name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.RingTheory.LocalRing.ResidueField.Ideal.0.instIsFractionRingQuotientIdealResidueField._simp_3 | Mathlib.RingTheory.LocalRing.ResidueField.Ideal | [
"Semiring.toModule",
"AddGroupWithOne.toAddGroup",
"Ideal.Quotient.mk",
"HSub.hSub",
"RingHom",
"Membership.mem",
"Ideal.IsTwoSided",
"Ideal",
"SubNegMonoid.toSub",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"HasQuotient.Quotient",
"Ideal.Quotient.ring",
"RingHom.instFunLike",
"instHSub"... | false |
HomotopyEquiv.toHomologyIso._proof_1 | Mathlib.Algebra.Homology.Homotopy | [
"Eq.mpr",
"Homotopy.homologyMap_eq",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomologicalComplex.HasHomology",
"HomologicalComplex",
"CategoryTheory.CategoryStruct.id",
"id",
"HomologicalComplex.homologyMap_id",
"HomologicalComplex... | false |
IsOpen.is_const_of_deriv_eq_zero | Mathlib.Analysis.Calculus.MeanValue | [
"ContinuousLinearMap.ext_ring",
"ContinuousLinearMap.toSpanSingleton_zero",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedSpace.toIsBoundedSMul",
"RCLike.toNormedAlgebra",
"Norm... | true |
Std.IterM.fold_filterMapM | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Pure.pure",
"Std.IterM.filterMapM",
"LawfulMonadLiftT",
"congrArg",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"Std.Iterators.Types.FilterMap.instIteratorLoop",
"instMonadLiftT",
"Std.IteratorLoop",
"WeaklyLawfulMonadAttach",
"Std.Iterators.Finite",
"Std.Iterators.Types.FilterMap.instFini... | true |
CategoryTheory.PreGaloisCategory.PointedGaloisObject.Hom.mk | Mathlib.CategoryTheory.Galois.Prorepresentability | [
"CategoryTheory.PreGaloisCategory.PointedGaloisObject.pt",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"Finite",
"FintypeCat",
"CategoryTheory.PreGaloisCategory.PointedGaloisObject.obj",
"CategoryTheory.ObjectProperty.FullS... | true |
Std.DTreeMap.Internal.Impl.getKeyLE?.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Ord",
"Std.DTreeMap.Internal.Impl.getKeyLE?.go",
"Option.none",
"Std.DTreeMap.Internal.Impl.getKeyLE?",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Option"
] | true |
MulAction.stabilizer_smul_eq_right | Mathlib.GroupTheory.GroupAction.Defs | [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHSMul",
"LE.le.trans_eq",
"DivInvOneMonoid.toInvOneClass",
"LE.le.antisymm'",
"congrArg",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"id",
"DivInvMonoid.toMonoid",
"Subgroup",
"... | true |
map_eq_zero._simp_1 | Mathlib.Algebra.GroupWithZero.Units.Lemmas | [
"Nontrivial",
"GroupWithZero.toMonoidWithZero",
"GroupWithZero",
"map_eq_zero",
"MulZeroOneClass",
"MonoidWithZeroHomClass",
"MonoidWithZero.toMulZeroOneClass",
"propext",
"Zero.toOfNat0",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"FunLike",
"MulZeroClass.toZ... | false |
Std.Internal.IO.Async.System.OSInfo.mk.inj | Std.Internal.Async.System | [
"Std.Internal.IO.Async.System.OSInfo",
"Std.Internal.IO.Async.System.OSInfo.mk",
"String",
"And",
"And.intro",
"Std.Internal.IO.Async.System.OSInfo.mk.noConfusion",
"Eq"
] | true |
Lean.Expr.NumApps.State.counters | Lean.Util.NumApps | [
"Lean.NameMap",
"Lean.Expr.NumApps.State",
"Nat"
] | true |
_private.Mathlib.RingTheory.HahnSeries.Multiplication.0.HahnModule.smul_add._simp_1_1 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"Set.IsPWO",
"Set.instUnion",
"Set.isPWO_union",
"And",
"propext",
"Union.union",
"Eq",
"Preorder",
"Set"
] | false |
NumberField.IsCMField.isConj_complexConj | Mathlib.NumberTheory.NumberField.CMField | [
"Exists.choose_spec",
"Subfield.toAlgebra",
"NumberField.ComplexEmbedding.IsConj",
"NumberField.maximalRealSubfield",
"congrArg",
"Subfield.instSubfieldClass",
"Rat.nontrivial",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Classical.choice",
"RingHom",
"Membership.mem",
"Exists",
"Field.t... | true |
Nat.nth_add_one | Mathlib.Data.Nat.Nth | [
