name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Triangulated.TStructure.instIsGEObjιHeartOfNatInt | Mathlib.CategoryTheory.Triangulated.TStructure.Heart | [
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Triangulated.TStructure.ιHeart_obj_mem",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Preadditive",
"CategoryTheory.Triangulated.TStructure",
"And.right",
"instOfNat",
"CategoryTheory.Triangulated.TStructure.ιHeart",
... | true |
TensorProduct.equivFinsuppOfBasisLeft_symm | Mathlib.LinearAlgebra.TensorProduct.Basis | [
"Pi.Function.module",
"LinearEquiv.symm",
"Pi.addCommMonoid",
"Finsupp.module",
"TensorProduct.comm",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"Finsupp.sum_single_index",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Finsupp.sum",
"Fins... | true |
Lean.Elab.DefsParsedSnapshot.casesOn | Lean.Elab.DefView | [
"Lean.Elab.DefParsed",
"Lean.Elab.DefsParsedSnapshot",
"Array",
"Lean.Elab.DefsParsedSnapshot.rec",
"Lean.Elab.DefsParsedSnapshot.mk",
"Lean.Language.Snapshot"
] | false |
_private.Mathlib.Data.Finsupp.NeLocus.0.Finsupp.subset_mapRange_neLocus._simp_1_1 | Mathlib.Data.Finsupp.NeLocus | [
"propext",
"Eq",
"Not",
"not_imp_not"
] | false |
_private.Mathlib.MeasureTheory.Function.LpSpace.Complete.0.MeasureTheory.Lp.eLpNorm'_lim_le_liminf_eLpNorm'._simp_1_1 | Mathlib.MeasureTheory.Function.LpSpace.Complete | [
"ENNReal.rpow_mul",
"Real",
"HMul.hMul",
"ENNReal.instPowReal",
"HPow.hPow",
"Real.instMul",
"ENNReal",
"instHPow",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Filter.isAddUnit_iff | Mathlib.Order.Filter.Pointwise | [
"Pure.pure",
"Filter.instAdd",
"Eq.mpr",
"AddUnits.val",
"Filter.add_eq_zero_iff",
"congrArg",
"IsAddUnit.filter",
"AddMonoid.toAddZeroClass",
"Filter.pure_injective",
"AddUnits.neg_add",
"Exists",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"IsAddUnit",
"Su... | true |
BoxIntegral.unitPartition.mem_prepartition_iff._simp_1 | Mathlib.Analysis.BoxIntegral.UnitPartition | [
"Nat.instMulZeroClass",
"Finset",
"Membership.mem",
"Exists",
"BoxIntegral.TaggedPrepartition.instMembershipBox",
"Int",
"BoxIntegral.unitPartition.admissibleIndex",
"BoxIntegral.unitPartition.prepartition",
"And",
"Fintype",
"Finset.instSetLike",
"Nat",
"BoxIntegral.unitPartition.mem_prepar... | false |
MeasureTheory.Measure.definition._@.Mathlib.MeasureTheory.Constructions.Pi.668077722._hygCtx._hyg.2 | Mathlib.MeasureTheory.Constructions.Pi | [
"MeasureTheory.Measure",
"MeasureTheory.OuterMeasure.pi",
"MeasureTheory.Measure.pi_caratheodory",
"MeasurableSpace",
"MeasureTheory.Measure.toOuterMeasure",
"Fintype",
"MeasureTheory.OuterMeasure.toMeasure",
"MeasurableSpace.pi"
] | false |
_private.Mathlib.Tactic.Widget.Conv.0.Mathlib.Tactic.Conv.Path.ofSubExprPosArray.appT | Mathlib.Tactic.Widget.Conv | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"instOfNatNat",
"Array",
"List",
"instHAdd",
"HAdd.hAdd",
"Lean.Meta.instInhabitedMetaM",
"Nat",
"instAddNat",
"Mathlib.Tactic.Conv.Path",
"OfNat.ofNat",
"Fin",
"List.length",
"Array.size",
"Option"
] | true |
Lean.Server.Test.Runner.Client.Hyp.isType? | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.Hyp",
"Bool",
"Option"
] | true |
_private.Std.Sat.AIG.Lemmas.0.Std.Sat.AIG.isConstant.match_1.splitter._sparseCasesOn_2 | Std.Sat.AIG.Lemmas | [
"Std.Sat.AIG.Decl",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Nat",
"Bool",
"Eq.refl",
"Std.Sat.AIG.Decl.gate",
"Std.Sat.AIG.Decl.rec",
"Std.Sat.AIG.Decl.atom",
"Std.Sat.AIG.Decl.false",
"Std.Sat.AIG.Decl.ctorIdx",
"OfNat.ofNat",
"Bool.fa... | false |
Plausible.Rand.up | Plausible.Random | [
"Pure.pure",
"RandomGen",
"Plausible.RandT.up",
"Monad.toApplicative",
"ULift",
"Id.run",
"Id",
"Applicative.toPure",
"Id.instMonad",
"ULift.up",
"Plausible.RandG"
] | true |
Matrix.conjTranspose_eq_zero._simp_1 | Mathlib.LinearAlgebra.Matrix.ConjTranspose | [
