name string | module string | deps list | allowCompletion bool |
|---|---|---|---|
LinearMap.BilinForm.apply_dualBasis_right | Mathlib.LinearAlgebra.BilinearForm.Properties | [
"Eq.mpr",
"Semiring.toModule",
"LinearMap.BilinForm",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.BilinForm.apply_dualBasis_left",
"Finite",
"LinearMap.BilinForm.IsSymm.eq",
"AddGroupWithOne.toAddMonoidWithOne",
"LinearMap.instFunLike",
"Field.toDivisionRi... | true |
SMulCommClass.symm | Mathlib.Algebra.Group.Action.Defs | [
"instHSMul",
"SMul",
"HSMul.hSMul",
"SMulCommClass.smul_comm",
"SMulCommClass.mk",
"Eq.symm",
"SMulCommClass"
] | true |
CategoryTheory.ShortComplex.opcyclesIsoCokernel_inv | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.cokernel.desc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.opcyclesIsoCokernel._proof_1",
... | true |
_private.Mathlib.Algebra.Lie.Extension.0.LieAlgebra.instOfTwoCocycle._simp_1 | Mathlib.Algebra.Lie.Extension | [
"instHSMul",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"DistribSMul",
"AddZero.toAdd",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"Eq.symm",
"Eq",
"smul_add"
] | false |
_private.Mathlib.Order.Bounds.Basic.0.bddBelow_bddAbove_iff_subset_Icc._simp_1_1 | Mathlib.Order.Bounds.Basic | [
"Set.subset_inter_iff",
"HasSubset.Subset",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
Lean.Meta.Grind.Arith.CommRing.CommRing.casesOn | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Expr.instBEq",
"Lean.PArray",
"Lean.Expr",
"Lean.Meta.Grind.Arith.CommRing.CommRing.rec",
"Lean.Meta.Grind.Arith.CommRing.CommRing.mk",
"Lean.PHashSet",
"List",
"Lean.Meta.Grind.Arith.CommRing.RingExpr",
"Nat",
"Lean.Meta.Grind.Arith.CommRing.CommRing",
"Bool",
"Lean.Expr.instHashable",
... | false |
Std.«term_..._» | Init.Data.Range.Polymorphic.PRange | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
Std.Http.Request.Head.rec | Std.Http.Data.Request | [
"Std.Http.Request.Head.mk",
"Std.Http.Method",
"Std.Http.Version",
"Std.Http.RequestTarget",
"Std.Http.Request.Head",
"Std.Http.Headers"
] | false |
AddMonoidAlgebra.mapDomainRingEquiv._proof_1 | Mathlib.Algebra.MonoidAlgebra.MapDomain | [
"AddEquivClass.instAddMonoidHomClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoidAlgebra.semiring",
"AddMonoidHomClass.toAddMonoidHom",
"congrArg",
"Finsupp.mapDomain",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"map_zero",
"AddMonoidAlgebra.mapDomainRingHom",
... | false |
Lean.Grind.Config.detailed | Init.Grind.Config | [
"Lean.Grind.Config",
"Nat"
] | true |
Int8.toISize_toInt64 | Init.Data.SInt.Lemmas | [
"instPowNat",
"Int64.toInt",
"congrArg",
"Int8.toInt_toInt64",
"Int8.toISize",
"Int8.toInt64",
"Int8",
"Int8.toInt",
"ISize.toInt.inj",
"instOfNatNat",
"Int",
"Int8.toInt_bmod_two_pow_numBits",
"instNatPowNat",
"System.Platform.numBits",
"HPow.hPow",
"Int.bmod",
"Nat",
"congr",
"... | true |
Nat.testBit_add | Init.Data.Nat.Bitwise.Lemmas | [
"instPowNat",
"Eq.mpr",
"Nat.recAux",
"instHDiv",
"HMul.hMul",
"congrArg",
"Nat.pow_succ",
"id",
"HDiv.hDiv",
"instMulNat",
"instOfNatNat",
"Nat.div_one",
"Nat.mul_comm",
"instNatPowNat",
"instHAdd",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"True",
"Nat.testBit",
"eq_self",
"Nat.in... | true |
Std.HashMap.Raw.getKey!_insertManyIfNewUnit_list_of_not_mem_of_mem | Std.Data.HashMap.RawLemmas | [
"Std.DHashMap.Raw.Const.getKey!_insertManyIfNewUnit_list_of_not_mem_of_mem",
"List.Pairwise",
"Std.HashMap.Raw.WF.out",
"instForInOfForIn'",
"Membership.mem",
"inferInstance",
"Std.HashMap.Raw.WF",
"Id",
"Membership",
"LawfulHashable",
"Std.HashMap.Raw",
"Bool.true",
"List",
"BEq.beq",
"... | true |
