name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Analysis.Complex.Conformal.0.isConformalMap_complex_linear._simp_1_6 | Mathlib.Analysis.Complex.Conformal | [
"False",
"HMul.hMul",
"eq_false",
"Mul",
"Ne",
"NoZeroDivisors",
"Zero.toOfNat0",
"mul_ne_zero",
"OfNat.ofNat",
"Eq",
"instHMul",
"Zero"
] | false |
Polynomial.trailingDegree_eq_zero._simp_1 | Mathlib.Algebra.Polynomial.Degree.TrailingDegree | [
"CommSemiring.toSemiring",
"Polynomial.trailingDegree_eq_zero",
"Ne",
"instOfNatNat",
"Polynomial",
"Polynomial.coeff",
"Nat",
"ENat",
"Polynomial.trailingDegree",
"propext",
"instCommSemiringENat",
"Semiring",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero",
"instMulZero... | false |
groupCohomology.mapShortComplex₁_exact | Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | [
"CategoryTheory.Abelian.toPreadditive",
"CommRing",
"groupCohomology.instPreservesZeroMorphismsRepCochainComplexModuleCatNatCochainsFunctor",
"HomologicalComplex.instCategory",
"Nat.instOne",
"ModuleCat",
"CommSemiring.toSemiring",
"CategoryTheory.ShortComplex",
"AddRightCancelSemigroup.toAddSemigro... | true |
TopCat.isColimitCoconeOfForget | Mathlib.Topology.Category.TopCat.Limits.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.mapCocone",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap.mk",
"ContinuousMap",
"CategoryTheory.Functor.comp",
"TopCat.coconeOfCoconeForget",
"TypeCat.instFunLikeFun",
"TopCat.coconeP... | true |
_private.Mathlib.Combinatorics.Graph.Delete.0.Graph.deleteEdges_isLoopAt._simp_1_2 | Mathlib.Combinatorics.Graph.Delete | [
"and_congr_right_iff",
"And",
"Iff",
"propext",
"Eq"
] | false |
SlashInvariantForm.coe_const | Mathlib.NumberTheory.ModularForms.SlashInvariantForms | [
"SlashInvariantForm",
"Real",
"Subgroup.HasDetOne",
"SlashInvariantForm.const",
"Matrix",
"instDecidableEqFin",
"SlashInvariantForm.funLike",
"Real.semiring",
"Subgroup",
"instOfNatNat",
"Int",
"Units.instGroup",
"Real.commRing",
"Fin.fintype",
"instOfNat",
"UpperHalfPlane",
"Nat",
... | true |
Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.neg.inj | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.neg",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof.neg.noConfusion",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstr",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstrProof"
] | true |
Std.Time.TimeZone.TZif.TZifV2.mk.noConfusion | Std.Time.Zoned.Database.TzIf | [
"String",
"Std.Time.TimeZone.TZif.TZifV2",
"Std.Time.TimeZone.TZif.TZifV2.noConfusion",
"id",
"Std.Time.TimeZone.TZif.TZifV1",
"Eq",
"Std.Time.TimeZone.TZif.TZifV2.mk",
"Option"
] | false |
FormalMultilinearSeries.rightInv._proof_14 | Mathlib.Analysis.Analytic.Inverse | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.toUniformContinuousConstSMul"... | false |
CategoryTheory.Functor.instLaxMonoidalActionMapAction._proof_2 | Mathlib.CategoryTheory.Action.Monoidal | [
"Monoid",
"CategoryTheory.Functor",
"MonoidHom.instFunLike",
"Action.hom_ext",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"congrArg",
"CategoryTheory.MonoidalCategory",
"Action.Hom.mk",
"Action.instMonoidalCategory",
"CategoryTheory.End.monoi... | false |
ValuationRing.mk._flat_ctor | Mathlib.RingTheory.Valuation.ValuationRing | [
"IsDomain",
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"Exists",
"instDistribOfSemiring",
"CommRing.toCommSemiring",
"PreValuationRing.mk",
"Distrib.toMul",
"Or",
"ValuationRing",
"Eq",
"ValuationRing.mk",
"instHMul"
] | false |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RatAddResult.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.nodup_insertRatUnits._proof_1_6 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RatAddResult | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"Prod.fst",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.ratUnits",