"Matrix",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"StarAddMonoid.toInvolutiveStar",
"AddZero.toZero",
"AddMonoid",
"propext",
"StarAddMonoid",
"Matrix.conjTranspose_eq_zero",
"Zero.toOfNat0",
"InvolutiveStar.toStar",
"OfNat.ofNat",
"Matrix.conjTranspose",
"Eq",
"Matrix.zero... | false |
Set.mem_center_iff_addMonoidHom | Mathlib.RingTheory.NonUnitalSubsemiring.Basic | [
"Eq.mpr",
"HMul.hMul",
"_private.Mathlib.RingTheory.NonUnitalSubsemiring.Basic.0.Set.mem_center_iff_addMonoidHom._simp_1_1",
"congrArg",
"AddMonoidHom.compl₂",
"AddMonoidHom.compr₂",
"AddMonoid.toAddZeroClass",
"Commute",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"AddMonoidHom.mul",
... | true |
LieSubmodule.toSubmodule_eq_top._simp_1 | Mathlib.Algebra.Lie.Submodule | [
"Submodule",
"CommRing",
"LieSubmodule.instTop",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieSubmodule.toSubmodule",
"LieSubmodule",
"AddCommGroup",
"Submodule.instTop",
"LieRing",
"CommRing.toCommSemiring",
"LieRingModule",
"propext",
"Module",
"LieSubmodule.toSubmodu... | false |
mdifferentiableOn_iff_of_subset_source | Mathlib.Geometry.Manifold.MFDeriv.Basic | [
"extChartAt",
"instAddMonoidWithOneENat",
"NormedSpace",
"chartAt",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Function.comp",
"PartialEquiv.symm",
"IsManifold",
"HasSubset.Subset",
"IsManifold.chart_mem_maximalAtlas",
"MDifferentiableOn",
"AddMonoidWithOne.toOne",
"Topol... | true |
Part.mem_map_iff._simp_1 | Mathlib.Data.Part | [
"Part",
"Membership.mem",
"Exists",
"Part.instMembership",
"And",
"propext",
"Part.mem_map_iff",
"Eq",
"Part.map"
] | false |
Matrix.SpecialLinearGroup.coe_pow | Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | [
"CommRing",
"Matrix.SpecialLinearGroup",
"CommSemiring.toSemiring",
"Matrix",
"AddGroupWithOne.toAddMonoidWithOne",
"Matrix.SpecialLinearGroup.instPowNat",
"Monoid.toPow",
"AddMonoidWithOne.toOne",
"CommRing.toCommSemiring",
"Fintype",
"HPow.hPow",
"Nat",
"Semiring.toMonoid",
"One.toOfNat1... | true |
_private.Init.NotationExtra.0.Lean.expandBracketedBindersAux.loop._f | Init.NotationExtra | [
"Pure.pure",
"Lean.Syntax.getArgs",
"Nat.le_of_succ_le",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Option.some",
"Lean.Syntax",
"ReaderT.instMonad",
"instOfNatNat",
"LE.le",
"Lean.MacroM",
"instLENat",
"Applicative.toPure",
"Lean.Macro.Context",
"Array",
"GetElem.getElem",
"Nat.b... | false |
CategoryTheory.CategoryOfElements.homMk.congr_simp | Mathlib.CategoryTheory.Elements | [
"CategoryTheory.categoryOfElements",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"Eq.rec",
"Sigma.fst",
"CategoryTheory.CategoryOfElements.homMk",
"CategoryTh... | true |
Polynomial.isRoot_iterate_derivative_of_lt_rootMultiplicity | Mathlib.Algebra.Polynomial.FieldDivision | [
"Polynomial.derivative",
"Polynomial.C",
"Polynomial.pow_rootMultiplicity_dvd",
"CommRing",
"Dvd.dvd",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Polynomial.IsRoot",
"semigroupDvd",
"LinearMap.instFunLike",
"HSub.hSub",
"RingHom",
"SemigroupWithZero.to... | true |
AddHom.addHomClass | Mathlib.Algebra.Group.Hom.Defs | [
"AddHom",
"AddHom.map_add'",
"AddHom.funLike",
"AddHomClass",
"AddHomClass.mk",
"Add"
] | true |
Convex.convex_remove_iff_notMem_convexHull_remove | Mathlib.Analysis.Convex.Hull | [
"Set.Subset.antisymm",
"Set.mem_singleton",
"Eq.mpr",
"Set.diff_subset",
"False",
"ChainCompletePartialOrder.instOfCompleteLattice",
"congrArg",
"DistribMulAction.toDistribSMul",
"subset_convexHull",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Membership.mem",
"AddZeroClass.toAdd... | true |
_private.Mathlib.Order.Partition.Basic.0.Partition.instSemilatticeInf._proof_17 | Mathlib.Order.Partition.Basic | [
"Lean.Grind.eq_false_of_not_eq_true",
"of_eq_false",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"forall_not_of_not_exists",
"Lean.Grind.not_and",
"eq_false",
