name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
commutatorElement_def | Mathlib.Algebra.Group.Commutator | [
"DivInvMonoid.toInv",
"HMul.hMul",
"Monoid.toMulOneClass",
"Bracket.bracket",
"Group",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"commutatorElement",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"Eq",
"rfl",
"instHMul"
] | true |
Polynomial.leadingCoeff_X_pow_sub_one | Mathlib.Algebra.Polynomial.Degree.Operations | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Polynomial.instOne",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Polynomial.leadingCoeff_X_pow_sub_C",
"Polynomial.leadingCoeff",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Polynomial",
"Monoid.toPow",
"AddMonoidWithOne.toOne",... | true |
IsGreatest.nnnorm_cfcₙ_nnreal._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Monotone.of_left_le_map_sup | Mathlib.Order.Lattice | [
"Iff.mpr",
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"SemilatticeSup.toMax",
"id",
"LE.le",
"Max.max",
"sup_eq_right",
"SemilatticeSup.toPartialOrder",
"Eq.symm",
"Eq",
"SemilatticeSup",
"Preorder"
] | true |
Aesop.NormRuleResult.proved.injEq | Aesop.Search.Expansion.Norm | [
"Aesop.NormRuleResult",
"Eq.propIntro",
"Aesop.NormRuleResult.proved.inj",
"Array",
"Aesop.NormRuleResult.proved",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Aesop.Script.LazyStep",
"Option"
] | true |
_private.Lean.Elab.DocString.0.Lean.Doc.commandExpandersForUnsafe | Lean.Elab.DocString | [
"Pure.pure",
"Lean.ScopedEnvExtension.StateStack",
"Lean.instMonadEnvOfMonadLift",
"Lean.TSyntax",
"Array.instAppend",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.NameMap",
"Lean.TSyntax.getId",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMon... | true |
Matroid.IsBasis.isBasis_isRestriction | Mathlib.Combinatorics.Matroid.Minor.Restrict | [
"Eq.mpr",
"congrArg",
"Matroid.isBasis_restrict_iff",
"Matroid.E",
"and_iff_left",
"id",
"HasSubset.Subset",
"Matroid.IsRestriction",
"And.casesOn",
"And",
"Exists.casesOn",
"propext",
"Eq.ndrec",
"Matroid.restrict",
"Matroid.IsBasis",
"Eq.symm",
"Eq",
"Matroid",
"Set.instHasSubs... | true |
Lean.Meta.SolveByElim.SolveByElimConfig.testPartialSolutions | Lean.Meta.Tactic.SolveByElim | [
"guard",
"Pure.pure",
"Lean.Meta.SolveByElim.SolveByElimConfig.toApplyRulesConfig",
"Lean.instantiateMVars",
"Lean.MVarId.withContext",
"Lean.Meta.Tactic.Backtrack.BacktrackConfig.maxDepth",
"Lean.Meta.Tactic.Backtrack.BacktrackConfig.proc",
"Lean.Meta.SolveByElim.SolveByElimConfig.backtracking",
"L... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.unsat_of_encounteredBoth._proof_1_6 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddSound | [
"False",
"Std.Tactic.BVDecide.LRAT.Internal.ReduceResult.reducedToUnit",
"Bool.not",
"eq_false",
"congrArg",
"Std.Tactic.BVDecide.LRAT.Internal.Unsatisfiable",
"False.elim",
"Classical.byContradiction",
"Lean.Grind.Nat.lt_eq",
"noConfusion_of_Nat",
"id",
"instDecidableEqBool",
"Prod.mk",
"... | false |
CategoryTheory.Functor.sheafPushforwardContinuousComp' | Mathlib.CategoryTheory.Sites.Continuous | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.sheafPushforwardContinuousComp",
"CategoryTheory.Functor.sheafPushforwardContinuousIso",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryTheory.Functor.isContinuous_comp",
"CategoryTheory.G... | true |
Array.merge.go._unsafe_rec | Batteries.Data.Array.Merge | [
"Array.instAppend",
"Array.push",
"Array.toSubarray",
"Subarray.copy",
"GE.ge",
"instDecidableEqBool",
"instOfNatNat",
"Array.merge._proof_2",
"instLENat",
"dite",
"Array",
"GetElem.getElem",
"Bool.true",
"instHAppendOfAppend",
"instHAdd",
"Array.instGetElemNatLtSize",
"HAdd.hAdd",
... | false |
