Eq.mp",
"DistribLattice.toLattice",
"id",
"Icc_... | true |
CategoryTheory.Pi.equivalenceOfEquiv._proof_4 | Mathlib.CategoryTheory.Pi.Basic | [
"CategoryTheory.Functor",
"Equiv.apply_symm_apply",
"CategoryTheory.Pi.evalCompEqToEquivalenceFunctor",
"CategoryTheory.Pi.equivalenceOfEquiv._proof_1",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Equiv.symm_apply_apply",
"CategoryTheory.eqToHom_map"... | false |
CategoryTheory.Oplax.OplaxTrans.Modification.mk.injEq | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.propIntro",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Oplax.OplaxTrans.Modification.mk",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFuncto... | true |
ContinuousEval.rec | Mathlib.Topology.Hom.ContinuousEval | [
"Continuous",
"ContinuousEval",
"instTopologicalSpaceProd",
"Prod.fst",
"TopologicalSpace",
"ContinuousEval.mk",
"Prod",
"Prod.snd",
"DFunLike.coe",
"FunLike"
] | false |
Std.Rii.Sliceable.casesOn | Init.Data.Slice.Notation | [
"Std.Rii.Sliceable",
"Std.Rii.Sliceable.rec",
"Std.Rii.Sliceable.mk",
"Std.Rii"
] | false |
AddAction.period_dvd_addOrderOf | Mathlib.GroupTheory.GroupAction.Period | [
"Eq.mpr",
"instHSMul",
"Dvd.dvd",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"addOrderOf",
"AddMonoid.toNSMul",
"AddAction.period",
"AddZeroClass.toAddZero",
"id",
"HVAdd.hVAdd",
"AddAction.nsmul_vadd_eq_iff_period_dvd",
"AddAction",
"AddZero.toZero",
"AddActio... | true |
Algebra.TensorProduct.mapOfCompatibleSMul' | Mathlib.RingTheory.TensorProduct.Maps | [
"TensorProduct.CompatibleSMul",
"CommSemiring.toSemiring",
"AlgHom",
"Algebra",
"Algebra.toSMul",
"Algebra.toModule",
"Algebra.TensorProduct.leftAlgebra",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Algebra.TensorProduct.mapOfCompatibleSMul",
"NonAssocSemiring.toNonUnitalNonAss... | true |
Polynomial.cancelLeads | Mathlib.Algebra.Polynomial.CancelLeads | [
"Polynomial.C",
"HMul.hMul",
"HSub.hSub",
"RingHom",
"Polynomial.leadingCoeff",
"instSubNat",
"Polynomial",
"Monoid.toPow",
"RingHom.instFunLike",
"instHSub",
"HPow.hPow",
"Polynomial.semiring",
"Nat",
"Polynomial.instSub",
"Semiring.toMonoid",
"Polynomial.instMul",
"instHPow",
"Po... | true |
Int.ofNat_one | Init.Data.Int.Basic | [
"instOfNatNat",
"Int",
"Nat.cast",
"instOfNat",
"Nat",
"instNatCastInt",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
BitVec.reduceExtractLsb'._regBuiltin.BitVec.reduceExtractLsb'.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec.3865625001._hygCtx._hyg.19 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | [
"BitVec.reduceExtractLsb'",
"IO",
"Bool.true",
"Unit",
"Lean.Meta.Simp.addSEvalprocBuiltinAttr",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.Simproc"
] | false |
_private.Std.Sat.CNF.Basic.0.Std.Sat.CNF.VarMem_add._simp_1 | Std.Sat.CNF.Basic | [
"Std.Sat.CNF",
"Std.Sat.CNF.Clause.Mem",
"Std.Sat.CNF.VarMem",
"Std.Sat.CNF.add",
"propext",
"Std.Sat.CNF.Clause",
"Std.Sat.CNF.VarMem_add",
"Or",
"Eq"
] | false |
CochainComplex.HomComplex.instAddCommGroupCohomologyClass._proof_16 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexCohomology | [
"CochainComplex.HomComplex.coboundaries",
"AddMonoid.toAddSemigroup",
"CochainComplex.HomComplex.instAddCommGroupCohomologyClass._proof_6",
"CochainComplex.HomComplex.instAddCommGroupCohomologyClass._aux_8",
"Add.mk",
"Neg.mk",
"CochainComplex.HomComplex.instAddCommGroupCohomologyClass._proof_10",
"Ad... | false |
CauSeq.instSub._proof_1 | Mathlib.Algebra.Order.CauSeq.Basic | [