"LT.lt",
"Eq.substr",
"Std.Sat.CNF.Clause",
"Bool",
"ins... | false |
Lean.Lsp.instOrdPosition | Lean.Data.Lsp.BasicAux | [
"Ord",
"Lean.Lsp.instOrdPosition.ord",
"Ord.mk",
"Lean.Lsp.Position"
] | true |
MeasureTheory.condExpL2_comp_continuousLinearMap | Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2 | [
"MeasureTheory.ae",
"NormedCommRing.toNormedRing",
"MeasureTheory.AEStronglyMeasurable.congr",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Continuous.comp_aestronglyMeasurable",
"Real",
"MeasureTheor... | true |
Int.one_ne_zero | Init.Data.Int.Order | [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"Ne",
"Int",
"Bool.true",
"instOfNat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable.decide",
"Eq"
] | true |
CategoryTheory.MorphismProperty.ofHoms_iff | Mathlib.CategoryTheory.MorphismProperty.Basic | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HEq.refl",
"Membership.mem",
"Exists",
"CategoryTheory.MorphismProperty.arrow_mk_mem_toSet_iff",
"id",
"CategoryTheory.MorphismProperty.toSet",
"CategoryTheory.MorphismProperty.ofHoms.casesOn",
"Iff",
"Exists.case... | true |
_private.Aesop.Search.ExpandSafePrefix.0.Aesop.isSafeExpansionFailedException.match_1 | Aesop.Search.ExpandSafePrefix | [
"Lean.Exception.internal",
"Lean.Exception.ctorIdx",
"Nat.hasNotBit",
"_private.Aesop.Search.ExpandSafePrefix.0.Aesop.isSafeExpansionFailedException._sparseCasesOn_1",
"Lean.InternalExceptionId",
"Lean.KVMap",
"Lean.Exception"
] | false |
Fin.attachFin_Ioo | Mathlib.Order.Interval.Finset.Fin | [
"Preorder.toLT",
"Finset",
"PartialOrder.toPreorder",
"Fin.instLocallyFiniteOrder",
"Nat.instLocallyFiniteOrder",
"Fin.isLt",
"Membership.mem",
"Fin.val",
"Finset.mem_Ioo",
"And",
"Fin.instPartialOrder",
"And.right",
"Finset.instSetLike",
"Nat.instPreorder",
"Nat",
"LT.lt",
"Iff.mp",... | true |
Submodule.LinearDisjoint.one_left | Mathlib.LinearAlgebra.LinearDisjoint | [
"Subalgebra.instSetLike",
"Submodule.mulMap",
"Eq.mpr",
"Submodule",
"Lattice.toSemilatticeSup",
"Submodule.LinearDisjoint",
"CompleteLattice.toLattice",
"congrArg",
"CommSemiring.toSemiring",
"Submodule.linearDisjoint_iff",
"Submodule.addCommMonoid",
"TensorProduct.addCommMonoid",
"OrderBot... | true |
LinearMap.toSpanSingleton | Mathlib.LinearAlgebra.Span.Basic | [
"LinearMap.id",
"Semiring.toModule",
"LinearMap.toSpanSingleton._proof_1",
"LinearMap",
"AddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"LinearMap.smulRight",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | true |
_private.Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities.0.MvPolynomial.NewtonIdentities.weight_add_weight_pairMap | Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | [
"Iff.mpr",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"add_neg_cancel",
"NegZeroClass.toNeg",
"Nat.instCanonicallyOrderedAdd",
"Finset.prod_erase_mul",
"MulOne.toOne",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Nat.instOrderedSub",
"Semigroup.toMul",
"C... | true |
_private.Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy.0.CategoryTheory.SimplicialObject.Homotopy.ToChainHomotopy.comm_succ._proof_1_28 | Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | [
"Lean.RArray.leaf",
"False",
"Lean.Grind.not_not",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Nat.ToInt.add_congr",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"Int.Linear.eq_le_subst_nonneg",
"instOfNatNat",
"I... | false |
Aesop.RuleResult._sizeOf_1 | Aesop.Search.Expansion | [
"Aesop.RuleResult.rec",
"ST.Ref._sizeOf_inst",
"instSizeOfDefault",
"Aesop.RappRef",
"IO.RealWorld",
"instOfNatNat",