"congrArg",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Lean.Grind.imp_false_eq",
"Member... | false |
Submonoid.fromLeftInv.eq_1 | Mathlib.GroupTheory.Submonoid.Inverses | [
"Submonoid.fromLeftInv",
"Monoid",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"Membership.mem",
"MulOne.toMul",
"Subtype",
"Submonoid.leftInv",
"MulOneClass.toMulOne",
"One.toOfNat1",
"Eq.refl",
"Exists.choose",
"Submonoid.instSetLike",
"OfNat.ofNat",
"Subtype.val",
"Eq",
... | true |
_private.Mathlib.Tactic.TacticAnalysis.0.Mathlib.TacticAnalysis.Entry.import.unsafe_impl_2 | Mathlib.Tactic.TacticAnalysis | [
"Classical.ofNonempty",
"Mathlib.TacticAnalysis.Config",
"instInhabitedExceptTOfMonad",
"String",
"Mathlib.TacticAnalysis.Entry",
"Id",
"ExceptT",
"String.instInhabited",
"instNonemptyOfInhabited",
"Pi.instNonempty",
"Id.instMonad",
"Lean.Options",
"Lean.Environment"
] | true |
CategoryTheory.Adjunction.CoreUnitCounit.mk | Mathlib.CategoryTheory.Adjunction.Basic | [
"CategoryTheory.Adjunction.CoreUnitCounit",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Functor.associator",
"CategoryTheory.Functor.whiskerLeft",
"a... | true |
Continuous.stronglyMeasurableAtFilter | Mathlib.MeasureTheory.Integral.IntegrableOn | [
"TopologicalSpace.PseudoMetrizableSpace",
"MeasureTheory.Measure",
"Continuous",
"StronglyMeasurableAtFilter",
"Continuous.stronglyMeasurable",
"MeasurableSpace",
"TopologicalSpace",
"OpensMeasurableSpace",
"SecondCountableTopologyEither",
"Filter",
"MeasureTheory.StronglyMeasurable.stronglyMeas... | true |
liminf_eq_top | Mathlib.Topology.Order.LiminfLimsup | [
"OrderTopology",
"Lattice.toSemilatticeSup",
"Filter.liminf",
"CompleteLattice.toLattice",
"instFirstCountableTopologyOrderDual",
"PartialOrder.toPreorder",
"limsup_eq_bot",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CoheytingAlgebra.toOrderTop",
"Filter.EventuallyEq",
"ConditionallyCo... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_492 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"List.countP",
"Finset.mem_singleton",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"GetElem",
"False",
"Equiv.instEquivLike",
"Lean.Grind.nestedProof",
"List.idxOfNth_lt_length_iff",
"eq_false",
"instLawfulBEq",
"List.Pairwise",
... | false |
_private.Mathlib.LinearAlgebra.CliffordAlgebra.Contraction.0.CliffordAlgebra.«term_⌋__1» | Mathlib.LinearAlgebra.CliffordAlgebra.Contraction | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Name.anonymous",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
Tropical.untrop_add | Mathlib.Algebra.Tropical.Basic | [
"LinearOrder",
"DistribLattice.toLattice",
"SemilatticeInf.toMin",
"Tropical",
"instHAdd",
"HAdd.hAdd",
"Eq",
"instDistribLatticeOfLinearOrder",
"Min.min",
"rfl",
"Lattice.toSemilatticeInf",
"Tropical.untrop",
"Tropical.instAdd"
] | true |
WithLp.instProdNorm | Mathlib.Analysis.Normed.Lp.ProdLp | [
"WithLp",
"Norm.norm",
"Real.instPow",
"Real",
"instHDiv",
"LinearOrder.toDecidableEq",
"Real.instZero",
"Real.instDivInvMonoid",
"Norm",
"HDiv.hDiv",
"WithLp.snd",
"dite",
"Real.instAdd",
"Real.instOne",
"WithLp.fst",
"instHAdd",
"ENNReal.toReal",
"Real.instMax",
"HPow.hPow",
... | true |
CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim._proof_5 | Mathlib.CategoryTheory.Limits.Fubini | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.instHasColimitProd",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.colim",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.uncurry",
... | false |
AddMonoidHom.surjective_of_surjective_of_injective_of_left_exact | Mathlib.Algebra.FiveLemma | [
"Function.Exact",
"_private.Mathlib.Algebra.FiveLemma.0.AddMonoidHom.surjective_of_surjective_of_injective_of_left_exact.match_1_1",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Unit.unit",
"Set.mem_range",
"AddMonoidHom.instAddMonoidHomClass",
"instZeroAddMonoidHom",
"congrArg",
"AddMonoid.toAddZer... | true |