"Eq.rec",
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Nat.lt_one_iff",
"LT.lt",
"Iff.mp",
"instAddNat",
"Nat.nth",
"instLTNat",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Not",
"Nat.nth_add"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Bipartite.0.SimpleGraph.completeBipartiteGraph_isContained_iff.match_1_7 | Mathlib.Combinatorics.SimpleGraph.Bipartite | [
"Sum.inr_injective",
"Finset.univ",
"RelHom.instFunLike",
"Finset",
"SimpleGraph.Adj",
"SimpleGraph.Copy.injective",
"Function.comp",
"Membership.mem",
"Exists",
"Function.Embedding.mk",
"SimpleGraph.Copy",
"Sum",
"Function.Embedding",
"SimpleGraph.Copy.instFunLike",
"And.casesOn",
"Si... | false |
CategoryTheory.ComposableArrows.fourδ₁Toδ₀._proof_2 | Mathlib.CategoryTheory.ComposableArrows.Four | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ComposableArrows.map'._proof_8",
"PartialOrder.toPreorder",
"CategoryTheory.CategoryStruct.id",
"Fin.mk",
"CategoryTheory.ComposableArrows.homMk₁._proof_4",
"Preorder.smallCategory",
"instOfNatNat",
"CategoryTheo... | false |
CategoryTheory.Pseudofunctor.CoGrothendieck.noConfusion | Mathlib.CategoryTheory.Bicategory.Grothendieck | [
"Opposite",
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Pseudofunctor.CoGrothendieck",
"CategoryTheory.Pseudofunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.toCategoryStruct"... | false |
CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHom | Mathlib.Algebra.Homology.DerivedCategory.SmallShiftedHom | [
"CochainComplex.HomComplex.coboundaries",
"CategoryTheory.Abelian.toPreadditive",
"Int.instAddCommMonoid",
"Int.instIsStrictOrderedRing",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.quasiIso",
"Int.instLinearOrder",
"AddCommGroup.t... | true |
Function.Surjective.involutiveNeg._proof_1 | Mathlib.Algebra.Group.InjSurj | [
"Eq.mpr",
"congrArg",
"neg_neg",
"id",
"Neg",
"InvolutiveNeg",
"Eq.refl",
"InvolutiveNeg.toNeg",
"Eq.symm",
"Eq",
"Neg.neg"
] | false |
_private.Init.Data.Array.Find.0.Array.getElem?_zero_flatten._simp_1_1 | Init.Data.Array.Find | [
"List.head?",
"List.instGetElem?NatLtLength",
"instOfNatNat",
"List.head?_eq_getElem?",
"List",
"Nat",
"LT.lt",
"instLTNat",
"GetElem?.getElem?",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"List.length",
"Option"
] | false |
Std.DTreeMap.Raw.Equiv.forIn_eq | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Internal.Impl.Equiv.forIn_eq",
"Std.DTreeMap.Raw.instForInSigmaOfMonad",
"Ord.mk",
"Ordering",
"Std.DTreeMap.Raw.Equiv",
"LawfulMonad",
"ForIn.forIn",
"Std.TransCmp",
"ForInStep",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.Equiv.inner",
"Sigma.mk",
... | true |
Subgroup.mulSingle_mem_pi._simp_2 | Mathlib.Algebra.Group.Subgroup.Basic | [
"Subgroup.mulSingle_mem_pi",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Pi.group",
"Subgroup",
"propext",
"Subgroup.pi",
"Eq",
"Set.instMembership",
"Pi.mulSingle",
"SetLike.instMembershi... | false |
CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcyclesE_X₁ | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.cokernelSequenceOpcyclesE",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.ShortComplex.X₁",
... | true |
_private.Mathlib.Algebra.Homology.DerivedCategory.TStructure.0.DerivedCategory.TStructure.t._proof_12 | Mathlib.Algebra.Homology.DerivedCategory.TStructure | [
"ComplexShape.instIsTruncLENatIntEmbeddingUpIntLE",
"_private.Mathlib.Algebra.Homology.DerivedCategory.TStructure.0.DerivedCategory.TStructure.t._proof_11",
"ComplexShape.embeddingUpIntLE",
"Nat.instOne",
"AddGroupWithOne.toAddMonoidWithOne",
"Int",
"AddMonoidWithOne.toOne",
"instOfNat",
"Int.instRi... | false |
_private.Init.Omega.Int.0.Lean.Omega.Fin.ne_iff_lt_or_gt._simp_1_1 | Init.Omega.Int | [
"Ne",
"Nat",
"LT.lt",
"propext",
"Or",
"instLTNat",
"Eq",
"Nat.ne_iff_lt_or_gt"
] | false |