"NegZeroClass.toNeg",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CauSeq.instNeg",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"IsStrictOrderedRing",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZero",
"DistribLattice.toLattice",
"Distrib.toAdd",
"Subtra... | false |
_private.Init.Data.Array.Range.0.Array.range_succ_eq_map._proof_1_3 | Init.Data.Array.Range | [
"Array.instAppend",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"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.ofNat_sub_dichotomy",
"Lean.Omega.Int.... | false |
_private.Std.Internal.Http.Data.Headers.0.Std.Http.Headers.filterMap.match_1 | Std.Internal.Http.Data.Headers | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Std.Http.Header.Value",
"Unit",
"Option"
] | false |
Polynomial.isUnit_map | Mathlib.Algebra.Polynomial.FieldDivision | [
"_private.Mathlib.Algebra.Polynomial.FieldDivision.0.Polynomial.isUnit_map._simp_1_1",
"Eq.mpr",
"Nat.instMulZeroClass",
"WithBot",
"congrArg",
"WithBot.zero",
"IsUnit",
"RingHom",
"Field.toDivisionRing",
"id",
"DivisionRing.toRing",
"Polynomial.degree",
"Field.toSemifield",
"Polynomial",
... | true |
modularCyclotomicCharacter.aux_spec | Mathlib.NumberTheory.Cyclotomic.CyclotomicCharacter | [
"Units.val",
"IsDomain",
"Exists.choose_spec",
"Nat.instMulZeroClass",
"CommRing",
"modularCyclotomicCharacter.aux",
"rootsOfUnity.integer_power_of_ringEquiv",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"DivInvMonoid.toZPow",
"Membership.mem",
"Units",
"Subtype",
"Distrib.toAdd"... | true |
infIccOrderIsoIccSup | Mathlib.Order.ModularLattice | [
"Lattice",
"Lattice.toSemilatticeSup",
"infIccOrderIsoIccSup._proof_3",
"RelIso.mk",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"Equiv.mk",
"Set.Elem",
"OrderIso",
"SemilatticeInf.toMin",
"LE.le",
"Subtype.mk",
... | true |
Lean.Meta.RecursorUnivLevelPos.recOn | Lean.Meta.RecursorInfo | [
"Lean.Meta.RecursorUnivLevelPos.rec",
"Lean.Meta.RecursorUnivLevelPos.motive",
"Lean.Meta.RecursorUnivLevelPos",
"Nat",
"Lean.Meta.RecursorUnivLevelPos.majorType"
] | false |
Module.Relations.Solution.directSumEquiv._proof_7 | Mathlib.Algebra.Module.Presentation.DirectSum | [
"Module.Relations.Solution.directSumEquiv._proof_6",
"Module.Relations.Solution.directSumEquiv._proof_5",
"Function.LeftInverse",
"Semiring.toModule",
"Finsupp.module",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup",
"Module.Relations.Solution.directSumEquiv.match_3",
"Mod... | false |
NumberField.HeightOneSpectrum.adicAbv.congr_simp | Mathlib.NumberTheory.NumberField.Completion.FinitePlace | [
"NumberField.HeightOneSpectrum.adicAbv",
"Real.partialOrder",
"Real",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"IsFractionRing",
"IsDedekindDomain.HeightOneSpectrum",
"Algebra",
"Eq.rec",
"Real.semiring",
"NonUnitalNonAssocRing.toNonUnitalNon... | true |
WithZero.instCommMonoidWithZero._proof_1 | Mathlib.Algebra.GroupWithZero.WithZero | [
"Semigroup.toMul",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"CommSemigroup.mul_comm",
"WithZero.instCommSemigroup",
"CommSemigroup.toSemigroup",
"WithZero",
"Eq",
"CommMonoid",
"instHMul"
] | false |
Array.instDecidableForallForallMemOfDecidablePred._proof_3 | Init.Data.Array.Lemmas | [
"Eq.mpr",
"congrArg",
"Array.instMembership",
"Membership.mem",
"Exists",
"id",
"_private.Init.Data.Array.Lemmas.0.Array.instDecidableForallForallMemOfDecidablePred._simp_1",
"_private.Init.Data.Array.Lemmas.0.Array.instDecidableForallForallMemOfDecidablePred._simp_2",
"Array",
"GetElem.getElem",
... | false |
Ordnode.All.eq_2 | Mathlib.Data.Ordmap.Invariants | [