Part.omegaCompletePartialOrder._proof_1 | Mathlib.Order.OmegaCompletePartialOrder | [
"Part",
"Eq.mpr",
"congrArg",
"Part.ωSup",
"Part.eq_some_iff",
"Part.some",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Part.instPartialOrder",
"Membership.mem",
"Eq.mp",
"id",
"Part.instMembership",
"LE.le",
"OmegaCompletePartialOrder.Chain",
"Nat",
"Part.ωSup_eq_some",
"propext"... | false |
AlgebraicGeometry.Scheme.Cover.LocallyDirected.trans_comp._autoParam | Mathlib.AlgebraicGeometry.Cover.Directed | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Mathlib.Explode.Status.sintro.elim | Mathlib.Tactic.Explode.Datatypes | [
"PULift.up",
"Mathlib.Explode.Status",
"Mathlib.Explode.Status.ctorIdx",
"Nat",
"Eq.symm",
"Mathlib.Explode.Status.ctorElim",
"Mathlib.Explode.Status.sintro",
"Eq"
] | false |
Lean.CodeAction.FindTacticResult.rec | Lean.Server.CodeActions.Provider | [
"Lean.CodeAction.FindTacticResult.tactic",
"Nat",
"Bool",
"Lean.CodeAction.FindTacticResult",
"Lean.CodeAction.FindTacticResult.tacticSeq",
"Lean.Syntax.Stack"
] | false |
Algebra.normalizedTrace_def | Mathlib.FieldTheory.NormalizedTrace | [
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"CommSemiring.toSemiring",
"IntermediateField",
"IntermediateField.AdjoinSimple.gen",
"IntermediateField.toField",
"AddGroupWithOne.toAddMonoidWithOne",
"LinearMap.instFunLi... | true |
Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor_aux | Mathlib.RingTheory.Invariant.Profinite | [
"Subalgebra.instSetLike",
"MulSemiringAction.toRingAut",
"QuotientGroup.map",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Submodule.instAddCommMonoidWithOne",
"CommRing",
"instHSMul",
"MonoidHom.instFunLike",
"Semiring.toModule",
"AlgHom.algHomClass",
"O... | true |
isCoprime_mul_unit_right_left | Mathlib.RingTheory.Coprime.Basic | [
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"CommSemiring.toSemiring",
"IsUnit",
"isCoprime_mul_unit_left_left",
"Eq.rec",
"CommMagma.toMul",
"NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring",
"instDistribOfSemiring",
"CommSemiring",
"Iff",
"Distrib.toMul",
"NonUnitalNonAssocC... | true |
_private.Mathlib.AlgebraicGeometry.Limits.0.AlgebraicGeometry.isCompl_opensRange_inl_inr._simp_1_1 | Mathlib.AlgebraicGeometry.Limits | [
"Codisjoint",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"PartialOrder",
"isCompl_iff",
"And",
"IsCompl",
"BoundedOrder.toOrderTop",
"BoundedOrder.toOrderBot",
"propext",
"BoundedOrder",
"Eq"
] | false |
HereditarilyLindelofSpace.isHereditarilyLindelof_univ | Mathlib.Topology.Compactness.Lindelof | [
"Set.univ",
"HereditarilyLindelofSpace",
"IsHereditarilyLindelof",
"TopologicalSpace"
] | true |
List.Vector.mem_map_succ_iff | Mathlib.Data.Vector.Mem | [
"Eq.mpr",
"List.Vector.mem_map_iff",
"congrArg",
"List.Vector.head",
"List.Vector.map",
"Iff.rfl",
"List.Vector",
"HSub.hSub",
"Membership.mem",
"Exists",
"id",
"instSubNat",
"instOfNatNat",
"eq_comm",
"List",
"instHAdd",
"And",
"Iff",
"instHSub",
"List.instMembership",
"HAdd... | true |
Set.finrank_empty | Mathlib.LinearAlgebra.Dimension.Finite | [
"Nontrivial",
"Eq.mpr",
"Submodule",
"congrArg",
"Submodule.addCommMonoid",
"Set.finrank.eq_1",
"Membership.mem",
"Set.finrank",
"id",
"Subtype",
"instOfNatNat",
"Bot.bot",
"Submodule.module",
"AddCommMonoid",
"Submodule.instBot",
"Nat",
"Submodule.setLike",
"Submodule.span",
"Se... | true |
_private.Mathlib.Analysis.Convex.Between.0.Wbtw.trans_left_right._simp_1_2 | Mathlib.Analysis.Convex.Between | [
"instHSMul",
"AddGroupWithOne.toAddGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"sub_smul",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"SubNegMonoid.toSub",
"AddZero... | false |
Lean.Meta.Tactic.TryThis.format.inputWidth | Lean.Meta.TryThis | [