CategoryTheory.LaxMonoidalFunctor.laxMonoidal._autoParam | Mathlib.CategoryTheory.Monoidal.Functor | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Con.ker_rel._simp_2 | Mathlib.GroupTheory.Congruence.Hom | [
"Con.ker_rel",
"Mul",
"MulHomClass",
"Con.ker",
"propext",
"Con",
"Eq",
"Con.instFunLikeForallProp",
"DFunLike.coe",
"FunLike"
] | false |
BitVec.toInt_sub_of_not_ssubOverflow | Init.Data.BitVec.Lemmas | [
"instPowNat",
"Eq.mpr",
"Int.instDiv",
"BitVec.toInt_zero",
"instHDiv",
"congrArg",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.toInt_sub_of_not_ssubOverflow._simp_1_2",
"Decidable.decide.congr_simp",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.toInt_sub_of_not_ssubOverflow._simp_1_4",
"BitVec.of_le... | true |
_private.Mathlib.Analysis.Analytic.Inverse.0.FormalMultilinearSeries.rightInv_removeZero.match_1_1 | Mathlib.Analysis.Analytic.Inverse | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
... | false |
CategoryTheory.Limits.IsLimit.conePointUniqueUpToIso | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.IsLimit.uniqueUpToIso",
"CategoryTheory.Iso",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Limits.Cone.category",
"CategoryTheory.Limits.Cone.forget",
"CategoryTheory.Functor.mapIso",
... | true |
Lean.Meta.Grind.Arith.CommRing.MonadCanon.noConfusion | Lean.Meta.Tactic.Grind.Arith.CommRing.MonadCanon | [
"HEq.refl",
"Lean.Expr",
"Lean.Meta.Grind.Arith.CommRing.MonadCanon.casesOn",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Lean.Meta.Grind.Arith.CommRing.MonadCanon",
"Eq",
"Lean.Meta.Grind.Arith.CommRing.MonadCanon.noConfusionType",
"Option"
] | false |
Cardinal.ofENat_le_lift._simp_1 | Mathlib.SetTheory.Cardinal.ENat | [
"Cardinal.ofENat_le_lift",
"Cardinal",
"Cardinal.lift",
"LE.le",
"Cardinal.instLE",
"Cardinal.ofENat",
"ENat",
"propext",
"Eq"
] | false |
List.minOn_eq_min | Init.Data.List.MinMaxOn | [
"List.minOn_cons_cons._proof_1",
"minOn",
"Eq.mpr",
"False",
"Nat.recAux",
"List.min_singleton",
"List.minOn.congr_simp",
"minOn_eq_min",
"List.minOn_cons_cons_nil._proof_1",
"eq_false",
"congrArg",
"List.min",
"False.elim",
"Std.LawfulOrderLeftLeaningMin",
"List.min_cons_cons_nil",
"L... | true |
nhds_subtype_eq_comap | Mathlib.Topology.Constructions | [
"nhds",
"Subtype",
"Subtype.mk",
"TopologicalSpace",
"nhds_induced",
"instTopologicalSpaceSubtype",
"Subtype.val",
"Eq",
"Filter",
"Filter.comap"
] | true |
lt_of_lt_add_of_nonpos_right | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"Preorder.toLT",
"add_le_of_nonpos_left",
"Preorder.toLE",
"AddRightMono",
"AddZeroClass.toAddZero",
"LE.le",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"LT.lt.trans_le",
"LT.lt",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Preorder"
] | true |
Std.Internal.IO.Async.System.instInhabitedGroupId.default | Std.Internal.Async.System | [
"Inhabited.default",
"Std.Internal.IO.Async.System.GroupId",
"instInhabitedNat",
"Nat",
"Std.Internal.IO.Async.System.GroupId.mk"
] | true |
_private.Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup.0.Algebra.GrothendieckGroup.of_injective._simp_1_1 | Mathlib.GroupTheory.MonoidLocalization.GrothendieckGroup | [
"Localization.mk",
"Monoid.toMulOneClass",
"Localization.mk_one_eq_monoidOf_mk",
"Membership.mem",
"Subtype",
"Localization",
"OreLocalization.instCommMonoid",
"OreLocalization.oreSetComm",
"CommMonoid.toMonoid",
"Submonoid.LocalizationMap",
"Submonoid.LocalizationMap.instFunLike",
"One.toOfNa... | false |
HomologicalComplex.restrictionMap_id | Mathlib.Algebra.Homology.Embedding.Restriction | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.restrictionMap",
"HomologicalComplex",
"CategoryTheory.CategoryStruct.id",
"ComplexShape",
"HomologicalComplex.restriction",
"ComplexShape.Embedd... | true |
Lean.Meta.AbstractNestedProofs.isNonTrivialProof | Lean.Meta.AbstractNestedProofs | [