genLoopEquivOfUnique._proof_3 | Mathlib.Topology.Homotopy.HomotopyGroup | [
"Real.instIsOrderedRing",
"Inhabited.default",
"Real.partialOrder",
"Real",
"genLoopEquivOfUnique._proof_2",
"Set.Icc.instZero",
"Pi.topologicalSpace",
"HEq.refl",
"ContinuousMap.mk",
"ContinuousMap",
"Unique",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Cube.boundary",
"Real.... | false |
Lean.Server.instMonadLiftCancellableMRequestM.match_1 | Lean.Server.Requests | [
"Except.ok",
"Lean.Server.RequestCancellation",
"Except.error",
"Except.casesOn",
"Except"
] | false |
CategoryTheory.PrelaxFunctorStruct.map₂ | Mathlib.CategoryTheory.Bicategory.Functor.Prelax | [
"Quiver.Hom",
"CategoryTheory.PrelaxFunctorStruct",
"Prefunctor.map",
"CategoryTheory.PrelaxFunctorStruct.toPrefunctor",
"Quiver",
"Prefunctor.obj"
] | true |
ArchimedeanClass.closedBallAddSubgroup.eq_1 | Mathlib.Algebra.Order.Archimedean.Class | [
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"PartialOrder.toPreorder",
"AddCommGroup.toAddGroup",
"SemilatticeInf.toPartialOrder",
"UpperSet.Ici",
"AddCommGroup",
"DistribLattice.toLattice",
"AddSubgroup",
"Eq.refl",
"ArchimedeanClass.closedBallAddSubgrou... | true |
Std.DTreeMap.Internal.Const.RicSliceData.rec | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"Std.DTreeMap.Internal.Const.RicSliceData.mk",
"Std.DTreeMap.Internal.Const.RicSliceData",
"Std.Ric",
"Std.DTreeMap.Internal.Impl"
] | false |
Lean.Data.AC.Variable.mk | Init.Data.AC | [
"Lean.Data.AC.Variable",
"PLift",
"Lean.Data.AC.Variable.mk",
"Std.LawfulIdentity",
"Option"
] | true |
_private.Mathlib.Combinatorics.Additive.ApproximateSubgroup.0.IsApproximateSubgroup.pow_inter_pow_covBySMul_sq_inter_sq._simp_1_10 | Mathlib.Combinatorics.Additive.ApproximateSubgroup | [
"Finset",
"Membership.mem",
"SetLike.coe",
"Finset.instSetLike",
"propext",
"Eq",
"Set.instMembership",
"Finset.mem_coe",
"SetLike.instMembership",
"Set"
] | false |
CommRingCat.Colimits.Prequotient.noConfusion | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CommRingCat.carrier",
"CommRingCat",
"HEq.refl",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.Prequotient",
"CommRingCat.Colimits.Prequotient.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq",
"CommRingCat.Colimits.Prequoti... | false |
PartOrd.dual | Mathlib.Order.Category.PartOrd | [
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartOrd.instCategory",
"CategoryTheory.Functor.mk",
"PartOrd.str",
"PartialOrder.toPreorder",
"Equiv",
"PartOrd",
"PartOrd.ofHom",
"OrderDual.instPartialOrder",
"PartOrd.carrier",
"Par... | true |
Int.ModEq.prod_one | Mathlib.Algebra.BigOperators.ModEq | [
"Int.instCommMonoid",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Int.ModEq.prod",
"Membership.mem",
"Eq.mp",
"Int",
"Finset.prod",
"Finset.prod_const_one",
"MulOneClass.toMulOne",
"instOfNat",
"Finset.instSetLike",
"CommMonoid.toMonoid",
"Int.ModEq",
"One.toOfNat1... | true |
Lean.Parser.Term.stateRefT._regBuiltin.Lean.Parser.Term.macroDollarArg.formatter_11 | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Lean.Parser.Term.macroDollarArg.formatter",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
CategoryTheory.Adjunction.leftAdjointUniq_trans_assoc | Mathlib.CategoryTheory.Adjunction.Unique | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Adjunction.leftAdjointUniq",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.CategoryStruct.comp"... | true |
_private.Mathlib.MeasureTheory.Integral.PeakFunction.0.tendsto_integral_comp_smul_smul_of_integrable._simp_1_3 | Mathlib.MeasureTheory.Integral.PeakFunction | [
"Lattice.toSemilatticeSup",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"LE.le",
"Max.max",
"propext",
"Or",
"le_max_iff",
"Eq",
"instDistribLatticeOfLinearOrder",
"Lattice.toSemilatticeIn... | false |
UInt64.toNat_neg | Init.Data.UInt.Lemmas | [
"UInt64.size",
"UInt64",
"HSub.hSub",
"Nat.instMod",
"instHMod",
