name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Function.ExtendByOne.hom._proof_2 | Mathlib.Algebra.Group.Pi.Lemmas | [
"MulOne.toOne",
"Function.extend_one",
"MulOneClass.toMulOne",
"Function.extend",
"Pi.instOne",
"One.toOfNat1",
"MulOneClass",
"OfNat.ofNat",
"Eq"
] | false |
OpenPartialHomeomorph.Simps.symm_apply | Mathlib.Topology.OpenPartialHomeomorph.Defs | [
"OpenPartialHomeomorph.toFun'",
"TopologicalSpace",
"OpenPartialHomeomorph",
"OpenPartialHomeomorph.symm"
] | true |
Std.Time.ZonedDateTime.ofPlainDateTimeAssumingUTC | Std.Time.Zoned.ZonedDateTime | [
"Std.Time.PlainDateTime.toTimestampAssumingUTC",
"Std.Time.ZonedDateTime.ofTimestamp",
"Std.Time.PlainDateTime",
"Std.Time.ZonedDateTime",
"Std.Time.TimeZone.ZoneRules"
] | true |
_private.Mathlib.Analysis.Calculus.UniformLimitsDeriv.0.uniformCauchySeqOn_ball_of_fderiv._simp_1_4 | Mathlib.Analysis.Calculus.UniformLimitsDeriv | [
"imp_true_iff",
"True",
"propext",
"Eq"
] | false |
_private.Std.Time.Date.Basic.0.Std.Time.Second.Offset.ofWeeks._proof_1 | Std.Time.Date.Basic | [
"Rat.instOfNat",
"Int.cast",
"Rat.instMul",
"instHDiv",
"HMul.hMul",
"of_decide_eq_true",
"Rat",
"Rat.instIntCast",
"id",
"HDiv.hDiv",
"Int",
"Bool.true",
"instOfNat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"instDecidableEqRat",
"Decidable.decide",
"Eq",
"Rat.instDiv",
"instHMul"
... | false |
_private.Mathlib.RingTheory.MvPolynomial.MonomialOrder.0.MonomialOrder.monic_X_add_C._simp_1_1 | Mathlib.RingTheory.MvPolynomial.MonomialOrder | [
"not_le",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"LT.lt",
"propext",
"Eq.symm",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin | Mathlib.FieldTheory.Galois.GaloisClosure | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField",
"IntermediateField.toField",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"CompleteLattice.toConditionallyCompleteLattice",
"Algebra.toModule",
"Subtype",
"NonUnitalNo... | true |
AlgebraicGeometry.germ_injective_of_isIntegral | Mathlib.AlgebraicGeometry.FunctionField | [
"AlgebraicGeometry.IsIntegral",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"RingHom.instRingHomClass",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"RingHomClass.toAddMonoidHomClass",
"CommRingCat.Hom.hom",
"Opposite",
"CommRingCat.carrier",
"Al... | true |
Set.prod_eq_biUnion_left | Mathlib.Data.Set.Lattice.Image | [
"Set.instSProd",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Membership.mem",
"id",
"Prod.mk",
"Set.image2_mk_eq_prod",
"Set.iUnion_image_left",
"Set.image2",
"Eq.refl",
"Set.image",
"Prod",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | true |
LowerSet.instPartialOrder._proof_1 | Mathlib.Order.UpperLower.CompleteLattice | [
"SetLike.coe_injective",
"LE",
"SetLike.coe",
"Function.Injective",
"LowerSet",
"Set",
"LowerSet.instSetLike"
] | false |
_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.succ_ascFactorial.match_1_1 | Mathlib.Data.Nat.Factorial.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
SimpleGraph.deleteEdges_sup | Mathlib.Combinatorics.SimpleGraph.DeleteEdges | [
"SimpleGraph.deleteEdges",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"SimpleGraph.fromEdgeSet",
"CompleteDistribLattice.toCoframe",
"SimpleGraph",
"Max.max",
"sup_sdiff",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"SimpleGraph.completeAtomicBooleanAlgebra",
"Eq",
"SimpleGraph.ins... | true |
LinearMap.BilinForm.isCompl_span_singleton_orthogonal | Mathlib.LinearAlgebra.BilinearForm.Orthogonal | [
"Submodule",
"LinearMap.BilinForm",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"Set.instSingletonSet",
"Submodule.instPartialOrder",
"LinearMap.BilinForm.IsOrtho",
"Field.toSemifield",
"IsCompl",
"Semifield.toDivisionSemiring"... | true |
MonCat.FilteredColimits.colimitCocone.eq_1 | Mathlib.Algebra.Category.MonCat.FilteredColimits | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"MonCat.FilteredColimits.colimit",