"Pure.pure",
"Bool.not",
"Option.any",
"Lean.withoutExporting",
"Lean.Meta.State",
"Lean.Expr.isAppOf",
"Lean.Expr.isAtomic",
"Lean.Core.instMonadOptionsCoreM",
"Lean.Name.mkStr3",
"Lean.instMonadOptionsOfMonadLift",
"Lean.Expr.const?",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"in... | true |
strictConcaveOn_of_slope_strict_anti_adjacent | Mathlib.Analysis.Convex.Slope | [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"le_refl",
"StrictConcaveOn",
"Mathlib.Meta.NormNum.instAddMonoidWithOne",
"Preorder.toLT",
"Pi.instNeg",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"neg_strictConvexOn_iff",
"HM... | true |
CategoryTheory.Pseudofunctor.DescentData.mk._flat_ctor | Mathlib.CategoryTheory.Sites.Descent.DescentData | [
"Opposite",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pseudofunctor.DescentData._auto_1",
"CategoryTheory.CategoryStruct.opposite",
"Quiver.Hom.op",
"CategoryTheory.Pseudofunctor.DescentData.hom_self._autoParam",
"CategoryTheory.loca... | false |
ModularForm.sub_apply | Mathlib.NumberTheory.ModularForms.Basic | [
"ModularForm.instSub",
"ModularForm",
"Real",
"Matrix",
"instDecidableEqFin",
"HSub.hSub",
"Real.semiring",
"Subgroup",
"instOfNatNat",
"Int",
"Units.instGroup",
"Fin.fintype",
"instHSub",
"UpperHalfPlane",
"Nat",
"Complex.instSub",
"Matrix.GeneralLinearGroup",
"Matrix.semiring",
... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_607 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.instEquivLike",
"Lean.Grind.Nat.lt_eq",
"List.getElem_filter_eq_getElem_getElem_findIdxs._proof_2",
"Equiv",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"List.cons",
"List.idxOfNth",
"List.findIdxs",
"instHAdd",
"HAdd.hAdd",
"Equiv.Perm",
"Nat",
"List.filter",
... | false |
_private.Lean.Meta.Offset.0.Lean.Meta.evalNat._sparseCasesOn_2 | Lean.Meta.Offset | [
"Nat.ne_of_beq_eq_false",
"Lean.Literal.strVal",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Literal",
"Lean.Literal.natVal",
"Nat.land",
"Nat",
"Bool",
"Eq.refl",
"Lean.Literal.ctorIdx",
"OfNat.ofNat",
"Bool.false",
"Lean.Literal.rec"
] | false |
Lean.Meta.DiscrTree.Trie.ctorIdx | Lean.Meta.DiscrTree.Types | [
"Lean.Meta.DiscrTree.Trie",
"Nat"
] | false |
_private.Mathlib.LinearAlgebra.QuadraticForm.Signature.0.QuadraticForm.posDef_spanSubset._simp_1_5 | Mathlib.LinearAlgebra.QuadraticForm.Signature | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
UniformSpace.Completion.instAddMonoid._proof_12 | Mathlib.Topology.Algebra.GroupCompletion | [
"UniformSpace",
"UniformSpace.Completion.coe'",
"instHSMul",
"AddMonoid.toAddSemigroup",
"AddMonoid.toNSMul",
"inferInstance",
"UniformSpace.Completion.instAddMonoid._proof_7",
"instOfNatNat",
"UniformSpace.Completion.continuous_map₂",
"instT3Space",
"IsUniformAddGroup",
"UniformSpace.Completi... | false |
_private.Mathlib.Topology.Compactness.Lindelof.0.Tendsto.isLindelof_insert_range_of_coLindelof._simp_1_3 | Mathlib.Topology.Compactness.Lindelof | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Set.not_disjoint_iff_nonempty_inter",
"Set.instInter",
"Set.instDistribLattice",
"Inter.inter",
"Set.Nonempty",
"Set.instBoundedOrder",
"BoundedOrder.toOrderBot",
"propext",
... | false |
IsLocalRing.ResidueField.map_id_apply | Mathlib.RingTheory.LocalRing.ResidueField.Basic | [
"CommRing",
"DFunLike.congr_fun",
"IsLocalRing.ResidueField.map",
"CommSemiring.toSemiring",
"RingHom",
"IsLocalRing.ResidueField.field",
"IsLocalRing",
"IsLocalRing.ResidueField.map_id",
"Field.toSemifield",
"isLocalHom_id",
"CommRing.toCommSemiring",
"IsLocalRing.ResidueField",
"RingHom.in... | true |
DomMulAct.instLeftCancelMonoidOfMulOpposite | Mathlib.GroupTheory.GroupAction.DomAct.Basic | [
"DomMulAct",
"MulOpposite",
"LeftCancelMonoid"