BoundedContinuousFunction.mk.inj | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"Real.instLE",
"Real",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"Exists",
"LE.le",
"TopologicalSpace",
"PseudoMetricSpace",
"BoundedContinuousFunction.mk",
"BoundedContinuousFunction.mk.noConfusion",
"eq_of_heq",
"HEq",
"ContinuousMap.toFun",
"Dist.dist",
"PseudoMetricSpace.t... | true |
Subgroup.leftCosetEquivSubgroup._proof_8 | Mathlib.GroupTheory.Coset.Basic | [
"Subgroup.leftCosetEquivSubgroup._proof_6",
"instHSMul",
"mem_leftCoset_iff",
"instSMulOfMul",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Set.Elem",
"Subgroup.leftCosetEquivSu... | false |
CategoryTheory.Equivalence.preregular_isSheaf_iff | Mathlib.CategoryTheory.Sites.Coherent.Equivalence | [
"CategoryTheory.Functor.op",
"Eq.mpr",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"CategoryTheory.Preregular",
"Opposite",
"CategoryTheory.Presheaf.isSheaf_of_iso_iff",
"congrArg",
"CategoryTheory.Functor.category",
"Catego... | true |
Asymptotics.IsBigOWith.congr_left | Mathlib.Analysis.Asymptotics.Defs | [
"Real",
"Asymptotics.IsBigOWith",
"Norm",
"Asymptotics.IsBigOWith.congr",
"Eq",
"Filter",
"rfl"
] | true |
T35Space.toT0Space | Mathlib.Topology.Separation.CompletelyRegular | [
"TopologicalSpace",
"T0Space",
"T35Space"
] | true |
DistribMulActionHomClass | Mathlib.GroupTheory.GroupAction.Hom | [
"Monoid",
"DistribMulActionSemiHomClass",
"MonoidHom.instFunLike",
"outParam",
"MonoidHom",
"Monoid.toMulOneClass",
"MulOneClass.toMulOne",
"MonoidHom.id",
"AddMonoid",
"DistribMulAction",
"DFunLike.coe",
"FunLike"
] | true |
Function.RightInverse.eq | Mathlib.Logic.Function.Basic | [
"Function.RightInverse",
"Eq"
] | true |
Lean.Doc.Parser.instOrdUnorderedListType.match_1 | Lean.DocString.Parser | [
"Unit.unit",
"Lean.Doc.Parser.UnorderedListType.casesOn",
"Lean.Doc.Parser.UnorderedListType.ctorIdx",
"Lean.Doc.Parser.instOrdUnorderedListType._sparseCasesOn_2",
"Nat.hasNotBit",
"Lean.Doc.Parser.UnorderedListType.plus",
"Unit",
"Lean.Doc.Parser.UnorderedListType.asterisk",
"Lean.Doc.Parser.Unorde... | false |
Polynomial.X_pow_sub_one_eq_prod | Mathlib.RingTheory.Polynomial.Cyclotomic.Basic | [
"Multiset.toFinset",
"Eq.mpr",
"Polynomial.C",
"IsDomain",
"Polynomial.instOne",
"Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq",
"CommRing",
"Polynomial.roots",
"Polynomial.natDegree_X_pow_sub_C",
"Multiset.map",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"Multiset.prod... | true |
_private.Mathlib.RingTheory.MvPolynomial.Groebner.0.MonomialOrder.degree_reduce_lt._simp_1_5 | Mathlib.RingTheory.MvPolynomial.Groebner | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"LE.le",
"sup_le_iff",
"And",
"Max.max",
"propext",
"SemilatticeSup.toPartialOrder",
"Eq",
"SemilatticeSup"
] | false |
Lean.Elab.Tactic.Grind.SavedState | Lean.Elab.Tactic.Grind.Basic | [
"Lean.Elab.Tactic.Grind.SavedState.mk"
] | true |
SetRel.isCover_id | Mathlib.Data.Rel.Cover | [
"SetRel.id",
"SetRel",
"congrArg",
"Membership.mem",
"Exists",
"Prod.mk",
"HasSubset.Subset",
"iff_self",
"exists_eq_right'._simp_1",
"funext",
"And",
"Iff",
"SetRel.IsCover",
"implies_congr",
"SetRel.mem_id._simp_1",
"True",
"of_eq_true",
"Eq.refl",
"congrFun'",
"Prod",
"Eq"... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.getKeyD_insertManyIfNewUnit_list_of_mem._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 |
HomologicalComplex.truncGE'.XIso.congr_simp | Mathlib.Algebra.Homology.Embedding.TruncGE | [
"ComplexShape.Embedding.BoundaryGE",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.HasHomology",
"HomologicalComplex",
"CategoryTheory.Iso",
"HomologicalComplex.truncGE'.XIso",
"ComplexShape",
"HomologicalComplex.truncGE'.X",
"ComplexShape.Embedding.f",
"ComplexShape.Embedding",
... | true |
MonoidAlgebra.mul_single_apply_of_not_exists_mul | Mathlib.Algebra.MonoidAlgebra.Defs | [
"Finsupp.instFunLike",
"not_exists._simp_1",