"CategoryTheory.Functor.category",
"MonCat.FilteredColimits.colimitCocone._proof_2",
"MonCat.FilteredColimits.coconeMorphism",
"CategoryTheory.Limits.Cocone.mk",
"MonCat",
"CategoryTheory.SmallCategory",
"... | true |
Std.Do.PredTrans.pure | Std.Do.PredTrans | [
"Std.Do.PostCond",
"Std.Do.Assertion",
"Std.Do.PostShape",
"Prod.fst",
"Std.Do.PredTrans.pure._proof_1",
"Std.Do.PredTrans.mk",
"Std.Do.PredTrans",
"Std.Do.ExceptConds"
] | true |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs.0.EisensteinSeries.D2_mul._simp_1_3 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs | [
"HMul.hMul",
"Mul",
"instHAdd",
"HAdd.hAdd",
"LeftDistribClass",
"mul_add",
"Eq.symm",
"Eq",
"Add",
"instHMul"
] | false |
CategoryTheory.CountableCategory.instCountableHomAsType | Mathlib.CategoryTheory.Countable | [
"Countable.of_equiv",
"CategoryTheory.CountableCategory.countableObj",
"CategoryTheory.CountableCategory.HomAsType",
"Countable",
"equivShrink",
"Countable.toSmall",
"CategoryTheory.CountableCategory",
"CategoryTheory.Category"
] | true |
Mathlib.Tactic.TFAE.Parser.tfaeHaveDecl.formatter | Mathlib.Tactic.TFAE | [
"Lean.PrettyPrinter.Formatter",
"Lean.PrettyPrinter.Formatter.orelse.formatter",
"Lean.ppSpace.formatter",
"Mathlib.Tactic.TFAE.Parser.tfaeHaveIdDecl.formatter",
"Lean.Name.mkStr5",
"Lean.Parser.withCache.formatter",
"Lean.Parser.leadingNode.formatter",
"instOfNatNat",
"Lean.PrettyPrinter.Formatter.... | true |
ContMDiffWithinAt.comp_of_eq | Mathlib.Geometry.Manifold.ContMDiff.Basic | [
"ContMDiffWithinAt",
"NormedSpace",
"Function.comp",
"TopologicalSpace",
"ModelWithCorners",
"Set.MapsTo",
"ENat",
"Eq.ndrec",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"NormedAddCommGroup",
"ContMDiffWithinAt.c... | true |
Order.aleph0_le_cof_iff._simp_1 | Mathlib.SetTheory.Cardinal.Cofinality.Basic | [
"Preorder.toLT",
"Cardinal.instOne",
"Cardinal",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Cardinal.aleph0",
"LE.le",
"Order.aleph0_le_cof_iff",
"Cardinal.instLE",
"Cardinal.partialOrder",
"LT.lt",
"propext",
"One.toOfNat1",
... | false |
WittVector.IsPoly.comp | Mathlib.RingTheory.WittVector.IsPoly | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"MvPolynomial.aeval",
"WittVector.IsPoly",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"Nat.instAddMonoid",
"Function.comp",
"Exists",
"WittVector.... | true |
_private.Mathlib.GroupTheory.GroupAction.ConjAct.0.ConjAct.fixedPoints_eq_center._simp_1_1 | Mathlib.GroupTheory.GroupAction.ConjAct | [
"HMul.hMul",
"Monoid.toMulOneClass",
"Group",
"Subgroup.mem_center_iff",
"Membership.mem",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"Subgroup.center",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"propext",
"Eq",
"SetLike.instMembership",
"Subgroup.instSetLike",
"instHMu... | false |
ENNReal.lintegral_Lp_add_le_of_le_one | Mathlib.MeasureTheory.Integral.MeanInequalities | [
"Iff.mpr",
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"ENNReal.instAdd",
"MeasureTheory.lintegral_add_left'",
"AEMeasurable.pow_const",
"le_refl",
"Mathlib.Meta.NormNum.isNat_add",
"Real.partialOrder",
"Real.instLE",
"Real... | true |
IsStarProjection.le_of_mul_eq_left | Mathlib.Algebra.Order.Star.Basic | [
"AddGroup.toSubtractionMonoid",
"HMul.hMul",
"IsStarProjection.sub_of_mul_eq_left",
"AddCommGroup.toAddCommMonoid",
"covariant_swap_add_of_covariant_add",
"NonUnitalNonAssocRing.toAddCommGroup",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"NonUnitalRing.to... | true |
contMDiffAt_subtype_iff | Mathlib.Geometry.Manifold.ContMDiff.Basic | [
"NormedSpace",
"contDiffGroupoid",
"TopologicalSpace.Opens.instChartedSpace",
"TopologicalSpace.Opens",
"Function.comp",
"Membership.mem",
"Subtype",
"contDiffWithinAt_localInvariantProp",