"instSubNat",
"UInt64.toNat",
"HMod.hMod",
"instHSub",
"Nat",
"Eq",
"Neg.neg",
"rfl",
"instNegUInt64"
] | true |
Aesop.GoalState.toNodeState | Aesop.Tree.Data | [
"Aesop.NodeState.proven",
"Aesop.NodeState.unknown",
"Aesop.NodeState.unprovable",
"Aesop.GoalState",
"Unit",
"Aesop.GoalState.instToString.match_1",
"Aesop.NodeState"
] | true |
MeasureTheory.Measure.FiniteSpanningSetsIn.disjointed_set_eq | Mathlib.MeasureTheory.Measure.Typeclasses.SFinite | [
"MeasureTheory.Measure",
"MeasurableSet",
"disjointed",
"setOf",
"BooleanAlgebra.toGeneralizedBooleanAlgebra",
"MeasureTheory.Measure.FiniteSpanningSetsIn.set",
"Nat.instLocallyFiniteOrder",
"LocallyFiniteOrder.toLocallyFiniteOrderBot",
"MeasurableSpace",
"Nat.instPreorder",
"Set.instBooleanAlge... | true |
NNReal.arith_mean_le_rpow_mean | Mathlib.Analysis.MeanInequalitiesPow | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.instPow",
"Real.instLE",
"Real",
"instHDiv",
"HMul.hMul",
"congrArg",
"Finset",
"Real.instDivInvMonoid",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Preorder.toLE",
"NNReal.coe_le_coe._simp_1",
"cast",
"Membership.mem... | true |
CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj._proof_2 | Mathlib.CategoryTheory.Idempotents.FunctorCategories | [
"CategoryTheory.Functor",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Idempotents.Karoubi.p",
"CategoryTheory.Idempotents.Karoubi.X",
"CategoryTheory.Idempotents.Karoubi.idem",
"CategoryTheory.Catego... | false |
String.isInt | Init.Data.String.Search | [
"String.toSlice",
"String",
"Bool",
"String.Slice.isInt"
] | true |
CategoryTheory.Under.forgetCone._proof_2 | Mathlib.CategoryTheory.Comma.Over.Basic | [
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"CategoryTheory.Comma.hom",
"CategoryTheory.Under",
"CategoryTheory.Func... | false |
CategoryTheory.MonoidalClosed.enrichedCategorySelf_id | Mathlib.CategoryTheory.Monoidal.Closed.Enrichment | [
"CategoryTheory.MonoidalClosed.id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.EnrichedCategory.Hom",
"CategoryTheory.MonoidalClosed",
"CategoryTheory.MonoidalClosed.enrichedCategorySelf",
"CategoryTheory.MonoidalClosed.closed",
"Catego... | true |
Lean.Parser.Term.letOptUsedOnly._regBuiltin.Lean.Parser.Term.letOptUsedOnly.docString_1 | Lean.Parser.Term | [
"Lean.addBuiltinDocString",
"IO",
"Unit",
"Lean.Name.mkStr4"
] | false |
Std.DTreeMap.Raw.get!_eq_default | Std.Data.DTreeMap.Raw.Lemmas | [
"Inhabited.default",
"Std.DTreeMap.Internal.Impl.get!_eq_default",
"Std.DTreeMap.Raw.instMembership",
"Ord.mk",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.Raw.get!",
"Std.DTreeMap.Raw.WF.out",
"Std.LawfulEqCmp",
"Std.DTreeMap.Raw.inner",
"Inhabited",
"Eq",
"Not",
"Std.DT... | true |
Finset.isScalarTower' | Mathlib.Algebra.Group.Action.Pointwise.Finset | [
"instHSMul",
"Finset.smul",
"smul_assoc",
"congrArg",
"Finset",
"IsScalarTower",
"SMul",
"Set.smul",
"Finset.smulFinset",
"Finset.coe_smul_finset",
"Finset.coe_injective",
"SetLike.coe",
"Finset.instSetLike",
"congr",
"True",
"eq_self",
"of_eq_true",
"HSMul.hSMul",
"congrFun'",
... | true |
_private.Mathlib.LinearAlgebra.Basis.Exact.0.Submodule.linearProjOfIsCompl_comp_bijective_of_exact._simp_1_1 | Mathlib.LinearAlgebra.Basis.Exact | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"LinearMap.ker",
"LinearMap.instFunLike",
"RingHom",
"Disjoint",
"AddCommGroup",
"Submodule.instPartialOrder",
"LinearMap",
"LinearMap.disjoint_ker_iff_injOn",
"SetLike.coe",
"Submodule.setLike",
"propext",
"Submodule.instOrderBot",
"Module",
... | false |
Mathlib.Linter.initFn._@.Mathlib.Tactic.Linter.MinImports.2495106528._hygCtx._hyg.4 | Mathlib.Tactic.Linter.MinImports | [
"Lean.Option",
"Lean.Name.mkStr5",
"IO",
"Lean.Name.mkStr3",
"Lean.Option.Decl.mk",
"Bool.true",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool"
] | false |