"Array._sizeOf_inst",
"Aesop.Rapp",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Aesop.RuleResult",
"OfNat.ofNat"
] | false |
List.map_injective_iff._simp_1 | Mathlib.Data.List.Basic | [
"List.map",
"List",
"List.map_injective_iff",
"propext",
"Function.Injective",
"Eq"
] | false |
Finsupp.instZero._proof_1 | Mathlib.Data.Finsupp.Defs | [
"Finset",
"False.elim",
"Membership.mem",
"Pi.instZero",
"Ne",
"Finset.instEmptyCollection",
"Finset.notMem_empty",
"Iff",
"Finset.instSetLike",
"Iff.intro",
"Zero.toOfNat0",
"EmptyCollection.emptyCollection",
"OfNat.ofNat",
"SetLike.instMembership",
"rfl",
"Zero"
] | false |
continuousSubring._proof_5 | Mathlib.Topology.ContinuousMap.Algebra | [
"Pi.addGroup",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"AddMonoid.toAddZeroClass",
"AddSubsemigroup.carrier",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"NonAssocRing.toNonUnitalNonAssocRing",
"AddSubsemigroup.add_mem'",
"IsTopologicalRing",
"Top... | false |
FundamentalGroupoid.termπₘ | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"OfNat.ofNat"
] | true |
Lean.Parser.checkSimpFailure | Init.Notation | [
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
Lean.Server.Test.Runner.Client.MsgEmbed._sizeOf_4_eq | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.MsgEmbed._sizeOf_5",
"congrArg",
"Array.rec",
"Lean.Server.Test.Runner.Client.MsgEmbed._sizeOf_5_eq",
"instOfNatNat",
"Lean.Server.Test.Runner.Client.MsgEmbed._sizeOf_inst",
"Array.mk.sizeOf_spec",
"Lean.Widget.TaggedText",
"Lean.Server.Test.Runner.Client.MsgEmbed",
... | false |
Metric.unitSphere.coe_pow | Mathlib.Analysis.Normed.Field.UnitBall | [
"NormOneClass",
"SeminormedRing.toNorm",
"Real",
"AddGroupWithOne.toAddMonoidWithOne",
"SeminormedRing.toRing",
"Membership.mem",
"Metric.unitSphere.instMonoid",
"Set.Elem",
"NormMulClass",
"instDistribOfSemiring",
"Monoid.toPow",
"Real.instOne",
"AddMonoidWithOne.toOne",
"HPow.hPow",
"D... | true |
SimpleGraph.deleteIncidenceSet | Mathlib.Combinatorics.SimpleGraph.DeleteEdges | [
"SimpleGraph.deleteEdges",
"SimpleGraph.incidenceSet",
"SimpleGraph"
] | true |
ExistsContDiffBumpBase.y | Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"ExistsContDiffBumpBase.w._proof_2",
"Semiring.toModule",
"RCLike.toNormedAlgebra",
"NormedSpace",
"Real.denselyNormedField",
"Real.instRCLike",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Semino... | true |
Finset.mem_map'._simp_1 | Mathlib.Data.Finset.Image | [
"Finset",
"Finset.map",
"Membership.mem",
"Function.Embedding",
"Finset.instSetLike",
"propext",
"Finset.mem_map'",
"Function.instFunLikeEmbedding",
"Eq",
"DFunLike.coe",
"SetLike.instMembership"
] | false |
_private.Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear.0.RootPairing.rootFormIn_self_smul_coroot._simp_1_3 | Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear | [
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass... | false |
CategoryTheory.Precoverage.RespectsIso | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.Precoverage",
"CategoryTheory.Precoverage.RespectsIso.mk",
"CategoryTheory.Category"
] | true |
Complex.equivRealProdAddHom_symm_apply_re | Mathlib.Data.Complex.Basic | [
"Real",
"Prod.instAdd",
"Complex.equivRealProdAddHom",
"Prod.fst",
"Real.instAdd",
"Complex.re",
"AddEquiv",
"Eq.refl",
"Complex.instAdd",
"Complex",
"Prod",
"AddEquiv.instEquivLike",
"Eq",
"DFunLike.coe",
"AddEquiv.symm",
"EquivLike.toFunLike"
] | true |
List.dropPrefix?_eq_some_iff._unary | Batteries.Data.List.Lemmas | [
"Eq.mpr",
"not_exists._simp_1",
"False",
"List.nil_beq_eq",
"Option.ctorIdx",
"congrArg",
"and_self",
"List.dropPrefix?.match_1",
"_private.Batteries.Data.List.Lemmas.0.List.dropPrefix?.match_1.splitter",