"TopologicalSpace.Opens.instSetLike",
"TopologicalSpace",
"ModelWithCorners",
"Iff",
"ENat",
"ContMDi... | true |
LeanSearchClient.SearchServer.searchTermSuggestions | LeanSearchClient.Syntax | [
"String.endsWith",
"Lean.TSyntax",
"Lean.MessageData",
"Std.instToFormatString",
"Lean.TSyntax.getString",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"Lean.Meta.Tactic.TryThis.SuggestionStyle",
"String",
"Lean.Meta.State",
"instMonadLiftT",
"Function.comp",
"Lean.Core.instMonadOptionsCo... | true |
Std.DTreeMap.Internal.Impl.Balanced.below.leaf | Std.Data.DTreeMap.Internal.Balanced | [
"Std.DTreeMap.Internal.Impl.Balanced.below.leaf",
"Std.DTreeMap.Internal.Impl.Balanced.below",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.leaf",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.Balanced.leaf"
] | true |
BitVec.extractLsb_not_of_lt | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"Bool.not",
"Bool.and_eq_right_iff_imp._simp_1",
"congrArg",
"HSub.hSub",
"BitVec",
"BitVec.getLsbD",
"id",
"Bool.and",
"instSubNat",
"instOfNatNat",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.extractLsb_not_of_lt._proof_1_1",
"LE.le",
"instLENat",
"GetElem.getElem",
"Bool.tr... | true |
Lean.Elab.Tactic.Ext.applyExtTheoremAt | Lean.Elab.Tactic.Ext | [
"guard",
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.MVarId.withContext",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.MetavarKind.natural",
"Lean.Meta.SavedState",
"Lean.Meta.ApplyNewGoals.all",
"Lean.Expr.isAppOfArity",
"instMonadExceptOfMonadExceptOf",
"inst... | true |
_private.Mathlib.Analysis.Distribution.TemperedDistribution.0._auto_26 | Mathlib.Analysis.Distribution.TemperedDistribution | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
ProbabilityTheory.gammaMeasure.eq_1 | Mathlib.Probability.Distributions.Gamma | [
"MeasureTheory.Measure.withDensity",
"Real",
"MeasureTheory.Measure",
"ProbabilityTheory.gammaMeasure",
"ProbabilityTheory.gammaPDF",
"MeasureTheory.MeasureSpace.toMeasurableSpace",
"Real.measureSpace",
"Real.measurableSpace",
"MeasureTheory.MeasureSpace.volume",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.FieldTheory.KrullTopology.0.krullTopology_mem_nhds_one_iff_of_normal.match_1_3 | Mathlib.FieldTheory.KrullTopology | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField",
"IntermediateField.toField",
"Algebra",
"Normal",
"Membership.mem",
"Exists",
"Field.toDivisionRing",
"DivisionRing.toDivisionSemiring",
"Algebra.toModule",
"IntermediateFie... | false |
MeasureTheory.ProgMeasurable.finset_sum | Mathlib.Probability.Process.Adapted | [
"Finset",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"MeasureTheory.IsStronglyProgressive",
"MeasureTheory.Filtration",
"AddCommMonoid",
"MeasurableSpace",
"TopologicalSpace",
"Finset.instSetLike",
"AddZero.toAdd",
"AddCommMonoid.toAddMonoid",
"MeasureTheory.IsSt... | true |
Submodule.prodEquivOfIsTopCompl._proof_1 | Mathlib.Topology.Algebra.Module.Complement | [
"RingHomInvPair",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Ring"
] | false |
Diffeology.DSmooth.continuous' | Mathlib.Geometry.Diffeology.Basic | [
"Eq.mpr",
"Continuous",
"congrArg",
"Diffeology.dTopology",
"HEq.refl",
"Eq.casesOn",
"id",
"Diffeology.DSmooth.continuous",
"TopologicalSpace",
"DiffeologicalSpace",
"eq_of_heq",
"Eq.ndrec",
"Diffeology.DSmooth",
"Eq.refl",
"HEq",
"Eq.symm",
"Diffeology.IsDTopologyCompatible.dTop_eq... | true |
CategoryTheory.Limits.ImageMap.map_uniq_aux | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"congrArg",
"CategoryTheory.Limits.image.ι",
"CategoryTheory.Arrow.left",
"id",
"CategoryTheory.Arrow.hom",
"CategoryTheory.cancel_mono",
"autoParam",
"CategoryTheory.Limits.instMonoι",
"Categ... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.LeCnstr.0.Lean.Meta.Grind.Arith.Cutsat.LeCnstr.applySubsts.match_1 | Lean.Meta.Tactic.Grind.Arith.Cutsat.LeCnstr | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Prod.mk",