"Ordnode",
"Ordnode.node",
"And",
"Nat",
"Ordnode.All",
"Eq.refl",
"Eq"
] | true |
OrderMonoidWithZeroHom.toFun_eq_coe | Mathlib.Algebra.Order.Hom.MonoidWithZero | [
"ZeroHom.toFun",
"OrderMonoidWithZeroHom",
"MonoidWithZeroHom.toZeroHom",
"MulZeroOneClass",
"MulZeroOneClass.toMulZeroClass",
"Eq",
"DFunLike.coe",
"rfl",
"Preorder",
"MulZeroClass.toZero",
"OrderMonoidWithZeroHom.toMonoidWithZeroHom",
"OrderMonoidWithZeroHom.instFunLike"
] | true |
WithCStarModule.equivL_apply | Mathlib.Analysis.CStarAlgebra.Module.Synonym | [
"UniformSpace",
"Equiv.instEquivLike",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Equiv",
"WithCStarModule.instUniformSpace",
"ContinuousLinearEquiv.equivLike",
"WithCStarModule.equivL",
"WithCStarModule.instModule",
"WithCStarModule",
"WithCStarModule.instAddCommGroup",
"ContinuousLinea... | true |
Std.DTreeMap.Internal.RccSliceData.noConfusionType | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"HEq",
"Std.DTreeMap.Internal.RccSliceData.casesOn",
"Std.Rcc",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.RccSliceData"
] | false |
WellFoundedGT.toOrderTop | Mathlib.Order.WellFounded | [
"Preorder.toLT",
"WellFoundedGT.toOrderTop._proof_3",
"Lattice.toSemilatticeSup",
"LinearOrder",
"Set.univ",
"WellFoundedGT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.univ_nonempty",
"DistribLattice.toLattice",
"Top.mk",
"OrderTop.mk",
"OrderTop",
"WellFounded.min",
"LT.lt",
"N... | true |
CategoryTheory.leftDistributor_inv | Mathlib.CategoryTheory.Monoidal.Preadditive | [
"CategoryTheory.Limits.biproduct.bicone",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Limits.biproduct.ι_π_assoc",
"dite_congr",
"instDecidableTrue",
"Finset.univ",
"CategoryTheory.leftDistributor._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg... | true |
AddMonoidHom.ofMapAddNeg._proof_2 | Mathlib.Algebra.Group.Hom.Basic | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"add_neg_cancel",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"neg_neg",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"zero_add",
"... | false |
Lean.Grind.CommRing.Mon.denote_mulPow_nc | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Power",
"Lean.Grind.CommRing.Mon.mult",
"HMul.hMul",
"congrArg",
"Lean.Grind.CommRing.Mon.mulPow_nc",
"Lean.Grind.Semiring.pow_add",
"Lean.Grind.CommRing.Power.x",
"Eq.mp",
"id",
"Lean.Grind.CommRing.Power.denote_eq",
"Lean.Grind.Semiring.toMul",
"instBEqOfDecidableEq",
... | true |
_private.Lean.Compiler.LCNF.ToImpure.0.Lean.Compiler.LCNF.lowerLet._sparseCasesOn_11 | Lean.Compiler.LCNF.ToImpure | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
Batteries.RBNode.balLeft._sparseCasesOn_1.else_eq | Batteries.Data.RBMap.WF | [
"Batteries.RBColor.casesOn",
"Batteries.RBNode.balLeft._sparseCasesOn_1",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Batteries.RBColor.ctorIdx",
"Bool.true",
"Nat.land",
"absurd",
"Batteries.RBColor.red",
"Batteries.RBColor",
"Nat",
"Bool",
"Eq.ndrec",
"Nat.eq_of_beq_eq_true",
... | false |
Int32.neg_one_and | Init.Data.SInt.Bitwise | [
"Eq.mpr",
"Int32.toBitVec",
"BitVec.instAndOp",
"instAndOpInt32",
"congrArg",
"Int32.toBitVec_neg",
"Int32.toBitVec_inj",
"BitVec.neg_one_eq_allOnes",
"BitVec.allOnes",
"BitVec",
"id",
"instOfNatNat",
"BitVec.ofNat",
"BitVec.instNeg",
"Nat",
"Int32.toBitVec_one",
"propext",
"Int32.... | true |
ModuleCat.restrictScalars_μ_tmul | Mathlib.Algebra.Category.ModuleCat.Monoidal.Adjunction | [
"Eq.mpr",