"HMul.hMul",
"eq_false",
"congrArg",
"Finsupp.sum_single_index",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"Classical.propDecidable",
"Mul",
"Exists",
"AddZeroClass.toAddZero",
"MonoidAlgebra.instMul",
"Eq.mp",
"id",
"instDistribOfSemiring"... | true |
IO.Error.noSuchThing | Init.System.IOError | [
"String",
"UInt32",
"IO.Error",
"IO.Error.noSuchThing",
"Option"
] | true |
CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction_actionAssocIso_op | Mathlib.CategoryTheory.Monoidal.Action.Opposites | [
"Opposite",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso",
"CategoryTheory.Iso.op",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj",
"CategoryTheory.Iso",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction.toMonoidalLef... | true |
CentroidHom.copy._proof_1 | Mathlib.Algebra.Ring.CentroidHom | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"CentroidHomClass.map_mul_left",
"CentroidHom.instCentroidHomClass",
"Distrib.toMul",
"congr",
"True",
"eq_self",
"of_eq_true",
"NonUnitalNonAssocSemiring.toDistrib",
"congrFun'",
"NonUnitalNonAssocSemiring",
"CentroidHom.instFunLike",
"Eq",
"... | false |
RingEquiv.ofLeftInverse._proof_4 | Mathlib.Algebra.Ring.Subring.Basic | [
"RingHom.map_add'",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Subring.instSetLike",
"AddMonoid.toAddZeroClass",
"RingHom",
"Membership.mem",
"Subring.instSubringClass",
"AddZeroClass.toAddZero",
"Subtype",
"NonAssocSemiring.toMulZeroOneClass",
"NonAssocRing",
"AddCommMonoid... | false |
Tree.node.elim | Mathlib.Data.Tree.Basic | [
"Tree.node",
"PULift.up",
"Tree.ctorElim",
"Tree",
"Nat",
"Tree.ctorIdx",
"Eq.symm",
"Eq"
] | false |
Lean.Meta.DiscrTree.Key.format | Lean.Meta.DiscrTree.Basic | [
"Std.Format.instAppend",
"String",
"Lean.FVarId",
"Lean.Meta.DiscrTree.Key",
"instToFormatOfToString",
"Std.ToFormat.format",
"instHAppendOfAppend",
"instToStringNat",
"Unit",
"Nat",
"Std.Format",
"Lean.Name",
"_private.Lean.Meta.DiscrTree.Basic.0.Lean.Meta.DiscrTree.Key.format.match_1",
"... | true |
CategoryTheory.CommSq.shortComplex'_X₁ | Mathlib.Algebra.Homology.CommSq | [
"CategoryTheory.CommSq.shortComplex'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CommSq",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Limits.HasBinaryBiproduct",
"CategoryTheory.Preadditive",
"CategoryTheory.Preadditive.preadditiveHasZeroMorphisms",
"Eq.refl",
"... | true |
_private.Mathlib.Algebra.Group.Subsemigroup.Basic.0.MulHom.ofDense._simp_1 | Mathlib.Algebra.Group.Subsemigroup.Basic | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Lean.Elab.Command.instMonadEvalTermElabMCommandElabM | Lean.Elab.Command | [
"Lean.Elab.Command.liftTermElabM",
"MonadEval.mk",
"Lean.Elab.Term.TermElabM",
"Lean.Elab.Command.CommandElabM",
"MonadEval"
] | true |
CategoryTheory.Iso.hom_inv_id_triangle_hom₂ | Mathlib.CategoryTheory.Triangulated.Basic | [
"CategoryTheory.Pretriangulated.TriangleMorphism.hom₂",
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.hom_inv_id",
"id",
"CategoryTheory.Iso",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Tri... | true |
Lean.Elab.Command.Structure.StructFieldInfo.numBinders | Lean.Elab.Structure | [
"Nat",
"Lean.Elab.Command.Structure.StructFieldInfo"
] | true |
IsSimpleOrder.completeBooleanAlgebra | Mathlib.Order.Atoms | [
"Lattice",
"BooleanAlgebra",
"BooleanAlgebra.sdiff_eq",
"IsSimpleOrder.completeBooleanAlgebra._proof_4",
"PartialOrder.toPreorder",
"IsSimpleOrder",
"Classical.propDecidable",
"Preorder.toLE",
"BooleanAlgebra.toCompl",
"SemilatticeInf.toPartialOrder",
"CompleteBooleanAlgebra.mk",
"BooleanAlgeb... | true |
Algebra.Extension.toBaseChange._proof_2 | Mathlib.RingTheory.Extension.Basic | [
"CommRing",
"Algebra.to_smulCommClass",
"Algebra.Extension.commRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra.TensorProduct.instCommRing",
"Algebra",
"RingHom",
"Algebra.toModule",