"Int",
"Int.Linear.Var",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.LeCnstr.0.Lean.Meta.Grind.Arith.Cutsat.LeCnstr.applySubsts._sparseCasesOn_1",
"Prod",
"Prod.casesOn",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstr",
"Option"
] | false |
SSet.spine.eq_1 | Mathlib.AlgebraicTopology.SimplicialSet.Path | [
"SSet.Path",
"Opposite",
"SSet.Truncated.spine",
"CategoryTheory.Functor.category",
"SSet.Truncated",
"SSet.truncation",
"instOfNatNat",
"SSet",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"CategoryTheory.types",
"SimplexCategory",
"in... | true |
Aesop.ForwardRule.instToString | Aesop.Rule.Forward | [
"Aesop.RuleName",
"Aesop.ForwardRule",
"String",
"Aesop.ForwardRule.prio",
"ToString.toString",
"instAppendString",
"instHAppendOfAppend",
"Aesop.RuleName.instToString",
"Aesop.ForwardRule.name",
"ToString",
"Aesop.ForwardRulePriority",
"ToString.mk",
"Aesop.ForwardRulePriority.instToString"... | true |
lt_abs | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Preorder.toLT",
"abs",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"AddGroup",
"Iff",
"LT.lt",
"Or",
... | true |
Lean.Parser.Term.let_fun._regBuiltin.Lean.Parser.Term.let_fun.formatter_9 | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Lean.Parser.Term.let_fun.formatter",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
_private.Mathlib.AlgebraicTopology.SimplexCategory.Basic.0.SimplexCategory.eq_of_one_to_one.match_1_3 | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"Unit.unit",
"False",
"Fin.casesOn",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Fin.mk",
"Fin.instOfNat",
"instOfNatNat",
"Nat.le.step",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat.le",
"Nat.instNeZeroSucc",
"SimplexCategory.mk",
"Nat",
"LT.lt",
"Eq.ndrec",
"Nat.ctorIdx",
"in... | false |
Finset.Colex.isInitSeg_empty | Mathlib.Combinatorics.Colex | [
"False",
"Preorder.toLT",
"Finset.coe_empty",
"Equiv.instEquivLike",
"Set.Sized",
"Colex",
"congrArg",
"and_self",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Set.sized_empty._simp_1",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Equiv",
"F... | true |
CategoryTheory.PreZeroHypercover.restrictIndex_I₀ | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.restrictIndex",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover",
"Eq.refl",
"Eq",
"CategoryTheory.Category"
] | true |
CategoryTheory.Limits.Cone.functoriality_obj_π_app | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Functor.map",
"Eq.refl",
"CategoryThe... | true |
MLList.fix?._unsafe_rec | Batteries.Data.MLList.Basic | [
"Pure.pure",
"MLList.nil",
"_private.Batteries.Data.MLList.Basic.0.MLList.fix?.match_1",
"Monad.toApplicative",
"Applicative.toPure",
"Unit",
"MLList.cons",
"MLList.squash",
"Monad.toBind",
"Bind.bind",
"Monad",
"MLList",
"MLList.fix?._unsafe_rec",
"Option"
] | false |
CategoryTheory.Limits.MultispanIndex.SymmStruct._sizeOf_inst | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.MultispanShape.prod",
"CategoryTheory.Limits.MultispanIndex.SymmStruct._sizeOf_1",
"CategoryTheory.Limits.MultispanIndex",
"SizeOf.mk",
"SizeOf",
"CategoryTheory.Limits.MultispanIndex.SymmStruct",
"CategoryTheory.Category"
] | false |
Differentiable.cosh._simp_1 | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | [
"Differentiable",
"Differentiable.cosh",
"Real",
"Semiring.toModule",
"NormedSpace",
"Real.denselyNormedField",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Real.instAddCommGroup",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"SeminormedAddCommG... | false |
_private.Mathlib.Data.Holor.0.Holor._aux_Mathlib_Data_Holor___unexpand_Holor_mul_1 | Mathlib.Data.Holor | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk... | false |
Function.Even.add | Mathlib.Algebra.Group.EvenFunction | [