] | true |
Equiv.Perm.subtypeEquivSubtypePerm_apply_of_not_mem | Mathlib.Algebra.Group.End | [
"Equiv.instEquivLike",
"Equiv",
"Subtype",
"Equiv.Perm",
"DecidablePred",
"Equiv.Perm.ofSubtype_apply_of_not_mem",
"Subtype.val",
"Eq",
"DFunLike.coe",
"Not",
"EquivLike.toFunLike",
"Equiv.Perm.subtypeEquivSubtypePerm"
] | true |
Finsupp.sumFinsuppLEquivProdFinsupp_symm_inr | Mathlib.LinearAlgebra.Finsupp.SumProd | [
"Finsupp.instFunLike",
"LinearEquiv.symm",
"Finsupp.module",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Sum",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"AddZero.toZero",
"Sum.inr",
"RingHomInvPair.ids",
"LinearEquiv",
"Finsupp.sumFinsuppLEquivProdFinsupp",
"Semiring",
"Li... | true |
CategoryTheory.Equivalence.toAdjunction_unit | Mathlib.CategoryTheory.Adjunction.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Equ... | true |
HomologicalComplex.xNextIso.eq_1 | Mathlib.Algebra.Homology.HomologicalComplex | [
"HomologicalComplex.xNext",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.eqToIso",
"HomologicalComplex",
"HomologicalComplex.xNextIso",
"CategoryTheory.Iso",
"HomologicalComplex.xNextIso._proof_1",
"ComplexShape",
"Eq.refl",
"HomologicalComplex.X",
"Eq",
"ComplexShape.Rel",
"Cat... | true |
NonUnitalSeminormedRing.noConfusion | Mathlib.Analysis.Normed.Ring.Basic | [
"Norm.norm",
"NonUnitalSeminormedRing",
"Real.instLE",
"Real",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"HEq.refl",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Norm",
"LE.le",
"NonUnitalSeminorm... | false |
Finset.sdiff_union_erase_cancel | Mathlib.Data.Finset.Basic | [
"Finset.instUnion",
"Finset",
"Finset.instSDiff",
"Membership.mem",
"HasSubset.Subset",
"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_union_erase_cancel._proof_1_1",
"SDiff.sdiff",
"Finset.instSetLike",
"Finset.instHasSubset",
"Union.union",
"Finset.erase",
"Eq",
"SetLike.instMembership... | true |
GrpCat.SurjectiveOfEpiAuxs.h_apply_fromCoset_nin_range | Mathlib.Algebra.Category.Grp.EpiMono | [
"GrpCat.SurjectiveOfEpiAuxs.g",
"Eq.mpr",
"MulOne.toOne",
"MonoidHom.range",
"False",
"Subtype.mk.congr_simp",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"instHSMul",
"GrpCat",
"MonoidHom.instFunLike",
"instSMulOfMul",
"inv_mul_cancel",
"InvOneClass.toOne",
"Equiv.instEquivLike",
"HMul.h... | true |
WittVector.toZModPow_compat | Mathlib.RingTheory.WittVector.Compare | [
"Eq.mpr",
"Trans.trans",
"Nat.Prime",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"ZMod.commRing",
"congrArg",
"WittVector.instCommRing",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"TruncatedWittVector.instAdd",
"pow_dvd_pow",
"RingHom",
"TruncatedWit... | true |
AlgebraicGeometry.morphismRestrictRestrictBasicOpen._simp_1 | Mathlib.AlgebraicGeometry.Restrict | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.types",
"propext",
"CategoryTheory.forget",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Types.instConcreteCategory",
"CategoryTheory.Types.instFunLike",
"Eq",
"CategoryTheory.Functor.obj",
"Mathlib.Tactic.Ele... | false |
Set.Intersecting.exists_mem_set | Mathlib.Combinatorics.SetFamily.Intersecting | [
"Set.Intersecting",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.instDistribLattice",
"Set.not_disjoint_iff",
"... | true |
_private.Mathlib.CategoryTheory.EssentiallySmall.0.CategoryTheory.essentiallySmall_iff_of_thin._simp_1_2 | Mathlib.CategoryTheory.EssentiallySmall | [
"CategoryTheory.locallySmall_of_thin",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.LocallySmall",
"Quiver.IsThin",
"True",
"eq_true",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor._proof_4 | Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.types_ext",
"LinearOrder",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Quiver.Hom.unop",