FirstOrder.Language.IsFraisse.is_equiv_invariant | Mathlib.ModelTheory.Fraisse | [
"FirstOrder.Language.Hereditary.is_equiv_invariant_of_fg",
"FirstOrder.Language.Equiv",
"Membership.mem",
"CategoryTheory.Bundled.structure",
"FirstOrder.Language.IsFraisse.FG",
"FirstOrder.Language.Structure",
"Iff",
"FirstOrder.Language.IsFraisse.hereditary",
"CategoryTheory.Bundled.α",
"FirstOr... | true |
PiLp.nnnorm_single | Mathlib.Analysis.Normed.Lp.PiLp | [
"zero_le",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"ENNReal.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"PiLp.single",
"MulOne.toOne",
"le_refl",
"NNReal.zero_rpow",
"Real",
"ENNReal.ofNNReal",
"DivInvMonoid.toInv",
"Preorder.toLT",
... | true |
String.take_eq | Batteries.Data.String.Lemmas | [
"String",
"String.toRawSubstring",
"Substring.Raw.ValidFor.take",
"instHAppendOfAppend",
"List",
"List.drop",
"Nat",
"String.toList",
"Char",
"String.validFor_toSubstring",
"List.instAppend",
"Eq",
"List.take",
"String.Legacy.take",
"Substring.Raw.take",
"HAppend.hAppend",
"String.of... | true |
Preord.inv_hom_apply | Mathlib.Order.Category.Preord | [
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Iso",
"Preord.instCategory",
"Preord.str",
"Preord",
"CategoryTheory.Iso.hom_inv_id_apply",
"OrderHom.instFunLike",
"True",
"eq_self",
"Preord.carrier",
"of_eq_true",
"congrFun'",
"CategoryTheory.Iso.hom",
"Eq",
"DFunLi... | true |
Batteries.RBSet.upperBound?_mem_toList | Batteries.Data.RBMap.Lemmas | [
"Batteries.RBSet",
"Option.some",
"Membership.mem",
"Ordering",
"Batteries.RBSet.upperBound?",
"List",
"List.instMembership",
"Batteries.RBSet.toList",
"Eq",
"Batteries.RBSet.upperBoundP?_mem_toList",
"Option"
] | true |
CategoryTheory.Presheaf.isSheaf_iff_extensiveSheaf_of_projective | Mathlib.CategoryTheory.Sites.Coherent.SheafComparison | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Preregular",
"Opposite",
"CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts",
"congrArg",
"CategoryTheory.FinitaryExtensive",
"Iff.rfl",
"id",
"CategoryTheory.Presheaf.isSheaf_iff_preservesFiniteProducts_of_projective",
"Iff",
"Cate... | true |
Frm.Hom.recOn | Mathlib.Order.Category.Frm | [
"Frm.Hom",
"FrameHom",
"Frm.Hom.rec",
"_private.Mathlib.Order.Category.Frm.0.Frm.Hom.mk",
"Frm.str",
"Order.Frame.toCompleteLattice",
"Frm.carrier",
"Frm"
] | false |
Polynomial.one_le_cauchyBound._simp_1 | Mathlib.Analysis.Polynomial.CauchyBound | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"NormedDivisionRing.toDivisionRing",
"DivisionRing.toDivisionSemiring",
"NNReal",
"LE.le",
"Polynomial",
"Polynomial.cauchyBound",
"NNReal.instPartialOrder",
"Polynomial.one_le_cauchyBound",
"True",
"eq_true",
"DivisionSemiring.toSemiring",
"One.... | false |
Std.ExtTreeMap.getKey!_congr | Std.Data.ExtTreeMap.Lemmas | [
"Ordering",
"Ordering.eq",
"Std.TransCmp",
"Std.ExtTreeMap.getKey!",
"Std.ExtTreeMap",
"Std.ExtDTreeMap.getKey!_congr",
"Std.ExtTreeMap.inner",
"Inhabited",
"Eq"
] | true |
Membership.noConfusionType | Init.Prelude | [
"Membership.casesOn",
"Membership",
"HEq"
] | false |
HahnSeries.SummableFamily.instModule._proof_10 | Mathlib.RingTheory.HahnSeries.Summable | [
"instHSMul",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HahnSeries.SummableFamily.instSMul_1",
"Module.toMulActionWithZero",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"HahnSeries.SummableFamily.... | false |
Bipointed.toProd | Mathlib.CategoryTheory.Category.Bipointed | [
"Bipointed.X",
"Bipointed",
"Prod"
] | true |
String.Pos.Raw.offsetOfPos | Init.Data.String.Basic | [
"String",
"String.Pos.Raw.offsetOfPosAux",
"instOfNatNat",
"String.Pos.Raw",
"Nat",
"String.instOfNatRaw",
"OfNat.ofNat"
] | true |
Mathlib.Tactic.IntervalCases.Methods.roundDown | Mathlib.Tactic.IntervalCases | [
"Lean.Expr",
"Lean.Meta.MetaM",
"Mathlib.Tactic.IntervalCases.Methods"
] | true |