"congrArg",
"Function.Even",
"instHAdd",
"Neg",
"Pi.instAdd",
"HAdd.hAdd",
"congr",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Neg.neg",
"Add",
"Eq.trans"
] | true |
CategoryTheory.Pretriangulated.productTriangle.π._proof_6 | Mathlib.CategoryTheory.Triangulated.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasProduct",
"CategoryTheory.Limits.piComparison",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.Pretriangulated.Triangle.obj₃",
"CategoryTheory.Pretriangulat... | false |
CategoryTheory.adjunctionOfStructuredArrowInitials | Mathlib.CategoryTheory.Adjunction.Comma | [
"CategoryTheory.Functor",
"CategoryTheory.leftAdjointOfStructuredArrowInitialsAux",
"CategoryTheory.Adjunction.adjunctionOfEquivLeft",
"CategoryTheory.leftAdjointOfStructuredArrowInitials",
"CategoryTheory.leftAdjointOfStructuredArrowInitials._proof_1",
"CategoryTheory.StructuredArrow.right",
"CategoryT... | true |
_private.Mathlib.AlgebraicGeometry.Gluing.0.AlgebraicGeometry.Scheme.IsLocallyDirected.glueData._simp_5 | Mathlib.AlgebraicGeometry.Gluing | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso.inv_comp_eq",
"CategoryTheory.Iso",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"CategoryTheory.Iso.hom",
"Eq",
"CategoryTheory.Iso.inv",
"CategoryTheory.Cate... | false |
Int.bitwise.eq_2 | Mathlib.Data.Int.Bitwise | [
"Int.natBitwise",
"Bool.not",
"Int.bitwise",
"Int.ofNat",
"Int",
"Nat",
"Bool",
"Eq.refl",
"Int.negSucc",
"Eq"
] | true |
Std.IterM.findSome?_eq_match_step | Init.Data.Iterators.Lemmas.Consumers.Monadic.Loop | [
"Pure.pure",
"Eq.mpr",
"bind_congr",
"Std.IterStep",
"congrArg",
"Std.Shrink",
"Std.IterM.length_eq_match_step.match_1",
"Monad.toApplicative",
"Std.IteratorLoop",
"Option.some",
"Std.IterM.IsPlausibleStep",
"Std.Iterators.Finite",
"Std.IterStep.skip",
"id",
"LawfulMonad",
"Std.IterM.f... | true |
CategoryTheory.MonoidalCategory.MonoidalLeftAction.leftActionOfOppositeLeftAction_actionUnitIso | Mathlib.CategoryTheory.Monoidal.Action.Opposites | [
"Opposite",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj",
"CategoryTheory.Iso",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction.toMonoidalLeftActionStruct",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionUnitIso",
"CategoryT... | true |
Ideal.stabilizerEquiv | Mathlib.RingTheory.Ideal.Pointwise | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule.instAddCommMonoidWithOne",
"instHSMul",
"MulEquiv.instEquivLike",
"Semiring.toModule",
"Ideal.stabilizerEquiv._proof_4",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Ideal.stabilizerEquiv._proof_5",
"... | true |
MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.recOn | Mathlib.MeasureTheory.VectorMeasure.Decomposition.Lebesgue | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"IsSemitopologicalRin... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.get?_insert._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
AlgebraicGeometry.Scheme.Pullback.Triplet.specTensorTo_snd | Mathlib.AlgebraicGeometry.PullbackCarrier | [
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.Limits.pullback.lift_snd",
"AlgebraicGeometry.Scheme.Pullback.Triplet.tensorInl",
"AlgebraicGeometry.S... | true |
Std.ExtDTreeMap.Const.get!_inter_of_mem_right | Std.Data.ExtDTreeMap.Lemmas | [
"Std.ExtDTreeMap.mk",
"Std.DTreeMap",
"Std.ExtDTreeMap.instInterOfTransCmp",
"Std.ExtDTreeMap.inductionOn₂",
"Membership.mem",
"Std.DTreeMap.Const.get!_inter_of_mem_right",
"Ordering",
"Std.TransCmp",
"Inter.inter",
"Std.ExtDTreeMap",
"Inhabited",
"Eq",
"Std.ExtDTreeMap.instMembershipOfTrans... | true |
CategoryTheory.Functor.mapAddGrp | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.mapAddGrp._proof_4",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.AddGrp",
"CategoryTheory.Functor.mapAddGrp._proof_2",
"CategoryTheory.AddMon.instCategory",