"Inhabited.default",
"Lean.Option",
"instInhabitedNat",
"Nat",
"Lean.instInhabitedOption"
] | true |
Lean.Grind.CommRing.instBEqExpr.beq._sparseCasesOn_6 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Expr",
"Lean.Grind.CommRing.Expr.mul",
"Nat.ne_of_beq_eq_false",
"Lean.Grind.CommRing.Expr.var",
"Nat.shiftRight",
"Lean.Grind.CommRing.Expr.sub",
"Lean.Grind.CommRing.Expr.ctorIdx",
"Lean.Grind.CommRing.Expr.natCast",
"Lean.Grind.CommRing.Expr.neg",
"Nat.hasNotBit",
"instOf... | false |
Std.Http.URI.Query.contains | Std.Http.Data.URI.Basic | [
"Std.Http.URI.EncodedQueryParam.encode",
"String",
"Std.Http.URI.Query",
"Bool",
"Std.Http.URI.Query.containsEncoded"
] | true |
CategoryTheory.hasExt_iff | Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | [
"DerivedCategory.instIsLocalizationCochainComplexIntQQuasiIsoUp",
"CategoryTheory.Iso.homToEquiv",
"CochainComplex.IsStrictlyLE",
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"small_congr",
"CochainComplex.isStrictlyGE_shift",
"instCategoryDerivedCategory",
... | true |
Lean.Json.arr.noConfusion | Lean.Data.Json.Basic | [
"Lean.Json",
"Lean.Json.noConfusion",
"id",
"Array",
"Lean.Json.arr",
"Eq"
] | false |
_private.Mathlib.Algebra.Group.Subgroup.Basic.0.Subgroup.mem_normalizer_iff_conj_image_eq._simp_1_7 | Mathlib.Algebra.Group.Subgroup.Basic | [
"Exists",
"exists_eq_right",
"And",
"propext",
"Eq"
] | false |
Algebra.Extension.tensorToH1Cotangent._proof_10 | Mathlib.RingTheory.Extension.Cotangent.BaseChange | [
"Algebra.Extension.tensorToH1Cotangent._proof_9",
"CommRing",
"Algebra.to_smulCommClass",
"TensorProduct.leftHasSMul",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"Algebra.toModule",
"Algebra.id",
"CommRing.toCommSemiring",
"TensorProduct.i... | false |
EMetric.pair_reduction | Mathlib.Topology.EMetricSpace.PairReduction | [
"ENNReal.instCanonicallyOrderedAdd",
"CharP.cast_eq_zero",
"one_pow",
"Eq.mpr",
"ENNReal.instIsOrderedRing",
"Inhabited.default",
"ciSup_unique",
"MulOne.toOne",
"False",
"Subtype.mk.congr_simp",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Preorder.toLT",
"Finset.product_singleton",
"H... | true |
Nat.AtLeastTwo.ne_one | Mathlib.Data.Nat.Init | [
"Nat.AtLeastTwo.one_lt",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Nat.AtLeastTwo",
"Nat.ne_of_gt"
] | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.toNat_lt_twoPow_of_le._proof_1_1 | Init.Data.BitVec.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonneg_of_le",
"instOfNatNat",
"Int",
"Nat.cast... | false |
CategoryTheory.Bicategory.«term⊗𝟙» | Mathlib.Tactic.CategoryTheory.BicategoricalComp | [
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfMonoidalOppositeRightAction_actionHomRight | Mathlib.CategoryTheory.Monoidal.Action.Opposites | [
"CategoryTheory.MonoidalOpposite.mop",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalOpposite",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionObj",
"CategoryTheory.monoidalCategoryMop",
"CategoryTheory.MonoidalCate... | true |
CategoryTheory.kernelCokernelCompSequence.snakeInput_v₁₂_τ₃ | Mathlib.CategoryTheory.Abelian.DiagramLemmas.KernelCokernelComp | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.mk",
"CategoryTheory.kernelCokernelCompSequence.snakeInput",
"CategoryTheory.Abelian",
"CategoryTheory.kernelCokernelCompSequence.snakeInput._proof_5",
"CategoryTheory.Limits.bi... | true |
_private.Plausible.Testable.0.Plausible.Decorations._aux_Plausible_Testable___elabRules_Plausible_Decorations_tacticMk_decorations_1._sparseCasesOn_4 | Plausible.Testable | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
Std.Net.instInhabitedSocketAddress | Std.Net.Addr | [