_private.Lean.Linter.MissingDocs.0.Lean.Linter.MissingDocs.missingDocsExt.match_3 | Lean.Linter.MissingDocs | [
"Prod.mk",
"Lean.Linter.MissingDocs.Handler",
"Lean.Name",
"Prod",
"Prod.casesOn"
] | false |
CentroidHom.applyModule._proof_3 | Mathlib.Algebra.Ring.CentroidHom | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"map_zero",
"CentroidHom.instCentroidHomClass",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"CentroidHomClass.toAddMonoidHomClass",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"AddMonoidHomClass.toZeroHomClass",
"NonUnita... | false |
SheafOfModules.Presentation.isColimit._proof_1 | Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"Opposite",
"Equiv.instEquivLike",
"AddCommGrpCat.hasLimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"AddCommGr... | false |
SubmodulesRingBasis.mk._flat_ctor | Mathlib.Topology.Algebra.Nonarchimedean.Bases | [
"Submodule.pointwiseDistribMulAction",
"Submodule",
"IsScalarTower.to_smulCommClass'",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction... | false |
Lean.Server.Test.Runner.Client.InteractiveTermGoal.noConfusionType | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.InteractiveTermGoal.casesOn",
"Lean.Server.Test.Runner.Client.InteractiveGoalCore",
"Lean.Server.Test.Runner.Client.InteractiveTermGoal",
"Lean.Lsp.Range",
"Lean.Lsp.RpcRef",
"Eq"
] | false |
RelSeries.last_drop | Mathlib.Order.RelSeries | [
"SetRel",
"RelSeries.last",
"HSub.hSub",
"Fin.isLt",
"Eq.rec",
"Fin.mk",
"Nat.lt_succ_self",
"id",
"RelSeries.length",
"instSubNat",
"instOfNatNat",
"RelSeries",
"RelSeries.drop",
"Fin.val",
"RelSeries.drop._proof_6",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"_pri... | true |
Function.locallyFinsuppWithin.addSubgroup._proof_1 | Mathlib.Topology.LocallyFinsupp | [
"Filter.instMembership",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"False",
"Pi.addGroup",
"eq_false",
"congrArg",
"and_self",
"neg_eq_zero._simp_1",
"setOf",
"Set.Finite",
"Membership.mem",
"Exists",
"nhds",
"Eq.mp",
"id",
"HasSubset.Subset",
"SubtractionMonoid.toSubNe... | false |
CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE_X₁ | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.E",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.kernelSequenceOpcyclesE",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Abelian",
"CategoryTheory.Abelian.SpectralObject... | true |
_private.Lean.Server.CodeActions.Basic.0.Lean.Server.handleCodeActionResolve.match_3 | Lean.Server.CodeActions.Basic | [
"Option.ctorIdx",
"IO",
"Option.some",
"Nat.hasNotBit",
"Lean.Lsp.CodeAction",
"_private.Lean.Server.CodeActions.Basic.0.Lean.Server.CodeAction.getFileSource!._sparseCasesOn_1",
"Option"
] | false |
_private.Lean.Meta.Constructions.CtorElim.0.Lean.initFn._regBuiltin._private.Lean.Meta.Constructions.CtorElim.0.Lean.initFn.docString_1._@.Lean.Meta.Constructions.CtorElim.299025572._hygCtx._hyg.2 | Lean.Meta.Constructions.CtorElim | [
"Lean.addBuiltinDocString",
"IO",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.str",
"Lean.Name.anonymous",
"Unit",
"Nat",
"OfNat.ofNat"
] | false |
Lean.Syntax.TSepArray.mk | Init.Prelude | [
"Lean.Syntax.TSepArray.mk",
"String",
"Lean.SyntaxNodeKinds",
"Lean.Syntax",
"Lean.Syntax.TSepArray",
"Array"
] | true |
Lean.Int.mkInstHPow | Lean.Expr | [
"Lean.Int.mkInstPowNat",
"Lean.Expr",
"Lean.Level",
"Lean.mkConst",
"List.cons",
"Lean.levelZero",
"Lean.mkApp3",
"Lean.Int.mkType",
"Lean.Nat.mkType",
"Lean.Name.mkStr1",
"List.nil"
] | true |
ContMDiffSection.toFun | Mathlib.Geometry.Manifold.VectorBundle.SmoothSection | [
"NormedSpace",
"FiberBundle",
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace",
"ModelWithCorners",
"ContMDiffSection",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Bundle.TotalSpace",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSem... | true |