"CategoryTheory.AddGrp.homMk'",
"C... | true |
Polynomial.Bivariate.Transcendental.algEquivAdjoin_apply | Mathlib.RingTheory.Adjoin.Polynomial.Bivariate | [
"Subalgebra.instSetLike",
"CommRing",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Polynomial.Bivariate.Transcendental.algEquivAdjoin",
"Algebra",
"Algebra.adjoin",
"Membership.mem",
"Algebra.id",
"Set.instSingletonSet",
"Subtype",
"Polynomial.mapA... | true |
Std.Internal.IO.Async.Signal.toCtorIdx | Std.Internal.Async.Signal | [
"Std.Internal.IO.Async.Signal.ctorIdx",
"Nat",
"Std.Internal.IO.Async.Signal"
] | false |
UniformSpace.completelyNormalSpace_of_isCountablyGenerated_uniformity | Mathlib.Topology.UniformSpace.Separation | [
"UniformSpace",
"SetRel",
"uniformity",
"CompletelyNormalSpace",
"And",
"And.left",
"Filter.IsCountablyGenerated",
"Nat.instPreorder",
"UniformSpace.completelyNormalSpace_of_hasAntitoneBasis",
"Nat",
"SetRel.IsSymm",
"UniformSpace.has_seq_basis",
"Prod",
"UniformSpace.toTopologicalSpace",
... | true |
CategoryTheory.Limits.cokernel.mapIso._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.cokernel.map",
"CategoryTheory.Limits.cokernel.desc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.cokernel.map._proof_2",
"CategoryTheory.Limits.cokernel.π... | false |
Module.Presentation.directSum_relation | Mathlib.Algebra.Module.Presentation.DirectSum | [
"Module.Presentation.toRelations",
"Module.Presentation",
"DirectSum.instModule",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"DirectSum.instAddCommGroup",
"Sigma.fst",
"Module.Relations.relation",
"Function.Embedding.sigmaMk",
"Module.Relations.R",
"Module.Relations.G",
"Finsupp.embDomain... | true |
MeasureTheory.IsSetSemiring.rec | Mathlib.MeasureTheory.SetSemiring | [
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Finset",
"Set.PairwiseDisjoint",
"Set.sUnion",
"Membership.mem",
"Exists",
"CompleteLattice.toConditionallyCompleteLattice",
"id",
"HasSubset.Subset",
"Set.instInter",
"Inter.inter",
"MeasureTheory.IsSetSemiring.mk",
"MeasureTheory.IsSetSem... | false |
CStarMatrix.instNonUnitalNonAssocRing | Mathlib.Analysis.CStarAlgebra.CStarMatrix | [
"NonUnitalNonAssocRing",
"CStarMatrix.instNonUnitalNonAssocRing._proof_2",
"CStarMatrix.instNonUnitalNonAssocRing._proof_1",
"NonUnitalNonAssocRing.toAddCommGroup",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"CStarMatrix.instNonUnitalNonAssocRing._proof_4",
"CStarMatrix",
"NonUnitalNonAssocS... | true |
Ideal.qoutMapEquivTensorQout | Mathlib.LinearAlgebra.TensorProduct.Quotient | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"LinearEquiv.mk",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"... | true |
_private.Mathlib.Data.FinEnum.0.List.pfunFinEnum._simp_2 | Mathlib.Data.FinEnum | [
"funext_iff",
"propext",
"Eq"
] | false |
LinearEquiv.det_coe_symm | Mathlib.LinearAlgebra.Determinant | [
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst",
"False",
"LinearEquiv.symm",
"MonoidHom.instFunLike",
"instHDiv",
"NeZero.one",
"Mathlib.Tactic.FieldSimp.NF.cons_ne_zero",
"InvOneClass.toOne",
"HMul.hMul",
... | true |
Filter.EventuallyEq.hasFDerivAtFilter_iff | Mathlib.Analysis.Calculus.FDeriv.Congr | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"map_sub",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"Asymptotics.IsLittleOTVS",
"HSub.hSub",
"Pseu... | true |
Projectivization.rep | Mathlib.LinearAlgebra.Projectivization.Basic | [
"AddCommGroup.toAddCommMonoid",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"Subtype",
"Quotient.out",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"DivisionSemiring.toSemiring",
"Zero.toOfNat0",
"DivisionR... | true |
GrpCat.FilteredColimits.colimitGroup._proof_2 | Mathlib.Algebra.Category.Grp.FilteredColimits | [
"GrpCat.FilteredColimits.colimitInv",
"CategoryTheory.Functor",
"Mul.mk",
"Semigroup.toMul",
"GrpCat",