"Std.Net.SocketAddress",
"Inhabited",
"Std.Net.instInhabitedSocketAddress.default",
"Inhabited.mk"
] | true |
CategoryTheory.Pretriangulated.shortComplexOfDistTriangleIsoOfIso | Mathlib.CategoryTheory.Triangulated.Pretriangulated | [
"CategoryTheory.Pretriangulated.Triangle.π₃",
"CategoryTheory.Functor.Additive",
"CategoryTheory.ShortComplex",
"CategoryTheory.shiftFunctor",
"Membership.mem",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.Iso",
"CategoryTheory.Pretriangulated.Triangle.π₁",
"Int",
"Int.instAddMonoid... | true |
_private.Lean.Elab.DocString.0.Lean.Doc.ArgSpec.ctorElim | Lean.Elab.DocString | [
"_private.Lean.Elab.DocString.0.Lean.Doc.ArgSpec.many",
"_private.Lean.Elab.DocString.0.Lean.Doc.ArgSpec.casesOn",
"_private.Lean.Elab.DocString.0.Lean.Doc.ArgSpec.named",
"Lean.Expr",
"_private.Lean.Elab.DocString.0.Lean.Doc.ArgSpec.positional",
"_private.Lean.Elab.DocString.0.Lean.Doc.ArgSpec.flag",
"... | false |
AbstractCompletion.uniformStruct | Mathlib.Topology.UniformSpace.AbstractCompletion | [
"UniformSpace",
"AbstractCompletion",
"AbstractCompletion.space"
] | true |
instOfNatFloat | Init.Data.OfScientific | [
"Float",
"Float.ofNat",
"Nat",
"OfNat.mk",
"OfNat"
] | true |
CategoryTheory.HasCodetector.casesOn | Mathlib.CategoryTheory.Generator.Basic | [
"CategoryTheory.HasCodetector.mk",
"CategoryTheory.HasCodetector.rec",
"Exists",
"CategoryTheory.HasCodetector",
"CategoryTheory.IsCodetector",
"CategoryTheory.Category"
] | false |
hasDerivWithinAt_congr_set' | Mathlib.Analysis.Calculus.Deriv.Basic | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Compl.compl",
"nhdsWithin",
"NormedSpace.toModule",
"AddMonoid.toAddZ... | true |
Finpartition.IsEquipartition | Mathlib.Order.Partition.Equipartition | [
"Set.EquitableOn",
"Nat.instOne",
"Finset",
"instLENat",
"Finpartition.parts",
"SetLike.coe",
"Finset.instSetLike",
"Nat",
"Finset.instLattice",
"Finset.card",
"instAddNat",
"Finset.instOrderBot",
"Finpartition",
"DecidableEq"
] | true |
Array.zip_eq_zipWith | Init.Data.Array.Zip | [
"List.zipWith",
"congrArg",
"List.zip_toArray",
"Array.casesOn",
"Prod.mk",
"List.zip",
"List.toArray",
"Array",
"List",
"congr",
"True",
"eq_self",
"List.zip_eq_zipWith",
"of_eq_true",
"Eq.ndrec",
"List.zipWith_toArray",
"Eq.refl",
"Array.zip",
"Array.mk",
"Prod",
"Eq.symm",... | true |
_private.Mathlib.LinearAlgebra.BilinearForm.Orthogonal.0.LinearMap.BilinForm.ker_restrict_eq_of_codisjoint._simp_1_1 | Mathlib.LinearAlgebra.BilinearForm.Orthogonal | [
"Submodule",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"LinearMap.instFunLike",
"RingHom",
"Membership.mem",
"AddZeroClass.toAddZero",
"LinearMap",
"AddCommMonoid",
"LinearMap.mem_ker",
"AddZero.toZero",
"Submodule.setLike",
"propext",
"Semiring",
"Zero.toOfNat0",
"AddCommMonoid.toA... | false |
Lean.Elab.SyntaxDeprecationEntry.mk.injEq | Lean.Elab.DeprecatedSyntax | [
"Eq.propIntro",
"Lean.Elab.SyntaxDeprecationEntry.mk.inj",
"String",
"Lean.injEq_helper",
"And",
"Eq.ndrec",
"Eq.refl",
"Lean.Elab.SyntaxDeprecationEntry",
"Lean.SyntaxNodeKind",
"Eq",
"Lean.Elab.SyntaxDeprecationEntry.mk",
"Option"
] | true |
Mathlib.Tactic.ITauto.Proof.andRight.injEq | Mathlib.Tactic.ITauto | [
"Mathlib.Tactic.ITauto.Proof.andRight.inj",
"Mathlib.Tactic.ITauto.AndKind",
"Eq.propIntro",
"Lean.injEq_helper",
"And",
"Mathlib.Tactic.ITauto.Proof",
"Eq.ndrec",
"Mathlib.Tactic.ITauto.Proof.andRight",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Analysis.BoxIntegral.Partition.Basic.0.BoxIntegral.Prepartition.iUnion_inf._simp_1_1 | Mathlib.Analysis.BoxIntegral.Partition.Basic | [
"Set.instInter",
"Set.iUnion_inter",
"Inter.inter",
"Eq.symm",
"Eq",
"Set.iUnion",
"Set"
] | false |