"List.append_eq_nil_iff._simp_1",
"invImage",
"False.elim",
"Nat.lt_add_left_iff_pos._s... | false |
Topology.ContinuousMapGeneratedBy.continuousGeneratedBy_iff_uncurry | Mathlib.Topology.Convenient.HomSpace | [
"ContinuousMap.continuous",
"Eq.mpr",
"Continuous",
"Topology.ContinuousMapGeneratedBy.precomp",
"congrArg",
"ContinuousMap.curry",
"ContinuousMap.mk",
"ContinuousMap",
"Topology.ContinuousMapGeneratedBy.instTopologicalSpace",
"instTopologicalSpaceProd",
"Function.comp",
"id",
"_private.Math... | true |
_private.Mathlib.Order.Category.HeytAlg.0.HeytAlg.Hom.mk._flat_ctor | Mathlib.Order.Category.HeytAlg | [
"_private.Mathlib.Order.Category.HeytAlg.0.HeytAlg.Hom.mk",
"HeytAlg",
"HeytAlg.carrier",
"HeytAlg.Hom",
"HeytingHom",
"HeytAlg.str"
] | false |
_private.Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous.0.MvPolynomial.weightedTotalDegree'_eq_bot_iff._simp_1_2 | Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous | [
"Finset",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"Bot.bot",
"Finset.instSetLike",
"propext",
"Finset.sup",
"SemilatticeSup.toPartialOrder",
"Eq",
"SemilatticeSup",
"Finset.sup_eq_bot_iff",
"SetLike.instMembership"
] | false |
Sylow.normal_of_normalizer_normal | Mathlib.GroupTheory.Sylow | [
"Sylow.toSubgroup",
"Eq.mpr",
"Sylow.instSetLike",
"Nat.Prime",
"Lattice.toSemilatticeSup",
"Sylow",
"Sylow.normalizer_sup_eq_top'",
"congrArg",
"Finite",
"Group",
"Fact",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"id",
"Subgroup",
"sup_idem",
"Subgrou... | true |
_private.Mathlib.RingTheory.MvPowerSeries.LexOrder.0.MvPowerSeries.coeff_ne_zero_of_lexOrder._simp_1_5 | Mathlib.RingTheory.MvPowerSeries.LexOrder | [
"Equiv.instEquivLike",
"Membership.mem",
"Equiv",
"propext",
"Set.image",
"Equiv.symm",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"EquivLike.toFunLike",
"Set.mem_image_equiv",
"Set"
] | false |
BoxIntegral.Prepartition.splitMany_le_split | Mathlib.Analysis.BoxIntegral.Partition.Split | [
"Real",
"BoxIntegral.Prepartition",
"BoxIntegral.Prepartition.split",
"Finset",
"Membership.mem",
"BoxIntegral.Prepartition.instOrderTop",
"LE.le",
"Prod.fst",
"BoxIntegral.Prepartition.instSemilatticeInf",
"Finset.instSetLike",
"Finset.inf_le",
"Prod",
"BoxIntegral.Prepartition.splitMany",
... | true |
UInt64.zero_add | Init.Data.UInt.Lemmas | [
"UInt64.instOfNat",
"instAddUInt64",
"UInt64",
"UInt64.toBitVec_inj",
"BitVec",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Iff.mp",
"BitVec.zero_add",
"OfNat.ofNat",
"Eq",
"UInt64.toBitVec"
] | true |
Submodule.one | Mathlib.Algebra.Algebra.Operations | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"RingHomSurjective.ids",
"One",
"Semiring.toModule",
"One.mk",
"LinearMap.range",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddMonoidWithOne.toOne",
"NonAssocSemiring.toNonUnitalNonAssocSemirin... | true |
AlgebraicGeometry.instIsIsoSchemeCoprodComparisonOppositeCommRingCatSpec | Mathlib.AlgebraicGeometry.Limits | [
"Iff.mpr",
"CategoryTheory.Limits.limit.π",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.opProdIsoCoprod",
"CategoryTheory.Limits.Cone.π",
"AlgebraicGeometry.Spec",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
... | true |
LieRingModule.toEnd_apply_apply | Mathlib.Algebra.Lie.Basic | [
"LieRing.toAddCommGroup",
"AddMonoid.toAddZeroClass",
"Bracket.bracket",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"LieRingModule.toBracket",
"LieRing",
"AddGroup.toSubNegMonoid",
"AddMonoidHom.instAddCommGroup",
"LieRingModule",
"Eq.refl",
"SubNegMonoid.toAddMonoi... | true |
Lean.CodeAction.FindTacticResult.tactic.elim | Lean.Server.CodeActions.Provider | [
"Lean.CodeAction.FindTacticResult.tactic",