"One.mk",
"CategoryTheory.SmallCategory",
"Int",
"npowRec",
"MonCat.carrier",
"One.one",
"Inv.inv",
"instOfNat",
"GrpCat.instCategory",
"Inv.mk",
"Mul.mul",
"zpowRec",
"Monoid.toS... | false |
PosNum.isOne._sparseCasesOn_1 | Mathlib.Data.Num.Basic | [
"PosNum.ctorIdx",
"Nat.ne_of_beq_eq_false",
"PosNum.bit1",
"PosNum.rec",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"PosNum.bit0",
"Nat",
"Bool",
"Eq.refl",
"PosNum",
"OfNat.ofNat",
"Bool.false",
"PosNum.one"
] | false |
Lean.Grind.CommRing.instReprPoly.repr._f | Init.Grind.Ring.CommSolver | [
"Std.Format.instAppend",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.add",
"Std.Format.line",
"Std.Format.group",
"GE.ge",
"Lean.Grind.CommRing.Poly.below",
"instOfNatNat",
"Int",
"instLENat",
"Lean.Grind.CommRing.instReprMon",
"instHAppendOfAppend",
"instOfNat",
"_private.Init.G... | false |
Ordinal.one_add_of_omega0_le | Mathlib.SetTheory.Ordinal.Arithmetic | [
"Ordinal.omega0",
"Ordinal.partialOrder",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"cast",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"LE.le",
"Ordinal.natCast_add_of_omega0_le",
"Nat.cast",
"Ordinal.addMonoidWithOne",
"Ordinal.one",
"AddMonoidWithOne.toOne",
"instHAdd"... | true |
Orientation.oangle_eq_angle_or_eq_neg_angle | Mathlib.Geometry.Euclidean.Angle.Oriented.Basic | [
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"Orientation",
"Real.partialOrder",
"Real",
"Orientation.oangle",
"Real.Angle.cos_eq_real_cos_iff_eq_or_eq_neg",
"Real.Angle",
"Real.Angle.coe",
"Real.cos",
"Real.instRCLike",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"... | true |
_private.Mathlib.Algebra.Notation.Support.0.Function.range_subset_insert_image_mulSupport._simp_1_2 | Mathlib.Algebra.Notation.Support | [
"Membership.mem",
"Insert.insert",
"Set.instInsert",
"propext",
"Or",
"Set.mem_insert_iff",
"Eq",
"Set.instMembership",
"Set"
] | false |
Real.surjOn_log' | Mathlib.Analysis.SpecialFunctions.Log.Basic | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real.partialOrder",
"Real",
"Real.log_exp",
"Real.log_neg_eq_log",
"Real.instZero",
"congrArg",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Set.univ",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Set.Sur... | true |
LinearEquiv.ofLeftInverse | Mathlib.Algebra.Module.Submodule.Equiv | [
"Submodule",
"Function.LeftInverse",
"LinearEquiv.mk",
"Submodule.addCommMonoid",
"LinearMap.instFunLike",
"RingHom",
"RingHomSurjective.invPair",
"Function.comp",
"Membership.mem",
"LinearMap.range",
"Subtype",
"Submodule.module",
"LinearMap",
"LinearMap.rangeRestrict",
"AddCommMonoid",... | true |
Array.append_eq_toArray_iff | Init.Data.Array.Lemmas | [
"Array.instAppend",
"congrArg",
"Array.casesOn",
"List.append_toArray",
"Array.toList",
"List.toArray",
"Array",
"iff_self",
"instHAppendOfAppend",
"List",
"Array.mk.injEq",
"Iff",
"True",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"congrFun'",
"List.instAppend",
"Array.mk",
"Eq.symm... | true |
Int.toList_roc_eq_singleton_iff | Init.Data.Range.Polymorphic.IntLemmas | [
"Eq.mpr",
"Int.toList_roc_eq_toList_rco",
"congrArg",
"Std.PRange.instUpwardEnumerableInt",
"Int.decLe",
"Int.instDecidableEq",
"id",
"Std.Roc.toList",
"Int.add_lt_add_iff_right._simp_1",
"Int",
"LE.le",
"Int.toList_rco_eq_cons_iff._simp_1",
"List.cons",
"Std.PRange.instIsAlwaysFiniteInt_1... | true |
_private.Mathlib.Tactic.Variable.0.Mathlib.Command.Variable.completeBinders'._proof_9 | Mathlib.Tactic.Variable | [
"Lean.TSyntax",
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval"... | false |
AlgebraicGeometry.LocallyRingedSpace.restrictStalkIso_inv_eq_germ | Mathlib.Geometry.RingedSpace.LocallyRingedSpace | [
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
"PartialOrder.toPreorder",
"TopologicalSpace.O... | true |