_private.Mathlib.RingTheory.HahnSeries.Summable.0.HahnSeries.SummableFamily.hsum._simp_1 | Mathlib.RingTheory.HahnSeries.Summable | [
"HahnSeries.support",
"Membership.mem",
"PartialOrder",
"Ne",
"propext",
"HahnSeries.coeff",
"Zero.toOfNat0",
"OfNat.ofNat",
"HahnSeries",
"Eq",
"Set.instMembership",
"HahnSeries.mem_support",
"Zero",
"Set"
] | false |
Finsupp.mapRange.equiv._proof_2 | Mathlib.Data.Finsupp.Defs | [
"Finsupp.instFunLike",
"Equiv.instEquivLike",
"Equiv.symm_comp_self",
"Finsupp.ext",
"congrArg",
"Finsupp.mapRange.congr_simp",
"Finsupp.mapRange.equiv._proof_1",
"Function.comp",
"id",
"Equiv",
"Finsupp.mapRange_id",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Zero.toOfNat0",
"Eq.... | false |
WithTop.instMulZeroOneClass._proof_2 | Mathlib.Algebra.Order.Ring.WithTop | [
"Nontrivial",
"MulOne.toOne",
"NeZero.one",
"HMul.hMul",
"WithTop.top_mul",
"MulZeroClass.toMul",
"mt",
"MulZeroOneClass",
"WithTop.instMulZeroOneClass.match_1",
"WithTop.coe_eq_coe",
"WithTop.some",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",
"Unit",
"Iff.mp",
"One.toOfNa... | false |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_324 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Equiv.instEquivLike",
"List.idxOfNth_lt_length_iff",
"instLawfulBEq",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.Order.eq_of_le_of_le_0",
"congrArg",
"List.... | false |
_private.Std.Time.Format.Basic.0.Std.Time.GenericFormat.DateBuilder.MorL | Std.Time.Format.Basic | [
"_private.Std.Time.Format.Basic.0.Std.Time.GenericFormat.DateBuilder",
"Std.Time.Month.Ordinal",
"Option"
] | true |
Std.TreeMap.getKey_insert | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.insert",
"instDecidableEqOrdering",
"Std.TreeMap.mem_of_mem_insert",
"Std.TreeMap.getKey",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Std.TransCmp",
"dite",
"Std.TreeMap.instMembership",
"Std.DTreeMap.getKey_insert",
"Eq",
"Not",
"Std.TreeMap"
] | true |
Submodule.toLocalized' | Mathlib.Algebra.Module.LocalizedModule.Submodule | [
"Submodule",
"IsLocalization",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"IsLocalizedModule",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"DistribSMul.toSMulZe... | true |
le_sup_iff._simp_3 | Mathlib.Order.Lattice | [
"Lattice.toSemilatticeSup",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"LE.le",
"Max.max",
"propext",
"le_sup_iff",
"Or",
"LinearOrder.toLattice",
"Eq",
"Lattice.toSemilatticeInf"
] | false |
isGLB_ciInf_set | Mathlib.Order.ConditionallyCompleteLattice.Indexed | [
"iInf",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"Membership.mem",
"Set.Elem",
"Set.Nonempty",
"isLUB_ciSup_set",
"IsGLB",
"OrderDual.instConditionallyCompleteLattice",
"BddBelow",
"Set.image",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"Condi... | true |
Fin.one_eq_zero_iff | Init.Data.Fin.Lemmas | [
"Eq.mpr",
"congrArg",
"Zero.ofOfNat0",
"id",
"Fin.instOfNat",
"Fin.zero_eq_one_iff._simp_1",
"instOfNatNat",
"eq_comm",
"iff_self",
"Iff",
"Nat",
"True",
"propext",
"of_eq_true",
"congrFun'",
"NeZero",
"OfNat.ofNat",
"Fin",
"Eq",
"Eq.trans"
] | true |
Finset.attach_empty | Mathlib.Data.Finset.Basic | [
"Finset",
"Membership.mem",
"Subtype",
"Finset.instEmptyCollection",
"Finset.instSetLike",
"Finset.attach",
"EmptyCollection.emptyCollection",
"Eq",
"SetLike.instMembership",
"rfl"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.filter_equiv_self_iff._simp_1_4 | Std.Data.DTreeMap.Internal.Lemmas | [
"List.Perm",
"Std.DTreeMap.Internal.Impl.Equiv",
"propext",
"Std.DTreeMap.Internal.Impl.toListModel",
"Std.DTreeMap.Internal.Impl.equiv_iff_toListModel_perm",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Sigma"
] | false |
Finset.exists_subsuperset_card_eq | Mathlib.Data.Finset.Card | [
"_private.Mathlib.Data.Finset.Card.0.Finset.exists_subsuperset_card_eq._proof_1_3",
"subset_refl._simp_1",
"congrArg",
"and_self",
"Finset",
"Finset.instReflSubset",