"Algebra.id",
... | false |
_private.Init.Data.List.Perm.0.List.perm_iff_count._simp_1_3 | Init.Data.List.Perm | [
"Nat.succ_inj",
"Nat",
"propext",
"Nat.succ",
"Eq"
] | false |
Lean.Parser.Term.depArrow._regBuiltin.Lean.Parser.Term.depArrow.declRange_3 | Lean.Parser.Term | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"IO",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk",
"Lean.Name.mkStr4"
] | false |
LinearEquiv.congrLeft_symm_apply | Mathlib.Algebra.Module.Equiv.Basic | [
"LinearEquiv.symm",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.instAdd",
"LinearEquiv.automorphismGroup._proof_7",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"LinearEquiv.arrowCongrA... | true |
_private.Init.Data.Array.Lemmas.0.Array.toList_reverse._simp_1_7 | Init.Data.Array.Lemmas | [
"Nat.le_refl",
"LE.le",
"instLENat",
"Nat",
"True",
"eq_true",
"Eq"
] | false |
_private.Mathlib.Algebra.Module.ZLattice.Covolume.0._auto_43 | Mathlib.Algebra.Module.ZLattice.Covolume | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Equiv.embeddingFinSucc_snd | Mathlib.Logic.Equiv.Fin.Basic | [
"instNeZeroNatHAdd_1",
"Equiv.instEquivLike",
"Membership.mem",
"Fin.instOfNat",
"Equiv",
"Subtype",
"Sigma.fst",
"instOfNatNat",
"Equiv.embeddingFinSucc",
"Function.Embedding",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"Set.range",
"Function.instFunLikeEmbe... | true |
CommRingCat.HomTopology.precompHomeomorph._proof_4 | Mathlib.Algebra.Category.Ring.Topology | [
"Continuous",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommRingCat",
"CommRingCat.HomTopology.continuous_precomp",
"CommRingCat.instCategory",
"CategoryTheory.Iso",
"TopologicalSpace",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategor... | false |
CategoryTheory.Functor.instPreservesEffectiveEpiFamiliesOfIsEquivalence | Mathlib.CategoryTheory.EffectiveEpi.Preserves | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"inferInstance",
"CategoryTheory.Functor.PreservesEffectiveEpiFamilies",
"CategoryTheory.Functor.map",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Functor.IsEquivalence",
"CategoryTheory.instEffectiveEp... | true |
MultipliableLocallyUniformly.eq_1 | Mathlib.Topology.Algebra.InfiniteSum.UniformOn | [
"UniformSpace",
"HasProdLocallyUniformly",
"MultipliableLocallyUniformly",
"Exists",
"TopologicalSpace",
"Eq.refl",
"Eq",
"CommMonoid"
] | true |
_private.Mathlib.RingTheory.RingHom.Locally.0.RingHom.locally_stableUnderComposition._simp_1_8 | Mathlib.RingTheory.RingHom.Locally | [
"Finset",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"map_sum",
"AddCommMonoid",
"AddCommMonoid.toAddMonoid",
"Eq.symm",
"Eq",
"DFunLike.coe",
"Finset.sum",
"FunLike"
] | false |
CategoryTheory.Limits.Cone.extendHom | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Limits.ConeMorphism.mk",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.Cone.extend",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.Cone.extendHom._proof_1",
"CategoryTheory.Category.toC... | true |
DirectLimit.instGroup._proof_8 | Mathlib.Algebra.Colimit.DirectLimit | [
"DirectLimit.setoid",
"Semigroup.toMul",
"instHDiv",
"HMul.hMul",
"map_inv",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"DirectLimit.instMonoid",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"DirectLimit.map",
"HDiv.hDiv",
"DivInvM... | false |
Equiv.Perm.cycleFactorsAux._proof_13 | Mathlib.GroupTheory.Perm.Cycle.Factors | [
"Equiv.Perm.cycleOf_inv",
"Equiv.Perm.instDecidableRelSameCycle",
"Eq.mpr",
"False",
"DivInvMonoid.toInv",
"InvOneClass.toOne",
"Equiv.instEquivLike",
"HMul.hMul",
"Equiv.Perm.instInv",
"DivInvOneMonoid.toInvOneClass",
"Commute.inv_left_iff",
"eq_false",
"Monoid.toMulOneClass",
"congrArg",... | false |
_private.Mathlib.Logic.Relation.0.Relation.reflTransGen_transGen._simp_1_1 | Mathlib.Logic.Relation | [
"Relation.reflGen_transGen",
"Relation.TransGen",
"Eq.symm",