"Preorder.toLE... | false |
Setoid.mk_eq_bot | Mathlib.Data.Setoid.Basic | [
"Lattice.toSemilatticeSup",
"Setoid.completeLattice",
"CompleteLattice.toLattice",
"congrArg",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Equivalence",
"Setoid",
"Bot.bot",
"iff_self",
"Iff",
"Setoid.mk",
"BoundedOrder.toOrderBot",
... | true |
Real.sinhOrderIso_symm_apply | Mathlib.Analysis.SpecialFunctions.Arsinh | [
"Real.instLE",
"Real",
"Real.sinhOrderIso",
"RelIso.symm",
"LE.le",
"Real.arsinh",
"RelIso",
"RelIso.instFunLike",
"Eq.refl",
"Eq",
"DFunLike.coe"
] | true |
_private.Mathlib.Algebra.Homology.Monoidal.0.HomologicalComplex.instHasTensorTensorUnit_1._proof_1 | Mathlib.Algebra.Homology.Monoidal | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.Additive",
"HomologicalComplex.instHasTensorXTensorUnit_1",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.functorCategoryPreadditive",
"HomologicalComplex",
"PEmpty",
"ComplexShape",
"CategoryTheory.Preadditi... | false |
CategoryTheory.PreOneHypercover.Hom.mk | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.PreOneHypercover.Hom.w₁₂._autoParam",
"CategoryTheory.PreZeroHypercover.Hom.h₀",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PreOneHypercover",
"CategoryTheory.PreOneHypercover.I₁",
"CategoryTheory.PreOneHypercover.toPreZeroHypercover",
"CategoryTheory.PreOn... | true |
_private.Init.Data.List.Sublist.0.List.infix_filterMap_iff._simp_1_3 | Init.Data.List.Sublist | [
"List.filterMap_eq_append_iff",
"Exists",
"instHAppendOfAppend",
"List",
"And",
"propext",
"List.instAppend",
"List.filterMap",
"Eq",
"HAppend.hAppend",
"Option"
] | false |
CategoryTheory.Limits.Multicoequalizer.instHasCoequalizerFstSigmaMapSndSigmaMap | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.Multicofork",
"CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.WalkingMultispan",
"CategoryTheory.Limits.MultispanShape.L",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.MultispanShape",... | true |
_private.Mathlib.Algebra.Ring.Idempotent.0.IsIdempotentElem.sub_iff._simp_1_5 | Mathlib.Algebra.Ring.Idempotent | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
FreeMonoid.prodAux.eq_1 | Mathlib.Algebra.FreeMonoid.Basic | [
"Monoid",
"MulOne.toOne",
"FreeMonoid.prodAux",
"Monoid.toMulOneClass",
"MulOneClass.toMulOne",
"One.toOfNat1",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"List.nil"
] | true |
_private.Lean.Meta.Tactic.Simp.Types.0.Lean.Meta.Simp.Context.mk.sizeOf_spec | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.SimpCongrTheorems._sizeOf_inst",
"Lean.Meta.SimpCongrTheorems",
"Lean.Meta.Simp.Config",
"Option._sizeOf_inst",
"instSizeOfDefault",
"Lean.Expr",
"instOfNatNat",
"Array._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.Meta.SimpTheorems",
"_private.Lean.Meta.... | true |
borel_eq_generateFrom_Ioi | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | [
"OrderTopology",
"Set.Ioi",
"SecondCountableTopology",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"inferInstance",
"DistribLattice.toLattice",
"borel",
"MeasurableSpace.generateFrom",
"MeasurableSpace",
"TopologicalSpace",
"instOrderTopologyOrderDual",
"bore... | true |
CommAlgCat.binaryCofanIsColimit._proof_1 | Mathlib.Algebra.Category.CommAlgCat.Monoidal | [
"CommAlgCat.binaryCofan",
"Algebra.TensorProduct.lift_comp_includeLeft",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"CategoryTheory.Functor",
"CommRing",
"CommAlgCat.ofHom",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CategoryTheory.CategoryStr... | false |
iteratedFDeriv_zero | Mathlib.Analysis.Calculus.ContDiff.Basic | [
"NormedSpace",
"congrArg",
"Set.univ",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"_private.Mathlib.Analysis.Calculus.ContDiff.Basic.0.iteratedFDeriv_zero._simp_1_1",