"ModuleCat.instMonoidalExtendScalars",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"CommRing.toNonUnitalCommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"ModuleCat.extendRestrictScalarsAdj_homEqu... | true |
instReprTupleOfRepr | Init.Data.Repr | [
"ReprTuple.mk",
"ReprTuple",
"List.cons",
"List",
"Std.Format",
"Repr",
"repr"
] | true |
Lean.Language.SnapshotTree.foldSnaps.Control.recOn | Lean.Server.Requests | [
"Lean.Language.SnapshotTree.foldSnaps.Control.rec",
"Lean.Language.SnapshotTree.foldSnaps.Control.done",
"Lean.Language.SnapshotTree.foldSnaps.Control",
"Bool",
"Lean.Language.SnapshotTree.foldSnaps.Control.proceed"
] | false |
_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.MvPolynomialC.degBound_le_degBound.match_1 | Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | [
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"Nat.zero",
"instLTNat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
ByteArray.forIn.loop._proof_2 | Init.Data.ByteArray.Basic | [
"ByteArray.forIn._proof_1",
"HSub.hSub",
"Nat.zero_lt_of_lt",
"Nat.sub_lt",
"instSubNat",
"instOfNatNat",
"instHSub",
"Nat",
"LT.lt",
"instLTNat",
"ByteArray",
"OfNat.ofNat",
"ByteArray.size"
] | false |
_private.Lean.Compiler.NameMangling.0.String.mangleAux._unary._proof_2 | Lean.Compiler.NameMangling | [
"String.Pos.next",
"String",
"invImage",
"String.push",
"PSigma.casesOn",
"id",
"String.instLTPos",
"LT.lt",
"String.endPos",
"String.Pos",
"PSigma.mk",
"of_eq_true",
"String.Pos.lt_next._simp_1",
"String.Pos.instWellFoundedRelation",
"PSigma",
"Eq",
"Not",
"String.Pos.get"
] | false |
Order.PartialIso.comm._proof_2 | Mathlib.Order.CountableDenseLinearOrder | [
"Preorder.toLT",
"Equiv.instEquivLike",
"LinearOrder.toDecidableEq",
"instDecidableEqProd",
"Equiv.prodComm",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Membership.mem",
"Ordering",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Equiv",
"cmp",
"Prod.fst",
"Fins... | false |
CategoryTheory.MonoidalCategory.Limits.inr_comp_pushoutSymmetry_hom_whiskerRight | Mathlib.CategoryTheory.Monoidal.Limits.Shapes.Pullback | [
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Limits.hasPushout_symmetry",
"CategoryTheory.Monoid... | true |
Flow.omegaLimit_omegaLimit | Mathlib.Dynamics.OmegaLimit | [
"Filter.instMembership",
"omegaLimit",
"Eq.mpr",
"_private.Mathlib.Dynamics.OmegaLimit.0.Flow.omegaLimit_omegaLimit._simp_1_2",
"mem_closure_iff_nhds",
"_private.Mathlib.Dynamics.OmegaLimit.0.Flow.omegaLimit_omegaLimit._simp_1_1",
"mem_nhds_iff",
"Flow",
"AddCommGroup.toAddCommMonoid",
"AddCommGro... | true |
HasSubset.mk | Init.Core | [
"HasSubset.mk",
"HasSubset"
] | true |
_private.Init.Data.List.Nat.InsertIdx.0.List.getElem?_insertIdx_of_gt._proof_1_1 | Init.Data.List.Nat.InsertIdx | [
"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",
"id",
"instDecida... | false |
OrthogonalFamily.linearIsometry._proof_4 | Mathlib.Analysis.InnerProductSpace.l2Space | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"IsBoundedSMul",
"AddZe... | false |
Rat.cast_inv_of_ne_zero._simp_1 | Mathlib.Data.Rat.Cast.Defs | [
"Rat.cast_inv_of_ne_zero",
"Int.cast",
"Rat.num",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"DivisionRing.toRatCast",
"Rat",
"DivisionSemiring.toGroupWithZero",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionRing.toDivisionSemiring",
"Rat.cast",
"Ne",
"DivisionRing.toR... | false |
_private.Mathlib.RingTheory.Polynomial.UniversalFactorizationRing.0.MvPolynomial.universalFactorizationMapPresentation_jacobiMatrix._proof_1_6 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"Fin.castAdd",