"Classical.propDecidable",
"Finset.instSDiff",
"Membership.mem",
"Exists",
"Nat.decreasingInduction'",
"HasSubset.Subset",
"in... | true |
SheafOfModules.mk.noConfusion | Mathlib.Algebra.Category.ModuleCat.Sheaf | [
"CategoryTheory.Functor",
"SheafOfModules.noConfusion",
"Opposite",
"AddCommGrpCat.instCategory",
"SheafOfModules.mk",
"HEq.refl",
"CategoryTheory.Functor.category",
"id",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"Ab",
"RingCat",
"heq_of_eq",
"PresheafOfModules",
"CategoryTheor... | false |
Orientation.rotation_pi_div_two | Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | [
"LinearIsometry",
"LinearIsometryEquiv.instEquivLike",
"Module.End.instRing",
"LinearMap.id",
"InnerProductSpace.toNormedSpace",
"Real.sin_pi_div_two",
"Orientation",
"Real.partialOrder",
"Real",
"instHSMul",
"instHDiv",
"Real.pi",
"Real.Angle.coe",
"Real.instZero",
"Real.instRCLike",
... | true |
MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_innerRegular | Mathlib.MeasureTheory.Measure.Haar.Unique | [
"MeasureTheory.Measure.IsAddHaarMeasure.toIsFiniteMeasureOnCompacts",
"Eq.mpr",
"NNReal.instCommSemiring",
"instHSMul",
"MeasureTheory.Measure",
"IsScalarTower.right",
"MeasurableSet",
"congrArg",
"CommSemiring.toSemiring",
"iSup",
"HEq.refl",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreo... | true |
Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ring.elim | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.Meta.Grind.Arith.Linear.LinExpr",
"PULift.up",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ctorIdx",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ring",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ctorElim",
"Nat",
"Lean.Meta.Grind.Arith.Linear.Ri... | false |
String.posGE_eq_posGE_toSlice | Init.Data.String.Lemmas.FindPos | [
"String.toSlice",
"String",
"String.posGE_eq_posGE_toSlice._proof_1",
"String.posGE",
"LE.le",
"String.Pos.Raw",
"String.rawEndPos",
"String.Pos.ofToSlice",
"String.Slice.posGE",
"String.instLERaw",
"eq_self",
"String.Pos",
"of_eq_true",
"_private.Init.Data.String.FindPos.0.String.posGE._p... | true |
LaurentPolynomial.trunc | Mathlib.Algebra.Polynomial.Laurent | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Int.ofNat.inj",
"AddMonoid.toAddZeroClass",
"AddMonoidAlgebra.nonUnitalNonAssocSemiring",
"RingEquiv.toAddMonoidHom",
"LaurentPolynomial",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"Distrib.toAdd",
"Int.ofNat",
"Polynomial.instAdd",
"Int",
"Ad... | true |
CategoryTheory.Oplax.OplaxTrans.Hom.noConfusion | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.Oplax.OplaxTrans.Hom.casesOn",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Oplax.OplaxTrans.Hom",
"CategoryTheory.Oplax.OplaxTrans.Hom.noConfusionType",
"CategoryTheory.Bicategory",
"CategoryTheory.Oplax.OplaxTrans.categoryStruct",
"CategoryThe... | false |
_private.Mathlib.Order.Filter.FilterProduct.0.Filter.Germ.coe_lt._simp_1_4 | Mathlib.Order.Filter.FilterProduct | [
"Ultrafilter.eventually_not",
"Filter.Eventually",
"propext",
"Ultrafilter",
"Eq",
"Not",
"Ultrafilter.toFilter"
] | false |
CategoryTheory.mateEquiv_conjugateEquiv_vcomp | Mathlib.CategoryTheory.Adjunction.Mates | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.TwoSquare.whiskerBottom",
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.conjugateEquiv_apply_app",
"CategoryTheory.TwoSquare.ext",
"CategoryTheory.Two... | true |
NumberField.mixedEmbedding.unitSMul_smul | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone | [
"Units.val",
"Real",
"instHSMul",
"HMul.hMul",
"NumberField.mixedEmbedding",
"NumberField.instCommRingRingOfIntegers",
"CommSemiring.toSemiring",
"Prod.instMul",
"NumberField.InfinitePlace.IsComplex",
"NumberField.RingOfIntegers.instAlgebra_1",
"RingHom",
"Complex.instMul",
"algebraMap",
"... | true |
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