"Relation.ReflGen",
"Eq",
"Relation.ReflTransGen"
] | false |
_private.Lean.Elab.Match.0.Lean.Elab.Term.precheckMatch.match_9 | Lean.Elab.Match | [
"Lean.TSyntax",
"Unit.unit",
"Option.casesOn",
"Option.some",
"List.cons",
"Array",
"Option.none",
"Unit",
"Lean.SyntaxNodeKind",
"Prod",
"Lean.Name.mkStr1",
"List.nil",
"Option"
] | false |
Batteries.Tactic.generalizeProofsElab | Batteries.Tactic.GeneralizeProofs | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Parser.Tactic.location",
"Lean.Parser.Tactic.optConfig",
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.const",
"Lean.binderIdent",
"OfN... | true |
_private.Mathlib.GroupTheory.GroupAction.Blocks.0.MulAction.stabilizer_orbit_eq._simp_1_2 | Mathlib.GroupTheory.GroupAction.Blocks | [
"instHSMul",
"Group",
"Membership.mem",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"MulAction",
"propext",
"Monoid.toSemigroup",
"HSMul.hSMul",
"MulAction.mem_stabilizer_iff",
"SemigroupAction.toSMul",
"MulAction.stabilizer",
"MulAction.toSemigroupAction",
"Eq.symm",
... | false |
lp.instInvolutiveStar._proof_1 | Mathlib.Analysis.Normed.Lp.lpSpace | [
"Pi.instStarForall",
"Subtype.mk.congr_simp",
"star_star",
"congrArg",
"instAddCommGroupPreLp",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Subtype",
"StarAddMonoid.toInvolutiveStar",
"NormedStarGroup",
"Subtype.mk",
"AddSubgroup",
"funext",
"lp",
"AddGroup.toSubNegMonoid",
"AddSubgr... | false |
Std.DHashMap.Internal.Raw₀.reinsertAux_eq | Std.Data.DHashMap.Internal.Model | [
"Std.DHashMap.Internal.Raw₀.reinsertAux",
"Subtype",
"instOfNatNat",
"Array",
"Hashable.hash",
"Nat",
"LT.lt",
"Std.DHashMap.Internal.AssocList",
"Hashable",
"Std.DHashMap.Internal.AssocList.cons",
"instLTNat",
"OfNat.ofNat",
"Subtype.val",
"Eq",
"Array.size",
"rfl",
"Subtype.propert... | true |
Matrix.linfty_opNorm_replicateCol | Mathlib.Analysis.Matrix.Normed | [
"Norm.norm",
"Real",
"SeminormedAddCommGroup",
"Finset.univ",
"Matrix",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"Unique",
"Matrix.replicateCol",
"NNReal.instSemilatticeSup",
"NNReal",
"congr_arg",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"SeminormedAddCommGroup.toNorm",
"Ma... | true |
Lean.Grind.CommRing.instReprPoly.repr._unsafe_rec | Init.Grind.Ring.CommSolver | [
"Std.Format.instAppend",
"Lean.Grind.CommRing.Poly",
"Std.Format.line",
"Std.Format.group",
"GE.ge",
"instOfNatNat",
"Int",
"instLENat",
"Lean.Grind.CommRing.instReprMon",
"instHAppendOfAppend",
"instOfNat",
"_private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.instReprPoly.repr.match_1",... | false |
_private.Init.Data.String.Legacy.0.String.splitAux._unary._proof_1 | Init.Data.String.Legacy | [
"String",
"Nat.sub_lt_sub_left",
"HSub.hSub",
"decide_eq_true",
"String.utf8ByteSize",
"mt",
"Nat.gt_of_not_le",
"instSubNat",
"LE.le",
"instLENat",
"String.Pos.Raw",
"Bool.true",
"instHSub",
"String.Pos.Raw.atEnd",
"Nat",
"LT.lt",
"String.Pos.Raw.lt_next",
"Bool",
"instLTNat",
... | false |
_private.Batteries.Data.List.Lemmas.0.List.foldlIdx_const._proof_1_1 | Batteries.Data.List.Lemmas | [
"False",
"eq_false",
"Classical.byContradiction",
"Eq.mp",
"id",
"List.foldl",
"List.foldlIdx",
"List.foldlIdx_nil",
"List.foldl_nil",
"Nat",
"True",
"eq_true",
"Function.const",
"Eq.refl",
"Eq.symm",
"Eq",
"Not",
"Eq.trans",
"True.intro",
"List.nil"
] | false |
AbsoluteValue.toNormedRing._proof_7 | Mathlib.Analysis.Normed.Ring.Basic | [
"NegZeroClass.toNeg",
"Real.partialOrder",
"Real",
"ENNReal.ofReal",
"Real.semiring",
"Distrib.toAdd",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"instDistribOfSemiring",
"instHAdd",
"HAdd.hAdd",
"Ring.toAddCommGrou... | false |
Equiv.Finset.prod._proof_7 | Mathlib.Data.Finset.Prod | [
"Iff.mpr",
"SProd.sprod",
"Finset",
"Membership.mem",
"Subtype",
"Prod.mk",
"Prod.fst",
"Subtype.mk",
"And",
"Finset.instSProd",
"And.right",
"Finset.instSetLike",
"And.intro",
"Iff.mp",