"NormedField.toField",
"Pi.instZero",
"iteratedFDerivWithin",
"SubtractionMonoid.toS... | true |
Matrix.cramer | Mathlib.LinearAlgebra.Matrix.Adjugate | [
"Pi.Function.module",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"CommRing.toNonUnitalCommRing",
"Matrix.cramerMap",
"CommSemiring.toSemiring",
"Matrix",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"LinearMap",
"NonUnitalNonAs... | true |
WeierstrassCurve.Jacobian.add_of_Z_eq_zero | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"WeierstrassCurve.Jacobian.add",
"Nat.instMulZeroClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"WeierstrassCurve.Jacobian.polynomialX",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",... | true |
_private.Mathlib.Order.SupIndep.0.Finset.SupIndep.biUnion._proof_1_1 | Mathlib.Order.SupIndep | [
"Lattice",
"of_eq_false",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"forall_not_of_not_exists",
"Lattice.toSemilatticeSup",
"Lean.Grind.not_and",
"eq_false",
"Finset.instUnion",
"Lean.Grind.iff_eq",
"congrArg",
"HEq.refl",
"Finset",
"Classical.byContradiction",
"PartialOrder.toPreor... | false |
_private.Lean.Data.Json.FromToJson.Basic.0.Float.toJson.match_1 | Lean.Data.Json.FromToJson.Basic | [
"String",
"Lean.JsonNumber",
"Sum.casesOn",
"Sum",
"Sum.inl",
"Sum.inr"
] | false |
IsAddUnit.eq_add_neg_iff_add_eq | Mathlib.Algebra.Group.Units.Basic | [
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"IsAddUnit",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"instHAdd",
"Iff",
"HAdd.hAdd",
"SubtractionMonoid",
"AddUnits.eq_add_neg_iff_add_eq",
"AddZ... | true |
Batteries.RBNode.upperBound?_of_some | Batteries.Data.RBMap.Lemmas | [
"Ordering.gt",
"Batteries.RBNode",
"congrArg",
"_private.Batteries.Data.RBMap.Lemmas.0.Batteries.RBNode.ins.match_1.splitter",
"Option.some.injEq",
"Option.some",
"Exists",
"Ordering",
"Ordering.eq",
"id",
"Batteries.RBNode.upperBound?",
"Batteries.RBNode.nil",
"funext",
"Unit",
"Batteri... | true |
CompleteSemilatticeSup.toPartialOrder | Mathlib.Order.CompleteLattice.Defs | [
"CompleteSemilatticeSup",
"PartialOrder"
] | true |
HasSum.congr_fun | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"SummationFilter",
"Eq.rec",
"AddCommMonoid",
"TopologicalSpace",
"funext",
"HasSum",
"Eq.symm",
"Eq"
] | true |
Continuous.matrix_diagonal | Mathlib.Topology.Instances.Matrix | [
"Continuous",
"Pi.topologicalSpace",
"Matrix",
"Continuous.comp",
"continuous_matrix",
"Function.comp",
"Continuous.if_const",
"continuous_zero",
"TopologicalSpace",
"continuous_apply",
"Zero.toOfNat0",
"instTopologicalSpaceMatrix",
"OfNat.ofNat",
"Eq",
"Matrix.diagonal",
"DecidableEq"... | true |
Option.some_eq_dite_none_left._simp_1 | Init.Data.Option.Lemmas | [
"Decidable",
"Option.some",
"Exists",
"Option.some_eq_dite_none_left",
"dite",
"Option.none",
"propext",
"Eq",
"Not",
"Option"
] | false |
Bundle.Pretrivialization.symm_trans_symm | Mathlib.Topology.FiberBundle.Trivialization | [
"Eq.mpr",
"PartialEquiv.symm_symm",
"congrArg",
"PartialEquiv",
"PartialEquiv.trans",
"PartialEquiv.symm",
"id",
"Bundle.Pretrivialization",
"TopologicalSpace",
"Bundle.Pretrivialization.toPartialEquiv",
"PartialEquiv.trans_symm_eq_symm_trans_symm",
"Eq.refl",
"Prod",
"Eq"
] | true |
Aesop.GoalUnsafe.brecOn_5 | Aesop.Tree.Data | [
"Aesop.MVarClusterUnsafe.below",
"Aesop.GoalData",
"Aesop.GoalUnsafe.below_4",
"Aesop.RappUnsafe",
"Aesop.GoalUnsafe.below",
"Aesop.MVarClusterUnsafe",
"Array",
"List",
"Aesop.GoalUnsafe.below_7",
"Aesop.MVarClusterData",
"Aesop.GoalUnsafe.brecOn_5.go",
"Aesop.RappData",
"Aesop.GoalUnsafe.be... | false |
CategoryTheory.IsPullback.hasLiftingProperty | Mathlib.CategoryTheory.LiftingProperties.Limits | [
"CategoryTheory.HasLiftingProperty",