"Lean.CodeAction.FindTacticResult.ctorElim",
"PULift.up",
"Lean.CodeAction.FindTacticResult.ctorIdx",
"Nat",
"Lean.CodeAction.FindTacticResult",
"Lean.Syntax.Stack",
"Eq.symm",
"Eq"
] | false |
Aesop.BaseRuleSetMember.normForwardRule.sizeOf_spec | Aesop.RuleSet.Member | [
"Aesop.ForwardRule",
"Aesop.Rule._sizeOf_inst",
"Aesop.ForwardRule._sizeOf_inst",
"instOfNatNat",
"Aesop.BaseRuleSetMember._sizeOf_inst",
"Aesop.NormRule",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Aesop.BaseRuleSetMember.normForwardRule",
"SizeOf.sizeOf",
"Aesop.BaseRuleSetMember",
"instAddNat",
"... | true |
Complex.cpow_zero | Mathlib.Analysis.SpecialFunctions.Pow.Complex | [
"Complex.log",
"HMul.hMul",
"congrArg",
"Complex.exp_zero",
"ite_self",
"Complex.instZero",
"Complex.instPow",
"Complex.instMul",
"ite_cond_eq_true",
"MulZeroClass.mul_zero",
"HPow.hPow",
"True",
"eq_self",
"Complex.exp",
"of_eq_true",
"One.toOfNat1",
"Zero.toOfNat0",
"Eq.refl",
... | true |
Polynomial.root_right_of_root_gcd | Mathlib.Algebra.Polynomial.FieldDivision | [
"Eq.mpr",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"Polynomial.instDecidableEq",
"MulZeroClass.zero_mul",
"semigroupDvd",
"RingHom",
"SemigroupWithZero.toSemigroup",
"id",
"Polynomial.eval₂",
... | true |
Stream'.get_map | Mathlib.Data.Stream.Init | [
"Stream'",
"Stream'.get",
"Stream'.map",
"Nat",
"Eq",
"rfl"
] | true |
Subsingleton.intro._flat_ctor | Init.Core | [
"Subsingleton.intro",
"Subsingleton",
"Eq"
] | false |
Char.toString_eq_singleton | Init.Data.Char.Lemmas | [
"String",
"Char.toString",
"Char",
"String.singleton",
"Eq",
"rfl"
] | true |
Ideal.ramificationIdx_eq_of_isGaloisGroup | Mathlib.NumberTheory.RamificationInertia.Galois | [
"AlgEquiv.instEquivLike",
"Submodule.instAddCommMonoidWithOne",
"CommRing",
"instHSMul",
"Semiring.toModule",
"Ideal.exists_smul_eq_of_isGaloisGroup",
"MulSemiringAction.toAlgEquiv",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Finite",
"AddMonoid.toAddZeroClass",
"Group",
"... | true |
Lean.Elab.Tactic.Do.SpecAttr.SpecProof.noConfusion | Lean.Elab.Tactic.Do.Attr | [
"Lean.Syntax",
"Lean.Expr",
"Lean.FVarId",
"Eq.ndrec",
"Lean.Name",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof.casesOn",
"Eq.refl",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof.noConfusionType",
"Eq",
"Lean.Elab.Tactic.Do.SpecAttr.SpecProof"
] | false |
Lean.Elab.Command.CoinductiveElabData.ref | Lean.Elab.Coinductive | [
"Lean.Syntax",
"Lean.Elab.Command.CoinductiveElabData"
] | true |
Lean.Lsp.Range.mk.sizeOf_spec | Lean.Data.Lsp.BasicAux | [
"Lean.Lsp.Range.mk",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Lean.Lsp.Position._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Lean.Lsp.Position",
"Lean.Lsp.Range._sizeOf_inst",
"Lean.Lsp.Range",
"OfNat.ofNat",
"Eq"
] | true |
Monotone.mapsTo_Icc | Mathlib.Order.Interval.Set.Image | [
"Monotone",
"Set.Icc",
"Set.MapsTo",
"Monotone.monotoneOn",
"MonotoneOn.mapsTo_Icc",
"Preorder"
] | true |
Std.DTreeMap.Internal.Impl.Const.getEntryGE.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Ord",
"Std.TransOrd",
"False.elim",
"Std.DTreeMap.Internal.Impl.Ordered",
"Membership.mem",
"Exists",
"Ord.compare",
"Bool.true",
"And",
"Std.DTreeMap.Internal.Impl.leaf",
"Bool",
"Eq.refl",
"Ordering.isGE",
"Std.DTreeMap.Internal.Impl.Const.getEntryGE",
"Prod",
"Eq",
"Std.DTreeMap.... | true |
Std.Do.SPred.Tactic.instHasFrameAndOfSimpAnd_1 | Std.Do.SPred.DerivedLaws | [
"Std.Do.SPred.Tactic.SimpAnd",
"Std.Do.SPred.bientails.symm",
"Std.Do.SPred.Tactic.HasFrame.mk",
"Std.Do.SPred.and_congr_l",
"Std.Do.SPred.Tactic.HasFrame",
"Std.Do.SPred.pure",
"Std.Do.SPred.Tactic.HasFrame.reassoc",
"List",
"Std.Do.SPred.bientails.trans",
"Std.Do.SPred",
"Std.Do.SPred.and",