"HSub.hSub",
"Lean.Grind.Nat.lt_eq",
"Eq.rec",
"id",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Eq.mpr_prop",
"Eq"
] | false |
Mathlib.Tactic.BicategoryLike.MonadMor₂.rec | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.Mor₂Iso",
"Mathlib.Tactic.BicategoryLike.Mor₂",
"Mathlib.Tactic.BicategoryLike.CoherenceHom",
"Mathlib.Tactic.BicategoryLike.Atom",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"Mathlib.Tactic.BicategoryLike.AtomIso",
"Mathlib.Tactic.BicategoryLike.MonadMor₂",
"Mathlib.Tactic.B... | false |
ByteSlice.stop | Std.Data.ByteSlice | [
"ByteSlice",
"Std.Slice.internalRepresentation",
"Nat",
"Std.Slice.Internal.ByteSliceData",
"Std.Slice.Internal.ByteSliceData.stop"
] | true |
Valued.exists_coe_eq_v | Mathlib.Topology.Algebra.Valued.ValuedField | [
"WithZeroTopology.topologicalSpace",
"Valued.continuous_extension",
"Set.ext",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"UniformSpace.Completion.coe'",
"instZeroCompletion",
"ValuationClass.toMonoidWithZeroHomClass",
"Monoid.to... | true |
_private.Mathlib.Algebra.GCDMonoid.Basic.0.gcd_eq_zero_iff.match_1_5 | Mathlib.Algebra.GCDMonoid.Basic | [
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"GCDMonoid",
"semigroupDvd",
"SemigroupWithZero.toSemigroup",
"CommMonoidWithZero.toMonoidWithZero",
"GCDMonoid.gcd",
"MonoidWithZero.toSemigroupWithZero",
"Exists.casesOn",
"CommMonoidWithZero",
"Exists.intro",
"Eq",
"instHMul"
] | false |
MeasureTheory.integral_comp_mul_left_Ioi | Mathlib.MeasureTheory.Integral.IntegralEqImproper | [
"Iff.mpr",
"Set.preimage_const_mul_Ioi₀",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"MeasureTheory.integral_indicator",
"instClosedIicTopology",
"Real.partialOrder",
"Real",
"Set.Ioi",
"instHSMul",
"MeasureTheory.Measure",
"Preorder.toLT",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
... | true |
CategoryTheory.Adhesive.isColimitBinaryCofan._proof_4 | Mathlib.CategoryTheory.Adhesive.Subobject | [
"CategoryTheory.Limits.pullback",
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Functor",
"CategoryTheory.Subobject.underlying",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Category... | false |
Lean.Language.SnapshotTask.noConfusion | Lean.Language.Basic | [
"Task",
"HEq.refl",
"Lean.Syntax",
"Lean.Language.SnapshotTask.noConfusionType",
"Lean.Language.SnapshotTask",
"Lean.Language.SnapshotTask.casesOn",
"Lean.Language.SnapshotTask.ReportingRange",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"IO.CancelToken",
"Eq",
"Option"
] | false |
Int.Linear.cdiv | Init.Data.Int.Linear | [
"Int.instDiv",
"instHDiv",
"HDiv.hDiv",
"Int.instNegInt",
"Int",
"Neg.neg"
] | true |
CategoryTheory.Over.faithful_pullback | Mathlib.CategoryTheory.Comma.Over.Pullback | [
"CategoryTheory.Over.map",
"Eq.mpr",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Over.pullback._proof_2",
"CategoryTheory.Over",
"CategoryTheory.Epi",
"CategoryTheory.Over.mapPullbackAdj._proof_4",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Over.pul... | true |
div_neg_iff | Mathlib.Algebra.Order.Field.Basic | [
"GroupWithZero.toMonoidWithZero",
"DivInvMonoid.toInv",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"MulZeroClass.toMul",
"IsStrictOrderedRing.toMulPosStrictMono",
"Monoid.toMulOneClass",... | true |
MeasureTheory.prob_compl_eq_zero_iff | Mathlib.MeasureTheory.Measure.Typeclasses.Probability | [
"MeasureTheory.Measure",
"MeasureTheory.prob_compl_eq_zero_iff₀._simp_1",
"MeasurableSet",
"congrArg",
"Compl.compl",