_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.map.go._sunfold | Std.Data.DHashMap.Internal.AssocList.Basic | [
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.toList.match_1",
"Unit",
"_private.Std.Data.DHashMap.Internal.AssocList.Basic.0.Std.DHashMap.Internal.AssocList.map.go",
"Std.DHashMap.Internal.AssocList",
"Std.DHashMap.Internal.AssocList.cons"
] | false |
_private.Mathlib.LinearAlgebra.Matrix.PosDef.0.Matrix.PosDef.inv._simp_1_2 | Mathlib.LinearAlgebra.Matrix.PosDef | [
"CommRing",
"CommSemiring.toSemiring",
"Matrix",
"IsUnit",
"Matrix.inv",
"CommRing.toCommSemiring",
"Inv.inv",
"Fintype",
"Matrix.isUnit_nonsing_inv_iff",
"Semiring.toMonoid",
"propext",
"Matrix.semiring",
"Eq",
"DecidableEq"
] | false |
Fin.partialSum | Mathlib.Algebra.BigOperators.Fin | [
"AddMonoid.toAddZeroClass",
"List.sum",
"List.ofFn",
"AddZeroClass.toAddZero",
"instOfNatNat",
"Fin.val",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"Nat",
"AddMonoid",
"instAddNat",
"AddZero.toAdd",
"OfNat.ofNat",
"Fin",
"List.take"
] | true |
List.map_rightInverse_iff._simp_1 | Mathlib.Data.List.Basic | [
"List.map",
"List.map_rightInverse_iff",
"List",
"Function.RightInverse",
"propext",
"Eq"
] | false |
_private.Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings.0.NumberField.Embeddings.finite_of_norm_le._simp_1_1 | Mathlib.NumberTheory.NumberField.InfinitePlace.Embeddings | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
_private.Batteries.Data.BitVec.Lemmas.0.BitVec.getMsbD_ofFnBE._proof_1_5 | Batteries.Data.BitVec.Lemmas | [
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"BitVec.getElem_ofFnBE",
"False",
"dite_congr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"Lean.Grind.neste... | false |
groupHomology.inhomogeneousChains.d_comp_d | Mathlib.RepresentationTheory.Homological.GroupHomology.Basic | [
"dite_cond_eq_true",
"Rep.V",
"CommRing",
"Finsupp.module",
"of_decide_eq_true",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"ChainComplex.of.d._proof_1",
"CategoryTh... | true |
Lean.CollectLevelParams.State.visitedLevel | Lean.Util.CollectLevelParams | [
"Lean.CollectLevelParams.State",
"Lean.LevelSet"
] | true |
ISize.ofInt_tmod | Init.Data.SInt.Lemmas | [
"instPowNat",
"Int.tmod",
"Eq.mpr",
"ISize.toInt_mod",
"Int.instDiv",
"ISize.minValue",
"instHDiv",
"le_of_le_of_eq",
"ISize.maxValue",
"Int.lt_of_le_sub_one",
"ISize.ofInt",
"congrArg",
"HSub.hSub",
"id",
"HDiv.hDiv",
"instHMod",
"ISize.toInt_sub",
"Int.instNegInt",
"instSubNat"... | true |
CategoryTheory.ModObj.ofIso_smul | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj",
"CategoryTheory.IsMonHom",
"CategoryTheory.Iso",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction.toMonoidalLeftActionStruct",
"CategoryTh... | true |
_private.Std.Async.Basic.0.Std.Async.Async.ofIOTask.match_1 | Std.Async.Basic | [
"Task",
"Except.ok",
"Except.error",
"IO.Error",
"Except.casesOn",
"Except"
] | false |
CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyOppositeOp | Mathlib.CategoryTheory.MorphismProperty.Composition | [
"CategoryTheory.MorphismProperty.instHasOfPrecompPropertyOppositeOpOfHasOfPostcompProperty",
"CategoryTheory.MorphismProperty",
"Opposite",
"CategoryTheory.MorphismProperty.HasTwoOutOfThreeProperty.mk",
"CategoryTheory.MorphismProperty.IsStableUnderComposition.op",
"CategoryTheory.MorphismProperty.HasTwoO... | true |
Matrix.PosSemidef.nonneg | Mathlib.Analysis.Matrix.Order | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"NormedRing.toRing",
"Matrix",
"Preorder.toLE",
"NormedField.toField",
"RCLike.toPartialOrder",
"Matrix.nonneg_iff_posSemidef",
"LE.le",
"Field.toSemifield",
"RCLike.toDenselyNormedField",
"Matrix.PosSemidef",