... | true |
CategoryTheory.MorphismProperty.Comma.Hom.ctorIdx | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"Nat",
"CategoryTheory.MorphismProperty.Comma",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.MorphismProperty.Comma.Hom",
"CategoryTheory.Category"
] | false |
CategoryTheory.SymmetricCategory.mk | Mathlib.CategoryTheory.Monoidal.Braided.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.SymmetricCategory.symmetry._autoParam",
"CategoryTheory.CategoryStruct.id",
"autoParam",
"CategoryTheory.BraidedCategory",
"CategoryTheory.SymmetricCategory",
"CategoryTheory.MonoidalCategorySt... | true |
AddSubgroup.forall_mem_sup | Mathlib.Algebra.Group.Subgroup.Lattice | [
"AddSubgroup.instCompleteLattice",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"SemilatticeSup.toMax",
"AddCommGroup",
"AddSubgroup",
"instHAdd",
"Iff",
"AddGroup.toSubNegMonoid",
... | true |
Homotopy.noConfusion | Mathlib.Algebra.Homology.Homotopy | [
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Homotopy.casesOn",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"Homotopy.zero._autoParam",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"HomologicalComplex",
"AddZe... | false |
MulAction.IsMinimal.rec | Mathlib.Dynamics.Minimal | [
"Monoid",
"Dense",
"MulAction.IsMinimal",
"TopologicalSpace",
"MulAction.orbit",
"MulAction",
"Monoid.toSemigroup",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"MulAction.IsMinimal.mk"
] | false |
Complex.equivRealProdLm_symm_apply_im | Mathlib.LinearAlgebra.Complex.Module | [
"LinearEquiv.symm",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Complex.commRing",
"Complex.im",
"Real.semiring",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Complex.addCommGroup",
"NonUnitalNonAssocSemiring.toAddCommMo... | true |
Set.mem_ite_empty_right._simp_1 | Mathlib.Data.Set.Basic | [
"Decidable",
"Membership.mem",
"Set.mem_ite_empty_right",
"And",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instMembership",
"ite",
"Set"
] | false |
Function.Exact.of_ladder_linearEquiv_of_exact | Mathlib.Algebra.Exact | [
"Function.Exact",
"Eq.mpr",
"Function.Exact.iff_of_ladder_linearEquiv",
"congrArg",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"id",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"LinearMap.comp",
"LinearEquiv.toLinearMap",
"RingHomInvPair.ids",
"Lin... | true |
MeasureTheory.Measure.MutuallySingular.measure_compl_nullSet | Mathlib.MeasureTheory.Measure.MutuallySingular | [
"Exists.choose_spec",
"MeasureTheory.Measure",
"MeasurableSet",
"Compl.compl",
"Set.instCompl",
"MeasureTheory.Measure.MutuallySingular.nullSet",
"MeasurableSpace",
"And",
"And.right",
"MeasureTheory.Measure.MutuallySingular",
"ENNReal",
"Zero.toOfNat0",
"Exists.choose",
"ENNReal.instZero"... | true |
Topology.IsClosedEmbedding.units_map | Mathlib.Topology.Algebra.Group.Basic | [
"Monoid",
"MonoidHom.instFunLike",
"MulOpposite.opHomeomorph",
"Units.instTopologicalSpaceUnits",
"MonoidHom",
"Monoid.toMulOneClass",
"MulOpposite",
"instTopologicalSpaceProd",
"Topology.IsClosedEmbedding.comp",
"Prod.instMulOneClass",
"Function.comp",
"Units",
"MulOne.toMul",
"Prod.map",... | true |
_private.Mathlib.Algebra.Homology.ExactSequenceFour.0.CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac._proof_11 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"CategoryTheory.ComposableArrows.IsComplex.cokerToKer'._proof_2",
"_private.Mathlib.Algebra.Homology.ExactSequenceFour.0.CategoryTheory.ComposableArrows.Exact.opcyclesIsoCycles_hom_fac._proof_5",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"CategoryTheory.ComposableA... | false |
_private.Lean.Meta.Tactic.Grind.Arith.FieldNormNum.0.Lean.Meta.Grind.Arith.FieldNormNum.Context.noConfusion | Lean.Meta.Tactic.Grind.Arith.FieldNormNum | [