"MeasureTheory.NullMeasurableSet",
"Set.instCompl",
"iff_self",
"MeasurableSpace",
"Iff",
"MeasureTheory.IsProbabilityMeasure",
"True",
"ENNReal",
"of_eq_true",
"One.toOf... | true |
CategoryTheory.StructuredArrow.right | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.Functor.fromPUnit",
"CategoryTheory.StructuredArrow",
"CategoryTheory.Category",
"CategoryTheory.Discrete"
] | true |
DFinsupp.Lex.orderBot._proof_2 | Mathlib.Data.DFinsupp.Lex | [
"Equiv.instEquivLike",
"DFinsupp.instOrderBotOfIsBotZeroClass",
"DFinsupp.toLex_monotone",
"Lex",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"AddZeroClass.toAddZero",
"PartialOrder",
"Multiset",
"Equiv",
"Subtype",
"Pi.instZer... | false |
_private.Lean.Compiler.LCNF.Probing.0.Lean.Compiler.LCNF.Probe.filterByCases.go._unsafe_rec | Lean.Compiler.LCNF.Probing | [
"Pure.pure",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.Alt._auto_9",
"Lean.Compiler.LCNF.Alt._auto_11",
"Array.anyM",
"Lean.Expr",
"IO.RealWorld",
"Lean.Compiler.LCNF.FunDecl",
"Lean.FVarId",
"instDecidableEqBool",
"instOfNatNat",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Compiler... | false |
LinearIsometry.isComplete_map_iff' | Mathlib.Analysis.Normed.Operator.LinearIsometry | [
"LinearIsometry",
"Submodule",
"IsComplete",
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"LinearIsometry.isComplete_map_iff",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"Iff",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SetLike.coe",
"SeminormedAddCommGroup.toAddCommGroup"... | true |
Std.DTreeMap.Const.maxKeyD_modify_eq_maxKeyD | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.Internal.Impl.Const.maxKeyD_modify_eq_maxKeyD",
"Std.DTreeMap.Const.modify",
"Std.DTreeMap.maxKeyD",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.LawfulEqCmp",
"Std.DTreeMap.wf",
"Eq"
] | true |
finprod_mem_singleton | Mathlib.Algebra.BigOperators.Finprod | [
"Eq.mpr",
"Finset.coe_singleton",
"Finset.prod_singleton",
"congrArg",
"Finset",
"Membership.mem",
"Set.instSingletonSet",
"id",
"Finset.prod",
"finprod_mem_coe_finset",
"finprod",
"SetLike.coe",
"Finset.instSetLike",
"Eq.refl",
"Finset.instSingleton",
"Singleton.singleton",
"Eq.symm... | true |
_private.Mathlib.Topology.Sion.0.Sion.minimax._simp_1_7 | Mathlib.Topology.Sion | [
"Membership.mem",
"Set.preimage",
"propext",
"Eq",
"Set.instMembership",
"Set.mem_preimage",
"Set"
] | false |
CategoryTheory.MonoOver.inf | Mathlib.CategoryTheory.Subobject.Lattice | [
"CategoryTheory.MonoOver.inf._proof_1",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Limits.pullback.lift",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoOver.inf._proof_6",
"CategoryTheory.Limits.pullback.snd",
"C... | true |
Nat.toSuperscriptString | Init.Data.Repr | [
"String",
"Nat.toSuperDigits",
"Nat",
"String.ofList"
] | true |
Topology.IsScott.recOn | Mathlib.Topology.Order.ScottTopology | [
"TopologicalSpace",
"Topology.IsScott.rec",
"Topology.IsScott.mk",
"Topology.IsScott",
"Topology.scott",
"Eq",
"Preorder",
"Set"
] | false |
Lean.Compiler.LCNF.CacheExtension._sizeOf_1 | Lean.Compiler.LCNF.CompilerM | [
"Lean.PHashMap",
"instOfNatNat",
"List",
"instHAdd",
"Lean.PersistentHashMap._sizeOf_inst",
"HAdd.hAdd",
"Nat",
"List._sizeOf_inst",
"SizeOf.sizeOf",
"Lean.Compiler.LCNF.CacheExtension.rec",
"instAddNat",
"Lean.EnvExtension",
"Hashable",
"SizeOf",
"Prod._sizeOf_inst",
"Prod",
"OfNat.... | false |
_private.Lean.Expr.0.Lean.Expr.getAppNumArgsAux | Lean.Expr | [
"Lean.Expr.brecOn",
"Lean.Expr",
"_private.Lean.Expr.0.Lean.Expr.getAppNumArgsAux._f",