"RCLike",
"Semifield.toDivisionSemirin... | true |
Monoid.CoprodI.Word.empty._proof_1 | Mathlib.GroupTheory.CoprodI | [
"Monoid",
"MulOne.toOne",
"False",
"Monoid.toMulOneClass",
"Membership.mem",
"Ne",
"Sigma.fst",
"List.not_mem_nil._simp_1",
"List",
"MulOneClass.toMulOne",
"List.instMembership",
"implies_congr",
"True",
"of_eq_true",
"One.toOfNat1",
"Eq.refl",
"instIsEmptyFalse",
"implies_true",
... | false |
Lean.Lsp.MarkupKind.rec | Lean.Data.Lsp.Basic | [
"Lean.Lsp.MarkupKind",
"Lean.Lsp.MarkupKind.markdown",
"Lean.Lsp.MarkupKind.plaintext"
] | false |
NonUnitalAlgHom.prod._proof_2 | Mathlib.Algebra.Algebra.NonUnitalHom | [
"Monoid",
"MonoidHom.instFunLike",
"NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass",
"outParam",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Prod.instNonUnitalNonAssocSemiring",
"NonUnitalAlgHom.instFunLike_1"... | false |
Matroid.IsNonloop.contractElem_indep_iff | Mathlib.Combinatorics.Matroid.Minor.Contract | [
"Set.disjoint_singleton_right._simp_1",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"Disjoint",
"Membership.mem",
"Set.instUnion",
"Matroid.Indep",
"Set.instSingletonSet",
"Insert.insert",
"Matroid.IsNonloop",
"ChainComplete... | true |
IsometryClass.mk | Mathlib.Topology.MetricSpace.Isometry | [
"IsometryClass",
"outParam",
"IsometryClass.mk",
"PseudoEMetricSpace",
"DFunLike.coe",
"FunLike",
"Isometry"
] | true |
IsCoprime.add_mul_left_left_iff | Mathlib.RingTheory.Coprime.Basic | [
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"IsCoprime.of_add_mul_left_left",
"Distrib.toAdd",
"instDistribOfSemiring",
"instHAdd",
"CommRing.toCommSemiring",
"Iff",
"Distrib.toMul",
"HAdd.hAdd",
"Iff.intro",
"instHMul",
"IsCoprime",
"IsCoprime.add_mul_left_left"
] | true |
_private.Std.Data.Iterators.Lemmas.Combinators.TakeWhile.0.Std.Iter.step_takeWhile.match_3.eq_2 | Std.Data.Iterators.Lemmas.Combinators.TakeWhile | [
"Std.IterStep",
"Std.IterStep.skip",
"Id",
"Std.Iterator",
"Subtype.mk",
"Std.Iter",
"Std.IterStep.yield",
"Std.Iter.IsPlausibleStep",
"Std.IterStep.done",
"Eq.refl",
"Std.Iter.step_takeWhile.match_3",
"Eq",
"Std.Iter.Step"
] | true |
IsSuccArchimedean.linearOrder._proof_4 | Mathlib.Order.SuccPred.Archimedean | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"inferInstance",
"PartialOrder",
"LE.le",
"DecidableLE",
"Eq.refl",
"Eq",
"ite"
] | false |
Lean.Server.Reference.mk._flat_ctor | Lean.Server.References | [
"Lean.Syntax",
"Lean.Server.Reference",
"Lean.Elab.ContextInfo",
"Array",
"Bool",
"Lean.Lsp.Range",
"Lean.Elab.Info",
"Lean.Lsp.RefIdent",
"Lean.Server.Reference.mk"
] | false |
Array.getElem_zipWith | Init.Data.Array.Lemmas | [
"List.zipWith",
"congrArg",
"List.getElem_toArray._proof_1",
"Array.getElem_zipWith._proof_2",
"GetElem.getElem.congr_simp",
"Array.casesOn",
"List.lt_length_left_of_zipWith",
"List.toArray",
"Array",
"GetElem.getElem",
"List.lt_length_right_of_zipWith",
"List",
"Array.instGetElemNatLtSize",... | true |
CategoryTheory.Discrete.monoidal._proof_8 | Mathlib.CategoryTheory.Monoidal.Discrete | [
"Monoid",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Monoid.toMulOneClass",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Discrete.monoidal._proof_3",
"MulOne.toMul",
"CategoryTheory.Discrete.mk",
"MulOneClass.toMulOne",
"CategoryTheory.Discrete.as",
"Categ... | false |
_private.Mathlib.RingTheory.Valuation.Basic.0.Valuation.map_sub_of_left_eq_zero._simp_1_1 | Mathlib.RingTheory.Valuation.Basic | [
"Preorder.toLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Ne",
"IsBotZeroClass",
"LT.lt",
"propext",
"Zero.toOfNat0",
"zero_lt_iff",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