"Lean.Expr",
"Lean.Level",
"_private.Lean.Meta.Tactic.Grind.Arith.FieldNormNum.0.Lean.Meta.Grind.Arith.FieldNormNum.Context",
"Eq.ndrec",
"Eq.refl",
"_private.Lean.Meta.Tactic.Grind.Arith.FieldNormNum.0.Lean.Meta.Grind.Arith.FieldNormNum.Context.noConfusionType",
"Eq",
"_private.Lean.Meta.Tactic.Grind... | false |
MeasureTheory.SimpleFunc.lintegralₗ._proof_1 | Mathlib.MeasureTheory.Function.SimpleFunc | [
"instSMulOfMul",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra.toSMul",
"Algebra.id",
"ENNReal.instCommSemiring",
"instDistribOfSemiring",
"Distrib.toMul",
"ENNReal"
] | false |
isSeqCompact_iff_seqCompactSpace | Mathlib.Topology.Compactness.CountablyCompact | [
"Set.univ",
"Membership.mem",
"isSeqCompact_univ_iff",
"Set.Elem",
"TopologicalSpace",
"Iff",
"Iff.trans",
"SeqCompactSpace",
"instTopologicalSpaceSubtype",
"IsSeqCompact",
"Set.instMembership",
"isSeqCompact_iff_isSeqCompact_univ",
"Set"
] | true |
_private.Std.Data.DTreeMap.Internal.Zipper.0.Std.DTreeMap.Internal.Zipper.FinitenessRelation._simp_10 | Std.Data.DTreeMap.Internal.Zipper | [
"Nat.lt_add_one",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"eq_true",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | false |
CategoryTheory.Monad.instInhabitedAlgebra | Mathlib.CategoryTheory.Monad.Algebra | [
"Inhabited.default",
"CategoryTheory.Monad",
"Inhabited",
"CategoryTheory.Monad.free",
"CategoryTheory.Functor.obj",
"CategoryTheory.Monad.Algebra.eilenbergMoore",
"CategoryTheory.Category",
"Inhabited.mk",
"CategoryTheory.Monad.Algebra"
] | true |
Std.Time.Month.instReprQuarter._aux_1 | Std.Time.Date.Unit.Month | [
"Std.Time.Internal.Bounded",
"Std.Time.Month.Quarter",
"Int",
"LE.le",
"And",
"instOfNat",
"Nat",
"Std.Format",
"OfNat.ofNat",
"Subtype.val",
"Repr.reprPrec",
"Int.instLEInt",
"Int.instRepr"
] | false |
Nat.prod_factorization_pow_eq_self | Mathlib.Data.Nat.Factorization.Defs | [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"MulOne.toOne",
"Nat.instMulZeroClass",
"Finsupp.toMultiset",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"Multiset.prod",
"Multiset.instAddCancelCommMonoid",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"Multise... | true |
_private.Batteries.Data.RBMap.WF.0.Batteries.RBNode.balance2_All._simp_1_2 | Batteries.Data.RBMap.WF | [
"And",
"and_assoc",
"propext",
"Eq"
] | false |
Sym | Mathlib.Data.Sym.Basic | [
"Multiset",
"Subtype",
"Nat",
"Multiset.card",
"Eq"
] | true |
Lean.Server.RefInfo.casesOn | Lean.Server.References | [
"Lean.Server.RefInfo.mk",
"Lean.Server.Reference",
"Array",
"Lean.Server.RefInfo.rec",
"Lean.Server.RefInfo",
"Option"
] | false |
_private.Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting.0.CategoryTheory.Limits.termI₃_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
RelSeries.step | Mathlib.Order.RelSeries | [
"SetRel",
"Fin.succ",
"Membership.mem",
"RelSeries.length",
"Prod.mk",
"RelSeries",
"RelSeries.toFun",
"Fin.castSucc",
"Prod",
"Fin",
"Set.instMembership"
] | true |
Submonoid.pi_top | Mathlib.Algebra.Group.Submonoid.Operations | [
"congrArg",
"Membership.mem",
"Submonoid.ext",
"Submonoid.mem_top._simp_2",
"Submonoid.instTop",
"Pi.mulOneClass",
"iff_self",
"Submonoid.pi",
"_private.Mathlib.Algebra.Group.Submonoid.Operations.0.Submonoid.pi_top._simp_1_1",
"Iff",
"implies_congr",
"congr",
"True",
"of_eq_true",
"Eq.re... | true |
Equiv.Perm.ext | Mathlib.Logic.Equiv.Defs | [
"Equiv.instEquivLike",
"Equiv.ext",
"Equiv.Perm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Quaternion.normSq_le_zero._simp_1 | Mathlib.Algebra.Quaternion | [
"NegZeroClass.toNeg",
"CommRing",
"CommSemiring.toSemiring",