"Equiv.Finset.prod._proof_3",
"Prod",
"Subtype.val",
"Prod.snd",
"Finset.mem_product",
"Set... | false |
CategoryTheory.Equivalence.faithful_inverse | Mathlib.CategoryTheory.Equivalence | [
"CategoryTheory.Equivalence.fullyFaithfulInverse",
"CategoryTheory.Equivalence",
"CategoryTheory.Functor.FullyFaithful.faithful",
"CategoryTheory.Functor.Faithful",
"CategoryTheory.Category",
"CategoryTheory.Equivalence.inverse"
] | true |
CategoryTheory.Pseudofunctor.Grothendieck.Hom.mk | Mathlib.CategoryTheory.Bicategory.Grothendieck | [
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Pseudofunctor.Grothendieck",
"CategoryTheory.Cat.str",
"CategoryTheory.Pseudofunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.toCategoryStruct",
... | true |
instRingUniversalEnvelopingAlgebra._aux_43 | Mathlib.Algebra.Lie.UniversalEnveloping | [
"LieAlgebra.toModule",
"UniversalEnvelopingAlgebra.Rel",
"CommRing",
"LieRing.toAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"RingQuot.intCast",
"UniversalEnvelopingAlgebra",
"TensorAlgebra",
"Int",
"TensorAlgebra.instRing",
"LieRing",
"CommRing.toCommSemiring",
"LieAlgebra"
] | false |
CategoryTheory.Precoverage.Saturate.hcongr_5 | Mathlib.CategoryTheory.Sites.Coverage | [
"CategoryTheory.Precoverage",
"CategoryTheory.Precoverage.Saturate",
"HEq.refl",
"CategoryTheory.Sieve",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Analysis.Calculus.Implicit.0.HasStrictFDerivAt.implicitToOpenPartialHomeomorph._proof_1 | Mathlib.Analysis.Calculus.Implicit | [
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"NormedAddCommGroup.toMetricSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"EMetricSpace.metrizableSpace",
"PseudoM... | false |
AlgebraicGeometry.Scheme.Modules.pushforwardCongr._proof_1 | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommRingCat",
"TopCat.instCategory",
"Eq.rec",
"CommRingCat.instCategory",
"AlgebraicGeometry.LocallyRingedSpace.Hom.toHom",
"AlgebraicGeometry.Scheme.Hom.toLRSHom'",
... | false |
_private.Mathlib.Tactic.Algebra.Basic.0.Mathlib.Tactic.Algebra.RingCompute.cast.match_3 | Mathlib.Tactic.Algebra.Basic | [
"Mathlib.Tactic.Ring.Common.Result.mk",
"Mathlib.Tactic.Ring.RatCoeff",
"Lean.Expr.const",
"Mathlib.Tactic.Ring.Common.Result",
"Mathlib.Tactic.Ring.Common.ExSum",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Mathlib.Tactic.Ring.Common.Result.casesOn",
"Qq.Quoted.unsafeMk",
"Lean... | false |
Subgroup.map_map | Mathlib.Algebra.Group.Subgroup.Map | [
"Set.image_image",
"MonoidHom.instFunLike",
"MonoidHom",
"Subgroup.map",
"Monoid.toMulOneClass",
"Group",
"MonoidHom.comp",
"DivInvMonoid.toMonoid",
"Subgroup",
"SetLike.coe_injective",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"SetLike.coe",
"Eq",
"DFunLike.coe",
"Subgroup.instS... | true |
HasContDiffBump.rec | Mathlib.Analysis.Calculus.BumpFunction.Basic | [
"HasContDiffBump.mk",
"Real",
"NormedSpace",
"HasContDiffBump",
"Nonempty",
"Real.normedField",
"ContDiffBumpBase",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"NormedAddCommGroup"
] | false |
AddCommute.on_refl | Mathlib.Algebra.Group.Commute.Defs | [
"Std.Refl.mk",
"Std.Refl",
"AddCommute",
"AddCommute.refl",
"Add"
] | true |
Std.DTreeMap.Internal.Impl.isEmpty_filter!_key_iff | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.getKey",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.filter",
"Eq.mp",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Bool.true",
"Iff",
"Std.DTreeMap.Internal.Impl.filter_eq_filter!",
"Std.DTreeMap.Internal.Impl.conta... | true |
_private.Mathlib.Algebra.Module.StablyFree.FreeOfInvertible.0.Module.free_of_isStablyFree_of_invertible._proof_1_1 | Mathlib.Algebra.Module.StablyFree.FreeOfInvertible | [
"Nontrivial",
"CommRing",
"PrimeSpectrum.instNonemptyOfNontrivial",
"CommRing.toCommSemiring",
"PrimeSpectrum",
"Nonempty"
] | false |
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