_private.Aesop.Tree.Data.0.Aesop.NodeState.isIrrelevant.match_1 | Aesop.Tree.Data | [
"Unit.unit",
"Aesop.NodeState.proven",
"Aesop.NodeState.unknown",
"Aesop.NodeState.unprovable",
"Unit",
"Aesop.NodeState",
"Aesop.NodeState.casesOn"
] | false |
continuousOn_cfcₙ._auto_3 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Matrix.addZeroClass | Mathlib.LinearAlgebra.Matrix.Defs | [
"Matrix.addZeroClass._proof_1",
"Matrix.add",
"Matrix",
"AddZeroClass.mk",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"Matrix.addZeroClass._proof_2",
"AddZeroClass",
"AddZero.toAdd",
"AddZero.mk",
"Matrix.zero"
] | true |
normalClosure_def | Mathlib.FieldTheory.Normal.Closure | [
"iSup",
"IntermediateField",
"AlgHom",
"Algebra",
"IntermediateField.normalClosure",
"CompleteLattice.toConditionallyCompleteLattice",
"Field.toSemifield",
"AlgHom.fieldRange",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"ConditionallyCompleteLattice.toConditionallyCompletePar... | true |
_private.Mathlib.Topology.IndicatorConstPointwise.0.tendsto_indicator_const_apply_iff_eventually'._simp_1_1 | Mathlib.Topology.IndicatorConstPointwise | [
"Filter.instMembership",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"propext",
"Eq",
"Filter",
"Filter.le_def",
"Filter.instPartialOrder",
"Set"
] | false |
Lean.ParseImports.State.mk.sizeOf_spec | Lean.Elab.ParseImportsFast | [
"Lean.ParseImports.State._sizeOf_inst",
"Lean.ParseImports.State.mk",
"Lean.Import._sizeOf_inst",
"Lean.Import",
"Option._sizeOf_inst",
"String",
"String.Pos.Raw._sizeOf_inst",
"instOfNatNat",
"String.Pos.Raw",
"Array._sizeOf_inst",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf... | true |
IsDedekindDomain.HeightOneSpectrum.valuationSubringAtPrime_le_valuation | Mathlib.RingTheory.DedekindDomain.AdicValuation | [
"Int.instAddCommGroup",
"Algebra.cast",
"Eq.mpr",
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"False",
"Int.instIsStrictOrderedRing",
"Submodule.addSubmonoidClass",
"ValuationSubring.instPartialOrder",
"CommRing",
"DivInvMonoid.toInv",
"instHDiv",
"Semiring.toModule",
"HMul.hMul... | true |
Std.Iter.find? | Init.Data.Iterators.Consumers.Loop | [
"Pure.pure",
"Monad.toApplicative",
"ULift",
"Std.IteratorLoop",
"Id.run",
"Id",
"Applicative.toPure",
"Std.Iterator",
"Std.Iter.findM?",
"Std.Iter",
"Bool",
"Id.instMonad",
"ULift.up",
"Option"
] | true |
MvPolynomial.totalDegree_zero_iff_isHomogeneous | Mathlib.RingTheory.MvPolynomial.Homogeneous | [
"MvPolynomial.isWeightedHomogeneous_zero_iff_weightedTotalDegree_eq_zero",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"Nat.instLattice",
"Lattice.toSemilatticeSup",
"Nat.instOne",
"congrArg",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"MvPolynomial.weightedTotalDegree",
"AddZeroClass.toAddZero",
"... | true |
Nat.one_lt_of_mem_primesBelow | Mathlib.NumberTheory.PrimeCounting | [
"Nat.Prime.one_lt",
"Finset",
"Membership.mem",
"instOfNatNat",
"Finset.instSetLike",
"Nat",
"LT.lt",
"Nat.prime_of_mem_primesBelow",
"instLTNat",
"OfNat.ofNat",
"SetLike.instMembership",
"Nat.primesBelow"
] | true |
Locale.coe_of | Mathlib.Topology.Category.Locale | [
"Locale.of",
"Frm.carrier",
"Frm",
"Order.Frame",
"Eq",
"Opposite.unop",
"rfl"
] | true |
_private.Mathlib.Topology.Instances.Real.Lemmas.0.Real.isTopologicalBasis_Ioo_rat.match_1_3 | Mathlib.Topology.Instances.Real.Lemmas | [
"Real",
"Preorder.toLT",
"DivisionRing.toRatCast",
"Rat",
"PartialOrder.toPreorder",
"Exists",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Rat.cast",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"LT.lt",
"Exists.intro",
"Real.instFiel... | false |