"CategoryTheory.IsPullback.hom_ext",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CommSq",
"congrArg",
"CategoryTheory.IsPullback",
"CategoryTheory.sq_hasLift_of_hasLiftingProperty",
"Categ... | true |
_private.Mathlib.RingTheory.RootsOfUnity.Complex.0.Complex.mem_rootsOfUnity._simp_1_3 | Mathlib.RingTheory.RootsOfUnity.Complex | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
Fin.image_addNat_Ioc | Mathlib.Order.Interval.Set.Fin | [
"Eq.mpr",
"Set.Ioc",
"Set.Ioi",
"congrArg",
"PartialOrder.toPreorder",
"Eq.rec",
"HasSubset.Subset.trans",
"Set.image_subset_range",
"id",
"Set.instIsTransSubset",
"HasSubset.Subset",
"Set.Ioc_subset_Ioi_self",
"Fin.image_addNat_Ioi",
"instHAdd",
"Fin.instPartialOrder",
"Set.preimage",... | true |
List.findM?_pure | Init.Data.List.Control | [
"Pure.pure",
"congrArg",
"Monad.toApplicative",
"List.find?",
"List.filter.match_1",
"Option.some",
"id",
"LawfulMonad",
"List.rec",
"Applicative.toPure",
"List.findM?",
"List.cons",
"_private.Init.Data.List.Control.0.List.anyM.match_1",
"Bool.true",
"funext",
"Option.none",
"List",
... | true |
CommRingCat.hom_inv_apply | Mathlib.Algebra.Category.Ring.Basic | [
"CommRingCat.carrier",
"congrArg",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"CommRingCat.instConcreteCategoryRingHomCarrier",
"RingHom",
"CommRingCat.instCategory",
"CategoryTheory.Iso",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"True",
"eq_sel... | true |
_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.muFun'.eq_def | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Preorder.toLT",
"One",
"le_rfl",
"_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.muFun'._proof_5",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Finset",
"InvImage",
"WellFounded.Nat.fix",
"Preorder.toLE",
"Membership.mem",
"W... | true |
CategoryTheory.Bicategory.leftUnitorNatIso | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Bicategory.leftUnitorNatIso._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.precomposing",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",... | true |
_private.Mathlib.CategoryTheory.Sites.Coherent.RegularTopology.0.CategoryTheory.regularTopology.mem_sieves_iff_hasEffectiveEpi._simp_1_1 | Mathlib.CategoryTheory.Sites.Coherent.RegularTopology | [
"Lattice.toSemilatticeSup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteLattice.toLattice",
"CategoryTheory.Sieve.top_apply",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"OrderTop.toTop"... | false |
UniformSpace.mem_ball_comp | Mathlib.Topology.UniformSpace.Defs | [
"Membership.mem",
"UniformSpace.ball",
"SetRel.comp",
"SetRel.prodMk_mem_comp",
"Prod",
"Set.instMembership",
"Set"
] | true |
Qq.Impl.PatternVar.ctorIdx | Qq.Match | [
"Nat",
"Qq.Impl.PatternVar"
] | false |
Std.ExtHashMap.getD_map | Std.Data.ExtHashMap.Lemmas | [
"instLawfulHashableOfLawfulBEq",
"Std.ExtHashMap.getD",
"Std.ExtHashMap.inner",
"Option.getD",
"LawfulBEq",
"Membership.mem",
"Std.ExtHashMap",
"Option.map",
"Std.ExtDHashMap.Const.getD_map",
"Hashable",
"instEquivBEqOfLawfulBEq",
"GetElem?.getElem?",
"Std.ExtHashMap.instGetElem?Mem",
"Std... | true |
Lean.Diff.instToStringAction.match_1 | Lean.Util.Diff | [
"Unit.unit",
"Lean.Diff.Action.insert",
"Lean.Diff.Action",
"Lean.Diff.Action.delete",
"Unit",
"Lean.Diff.Action.casesOn",
"Lean.Diff.Action.skip"
] | false |
EReal.toReal | Mathlib.Data.EReal.Basic | [
"Real",
"Real.instZero",
"EReal.toReal.match_1",
"EReal",
"Unit",
"Zero.toOfNat0",
"OfNat.ofNat"
] | true |
Lean.Sym.Char.eq_eq_false | Init.Sym.Lemmas | [
"False",
"eq_false",
"congrArg",
"Eq.mp",
"id",
"decide_eq_false_iff_not._simp_1",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"Char",
"Bool.false",
"Decidable.decide",
"Eq",
"Not",
"Eq.trans",
"instDecidableEqChar"
] | true |