"Nat"
] | true |
PosSMulMono.smul_le_smul_of_nonneg_left | Mathlib.Algebra.Order.Module.Defs | [
"instHSMul",
"SMul",
"Preorder.toLE",
"PosSMulMono",
"LE.le",
"Zero.toOfNat0",
"HSMul.hSMul",
"OfNat.ofNat",
"Preorder",
"Zero"
] | true |
_private.Mathlib.Algebra.Lie.Weights.Cartan.0.LieAlgebra.mem_corootSpace._simp_1_14 | Mathlib.Algebra.Lie.Weights.Cartan | [
"Exists",
"exists_exists_exists_and_eq",
"And",
"propext",
"Eq"
] | false |
AlgHom.restrictDomain.eq_1 | Mathlib.RingTheory.Norm.Basic | [
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"IsScalarTower.toAlgHom",
"Algebra",
"Algebra.toSMul",
"CommSemiring",
"AlgHom.restrictDomain",
"Eq.refl",
"AlgHom.comp",
"Eq"
] | true |
SSet.stdSimplex.facePairComplIso.congr_simp | Mathlib.AlgebraicTopology.SimplicialSet.StdSimplex | [
"SSet.Subcomplex.toSSet",
"Opposite",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"Compl.compl",
"Finset",
"instDecidableEqFin",
"CategoryTheory.Functor.category",
"BooleanAlgebra.toCompl",
"SSet.stdSimplex.face",
"CategoryTheory.Iso",
"Insert.insert",
"instOfNatNat",
"SSe... | true |
CategoryTheory.Functor.essImage_comp_apply_of_essSurj | Mathlib.CategoryTheory.EssentialImage | [
"CategoryTheory.Functor",
"_private.Mathlib.CategoryTheory.EssentialImage.0.CategoryTheory.Functor.essImage_comp_apply_of_essSurj.match_1_3",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryTheory.Functor.essImage",
"CategoryTheory.Functor.EssSurj.mem_essImage",
"Nonempty.intro",
"Iff",
... | true |
Affine.Simplex.centroid_eq_of_range_eq | Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid | [
"Set.image_univ",
"Affine.Simplex.points",
"Finset.univ",
"Finset.coe_univ",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Finset",
"Set.univ",
"AddCommGroup.toAddGroup",
"Membership.mem",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"Eq.mp",
"AffineIndependent.injective",
"Affine.S... | true |
_private.Mathlib.Analysis.Asymptotics.Lemmas.0.Asymptotics.isBigO_iff_isBoundedUnder_le_div._simp_1_2 | Mathlib.Analysis.Asymptotics.Lemmas | [
"Filter.map",
"Filter.Eventually",
"Filter.eventually_map",
"propext",
"Eq",
"Filter"
] | false |
CategoryTheory.SimplicialObject.δ_δ₀Iter'._proof_6 | Mathlib.AlgebraicTopology.SimplicialObject.DeltaZeroIter | [
"autoParam",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"CategoryTheory.SimplicialObject.δ_δ₀Iter'._auto_1",
"Eq",
"_private.Mathlib.AlgebraicTopology.SimplicialObject.DeltaZeroIter.0.CategoryTheory.SimplicialObject.δ_δ₀Iter'._proof_5"
] | false |
_private.Init.Meta.Defs.0.Lean.Name.beq.match_1.eq_1 | Init.Meta.Defs | [
"Unit.unit",
"_private.Init.Prelude.0.Lean.Name.beq.match_1",
"String",
"Lean.Name.num",
"Lean.Name.str",
"Lean.Name.anonymous",
"Unit",
"Nat",
"Lean.Name",
"Eq.refl",
"Eq"
] | true |
Std.DTreeMap.Internal.Impl.Const.getD_inter_of_contains_right | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Std.Internal.List.List.getValueD_filter_containsKey_of_containsKey_right",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"Std.DTreeMap.Internal.Impl.contains_eq_containsKey",
"beqOfOrd",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",
... | true |
CategoryTheory.GrothendieckTopology.pseudofunctorOver_toPrelaxFunctor_toPrelaxFunctorStruct_toPrefunctor_map_toFunctor_map_hom_app | Mathlib.CategoryTheory.Sites.PseudofunctorSheafOver | [
"CategoryTheory.Over.map",
"CategoryTheory.Functor.op",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Functor.categ... | true |
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