CategoryTheory.Limits.IsInitial.uniqueUpToIso._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.IsTerminal | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.IsInitial.to_self",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.IsInitial",
"CategoryTheory.Limits.IsInitial.to_comp",
"CategoryTheory.Limits.IsInitial.to",
"True",
"eq_self",
"CategoryTheor... | false |
Condensed.isoLocallyConstantOfIsColimit | Mathlib.Condensed.Discrete.Colimit | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Functor.mapCocone",
"Opposite",
"Condensed.isoFinYoneda",
"Condensed.lanPresheafNatIso",
"Profinite.diagram",
"Finite",
"FintypeCat",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.com... | true |
Lean.Language.DynamicSnapshot.ctorIdx | Lean.Language.Basic | [
"Lean.Language.DynamicSnapshot",
"Nat"
] | false |
instFieldGaloisField._aux_59 | Mathlib.FieldTheory.Finite.GaloisField | [
"Nat.Prime",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"HSub.hSub",
"Polynomial.SplittingField",
"RingHom",
"GaloisField",
"Field.toDivisionRing",
"Fact",
"NNRat",
"Polynomial.SplittingField.instAlgebra_1",
"DivisionRing.toRing",
"Field.toSemifield",
"ZMod",
"P... | false |
Submodule.isOrtho_iSup_right | Mathlib.Analysis.InnerProductSpace.Orthogonal | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"congrArg",
"iSup",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"NormedSpace.toModule",
"NormedField.toField",
"CompleteLattice.toConditionallyCompleteLattice",
"Submodule.isOrtho_iSup_left",
"_private.Mathlib.Analysis.InnerProduct... | true |
ProjectiveSpectrum.zeroLocus_mul_homogeneousIdeal | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology | [
"SetLike",
"Set.ext",
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"instMulHomogeneousIdeal",
"Nat.instAddMonoid",
"ProjectiveSpectrum.isPrime",
"AddSubmonoidClass",
"Set.instUnion",
"Ideal.IsPrime.mul_le",
"Homogeneo... | true |
Homeomorph.quotientBot | Mathlib.Topology.Homeomorph.Quotient | [
"Homeomorph.mk",
"Lattice.toSemilatticeSup",
"Setoid.completeLattice",
"CompleteLattice.toLattice",
"Homeomorph.quotientBot._proof_2",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Equiv",
"Setoid",
"Bot.bot",
"instTopologicalSpaceQuotient",... | true |
CategoryTheory.Abelian.PreservesCoimage.iso_hom_π | Mathlib.CategoryTheory.Limits.Preserves.Shapes.AbelianImages | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.Limits.cokernel.map",
"CategoryTheory.Limits.cokernel.desc",
"CategoryTheory.Abelian.PreservesCoimage.iso._proof_2",
"CategoryTheory.Limits.PreservesCokernel.π_iso_hom_assoc",
"C... | true |
Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof.bound.sizeOf_spec | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Expr",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof.bound",
"instAddNat",
"Eq.refl",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof._sizeOf_inst",
"OfNat.ofNat",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstrProof",
"Lean.Expr._... | true |
Std.DTreeMap.Raw.maxKey!_alter_eq_self | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.get?",
"Std.DTreeMap.Raw.instMembership",
"Ord.mk",
"Membership.mem",
"Std.DTreeMap.Raw.alter",
"Ordering",
"Std.DTreeMap.Raw.isEmpty",
"Std.TransCmp",
"Std.DTreeMap.Internal.Impl.maxKey!_alter!_eq_self",
"Bool.true",
"And",
"Iff",
"Std.DTreeMap.Raw.WF.out",
"Std.LawfulEq... | true |
_private.Mathlib.Algebra.Order.Monovary.0.monovaryOn_iff_forall_smul_nonneg._simp_1_3 | Mathlib.Algebra.Order.Monovary | [
"AddGroup.toSubtractionMonoid",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddRightMono",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"LE",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
... | false |
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