"Quaternion.normSq_le_zero",
"LinearOrder",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Quaternion.normSq",
"IsStrictOrderedRing",
"MonoidWithZeroHom.funLike",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
... | false |
Lean.Doc.DocHighlight._sizeOf_1 | Lean.Elab.DocString.Builtin | [
"Option._sizeOf_inst",
"Lean.Doc.DocHighlight",
"Lean.FVarId._sizeOf_inst",
"Lean.FVarId",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"Std.Format._sizeOf_inst",
"Std.Format",
"instAddNat",
"Lean.Name",
"Lean.SyntaxNodeKind",
"OfNat.ofNat",
... | false |
Rat.natCast_le_cast._simp_1 | Mathlib.Data.Rat.Cast.Order | [
"DivisionRing.toRatCast",
"LinearOrder",
"Rat",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"IsStrictOrderedRing",
"Preorder.toLE",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Rat.natCast_le_cast",
"Rat.cast",
"AddMonoidWithOne.t... | false |
ONote._sizeOf_1 | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.rec",
"instSizeOfDefault",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"OfNat.ofNat",
"ONote",
"PNat"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof.0.Lean.Meta.Grind.Arith.Cutsat.caching.unsafe_1 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof | [
"UInt64.instOfNat",
"instShiftRightUInt64",
"UInt64",
"ptrAddrUnsafe",
"USize.toUInt64",
"instHShiftRightOfShiftRight",
"HShiftRight.hShiftRight",
"OfNat.ofNat"
] | true |
_private.Mathlib.FieldTheory.Separable.0.Polynomial.separable_of_subsingleton._simp_1_2 | Mathlib.FieldTheory.Separable | [
"True",
"propext",
"Subsingleton",
"Eq",
"eq_iff_true_of_subsingleton"
] | false |
Fin.Value.mk.injEq | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Fin | [
"Eq.propIntro",
"Lean.injEq_helper",
"HEq.homo_ndrec",
"Fin.Value.mk",
"Fin.Value.mk.inj",
"Fin.Value",
"And",
"Nat",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Fin",
"Eq"
] | true |
NonemptyFinLinOrd._sizeOf_1 | Mathlib.Order.Category.NonemptyFinLinOrd | [
"instSizeOfDefault",
"LinOrd.carrier",
"instOfNatNat",
"LinOrd",
"LinOrd._sizeOf_inst",
"instHAdd",
"Fintype",
"NonemptyFinLinOrd.rec",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Nonempty",
"instAddNat",
"OfNat.ofNat",
"NonemptyFinLinOrd"
] | false |
Equiv.vadd | Mathlib.Algebra.Group.TransferInstance | [
"Equiv.instEquivLike",
"VAdd",
"Equiv",
"VAdd.mk",
"HVAdd.hVAdd",
"instHVAdd",
"Equiv.symm",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
CategoryTheory.ShortComplex.homologyι_naturality | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.ShortComplex.opcycles",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ShortComplex.rightHomology",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.... | true |
Lean.JsonRpc.MessageDirection.toCtorIdx | Lean.Data.JsonRpc | [
"Lean.JsonRpc.MessageDirection.ctorIdx",
"Nat",
"Lean.JsonRpc.MessageDirection"
] | false |
isCoprime_mul_units_right | Mathlib.RingTheory.Coprime.Basic | [
"HMul.hMul",
"CommSemiring.toSemiring",
"isCoprime_mul_unit_right_right",
"IsUnit",
"isCoprime_mul_unit_right_left",
"instDistribOfSemiring",
"CommSemiring",
"Iff",
"Distrib.toMul",
"Semiring.toMonoid",
"Iff.trans",
"instHMul",
"IsCoprime"
] | true |
Path.Homotopy.reflTransSymmAux_mem_I | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"Real.instIsOrderedRing",
"Eq.mpr",
"mul_nonneg",
"Real.partialOrder",
"Real.instLE",
"Semigroup.toMul",
"Real",
"_private.Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic.0.Path.Homotopy.reflTransSymmAux_mem_I._proof_1_9",
"instHDiv",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"Real.instZe... | true |
IsStrictOrder.toIsTrans | Mathlib.Order.Defs.Unbundled | [
"IsStrictOrder",
"IsTrans"
] | true |
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