CategoryTheory.Grothendieck.pre._proof_1 | Mathlib.CategoryTheory.Grothendieck | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.fiber",
"CategoryTheory.Grothendieck.base",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Functor.comp",
"CategoryTheory.Grothendieck",
"CategoryT... | false |
Lean.Meta.Grind.Arith.Linear.RingEqCnstrProof.recOn | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"Lean.Meta.Grind.Arith.Linear.RingEqCnstrProof",
"Lean.Meta.Grind.Arith.Linear.RingEqCnstrProof.rec",
"Lean.Meta.Grind.Arith.Linear.RingEqCnstrProof.symm",
"Lean.Expr",
"Int",
"Lean.Grind.Linarith.Var",
"Lean.Meta.Grind.Arith.Linear.RingEqCnstr... | false |
PFunctor.M.corecOn | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.Obj",
"PFunctor.M",
"PFunctor.M.corec"
] | true |
Lean.MonadError.toMonadExceptOf | Lean.Exception | [
"Lean.MonadError",
"Lean.Exception",
"MonadExceptOf"
] | true |
NumberField.RingOfIntegers.withValEquiv_symm_apply | Mathlib.Topology.Algebra.Valued.WithVal | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"AlgEquiv.instEquivLike",
"IsIntegralClosure",
"NumberField.RingOfIntegers.instIsIntegralClosureIntWithVal",
"CommRing",
"IsIntegralClosure.equiv",
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"RingEquiv.inst... | true |
CategoryTheory.RegularMono._sizeOf_inst | Mathlib.CategoryTheory.Limits.Shapes.RegularMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.RegularMono._sizeOf_1",
"SizeOf.mk",
"CategoryTheory.RegularMono",
"CategoryTheory.Category.toCategoryStruct",
"SizeOf",
"CategoryTheory.Category"
] | false |
_private.Init.Data.UInt.Lemmas.0.UInt32.toUSize_le._simp_1_1 | Init.Data.UInt.Lemmas | [
"UInt32.toNat",
"LE.le",
"instLENat",
"Nat",
"propext",
"instLEUInt32",
"UInt32",
"Eq",
"UInt32.le_iff_toNat_le"
] | false |
Std.DTreeMap.contains_inter | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap.instInter",
"Std.DTreeMap",
"Ord.mk",
"Ordering",
"Bool.and",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Inter.inter",
"Std.DTreeMap.wf",
"Std.DTreeMap.Internal.Impl.contains_inter",
"Bool",
"Std.DTreeMap.contains",
"Eq"
] | true |
WeakDual.CharacterSpace.homeoEval._proof_1 | Mathlib.Topology.ContinuousMap.Ideals | [
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"IsTopologicalDivisionRing.toIsTopologicalRing",
"PseudoMetricSpace.toUniformSpace",
"NormedDivisionRing.toDivisionRing",
"Distrib.toAdd",
"NonUnitalNonAssocRing... | false |
Std.HashMap.Raw.size_add_size_eq_size_union_add_size_inter | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.WF.out",
"Std.DHashMap.Raw.size_add_size_eq_size_union_add_size_inter",
"Std.HashMap.Raw.WF",
"LawfulHashable",
"Std.HashMap.Raw",
"Inter.inter",
"instHAdd",
"EquivBEq",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Std.HashMap.Raw.inner",
"Std.HashMap.Raw.instInterOfBEqOfHashable",
... | true |
List.finite_toSet | Mathlib.Data.Set.Finite.Basic | [
"setOf",
"Set.Finite",
"Membership.mem",
"Multiset",
"Multiset.finite_toSet",
"Quotient.mk",
"List",
"List.instMembership",
"List.isSetoid"
] | true |
CategoryTheory.Retract.refl_r | Mathlib.CategoryTheory.Retract | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Retract.r",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category",
"CategoryTheory.Retract.refl"
] | true |
_private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.ElimApp.State.alts._default | Lean.Elab.Tactic.Induction | [
"id",
"List.toArray",
"Array",
"Lean.Elab.Tactic.ElimApp.Alt",
"List.nil"
] | false |
TensorProduct.map_comp_comm_eq | Mathlib.LinearAlgebra.TensorProduct.Map | [
"TensorProduct.comm",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"RingHom",
"RingHomCompTriple.right_ids",
"LinearMap.module",
"TensorProduct.map",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"LinearMap.comp",
"LinearEquiv.toLinearMap",
"CommMonoid.to... | true |
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