ZNum.mod_to_int | Mathlib.Data.Num.ZNum | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"NegZeroClass.toNeg",
"castPosNum",
"Nat.instMulZeroClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Nat.instOne",
"AddMonoid.toAddSemigroup",
"ZNum.cast_neg",
"PosNum.pred'",
"AddGroupWithOne.toAd... | true |
Std.Internal.UV.Loop.Options.mk.noConfusion | Std.Internal.UV.Loop | [
"Std.Internal.UV.Loop.Options.mk",
"Std.Internal.UV.Loop.Options",
"id",
"Std.Internal.UV.Loop.Options.noConfusion",
"Bool",
"Eq"
] | false |
Matrix.vecMulLinear_transpose | Mathlib.LinearAlgebra.Matrix.ToLin | [
"Pi.Function.module",
"Semiring.toModule",
"Pi.addCommMonoid",
"LinearMap.ext",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.vecMul",
"LinearMap.instFunLike",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"LinearMap",
"Matrix.vecMulLinea... | true |
Std.Tactic.BVDecide.Reflect.BitVec.add_congr | Std.Tactic.BVDecide.Reflect | [
"congrArg",
"BitVec.instAdd",
"BitVec",
"instHAdd",
"HAdd.hAdd",
"Nat",
"congr",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans"
] | true |
SheafOfModules.pushforwardSections_coe | Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"SheafOfModules.val",
"AddCommGroup.toAddGroup",
... | true |
SignType.instBoundedOrder | Mathlib.Data.Sign.Defs | [
"SignType.instOne",
"SignType.LE.of_pos",
"SignType.instNeg",
"SignType.instBoundedOrder._proof_1",
"Top.mk",
"OrderTop.mk",
"OrderBot.mk",
"SignType",
"One.toOfNat1",
"BoundedOrder.mk",
"OfNat.ofNat",
"BoundedOrder",
"Bot.mk",
"Neg.neg",
"SignType.instLE"
] | true |
_private.Mathlib.Topology.MetricSpace.Gluing.0.Metric.glueDist_swap.match_1_1 | Mathlib.Topology.MetricSpace.Gluing | [
"Sum.casesOn",
"Sum",
"Sum.inl",
"Sum.inr"
] | false |
UniqueAdd.addHom_preimage | Mathlib.Algebra.Group.UniqueProds.Basic | [
"Eq.mpr",
"congrArg",
"Function.Injective.injOn",
"AddHom",
"Finset",
"Function.Injective.eq_iff",
"Membership.mem",
"AddHom.addHomClass",
"Eq.mp",
"map_add",
"id",
"AddHom.funLike",
"Finset.mem_preimage",
"instHAdd",
"And",
"SetLike.coe",
"Set.preimage",
"Finset.instSetLike",
"H... | true |
Set.Nonempty.of_vadd_right | Mathlib.Algebra.Group.Pointwise.Set.Scalar | [
"VAdd",
"HVAdd.hVAdd",
"Set.Nonempty",
"instHVAdd",
"Set.Nonempty.of_image2_right",
"Set.vadd",
"Set"
] | true |
Prod.normedRing._proof_3 | Mathlib.Analysis.Normed.Ring.Basic | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"NormedRing.toNonUnitalNormedRing",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Prod.nonUnitalNormedRing",
"NonUnitalNormedRing.toNonUnitalRing",
"instHAdd",
"... | false |
Polynomial.coeff_eq_zero_of_lt_trailingDegree | Mathlib.Algebra.Polynomial.Degree.TrailingDegree | [
"ENat.instNatCast",
"Classical.not_not",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"mt",
"instPreorderENat",
"LE.le",
"Polynomial.trailingDegree_le_of_ne_zero",
"Nat.cast",
"Polynomial",
"Polynomial.coeff",
"instLEENat",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"ENat",
"L... | true |
ProofWidgets.Penrose.DiagramProps.maxOptSteps | ProofWidgets.Component.PenroseDiagram | [
"ProofWidgets.Penrose.DiagramProps",
"Nat"
] | true |
IsSimpleOrder.instFinite | Mathlib.Order.Atoms.Finite | [
"Finite",
"IsSimpleOrder",
"Classical.propDecidable",
"inferInstance",
"Finite.of_fintype",
"LE",
"IsSimpleOrder.instFintypeOfDecidableEq",
"BoundedOrder",
"Eq"
] | true |
CompactlySupportedContinuousMap.mk.sizeOf_spec | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"ContinuousMap._sizeOf_inst",
"CompactlySupportedContinuousMap",
"ContinuousMap",
"instOfNatNat",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"ContinuousMap.toFun",
"SizeOf",
"OfNat.ofNat",
"Eq",
"CompactlySupportedContinuousMap._sizeOf... | true |
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