name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.67M | allowCompletion bool 2
classes |
|---|---|---|---|
List.mul_length_le_sum_of_min?_eq_some_int | Init.Data.List.Int.Sum | ∀ {x : ℤ} {xs : List ℤ}, xs.min? = some x → x * ↑xs.length ≤ xs.sum | true |
IntermediateField.toSubalgebra_iSup_of_directed | Mathlib.FieldTheory.IntermediateField.Adjoin.Basic | ∀ {K : Type u_3} {L : Type u_4} [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] {ι : Type u_5}
{t : ι → IntermediateField K L}, Directed (fun x1 x2 => x1 ≤ x2) t → (iSup t).toSubalgebra = ⨆ i, (t i).toSubalgebra | true |
WithIdeal.mk | Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {R : Type u_2} → [inst : CommRing R] → Ideal R → WithIdeal R | true |
_private.Lean.Elab.Extra.0.Lean.Elab.Term.getMonadForIn.match_3 | Lean.Elab.Extra | (motive : Option Lean.Expr → Sort u_1) →
(expectedType? : Option Lean.Expr) →
(Unit → motive none) → ((expectedType : Lean.Expr) → motive (some expectedType)) → motive expectedType? | false |
String.Slice.Pattern.CharPred.instBackwardPatternForallCharBool._proof_4 | Init.Data.String.Pattern.Pred | ∀ (s : String.Slice), s.isEmpty = false → s.endPos ≠ s.startPos | false |
Lean.Firefox.ResourceTable.type | Lean.Util.Profiler | Lean.Firefox.ResourceTable → Array Lean.Json | true |
ZFSet.Definable.mk_out | Mathlib.SetTheory.ZFC.Basic | ∀ {n : ℕ} {f : (Fin n → ZFSet.{u}) → ZFSet.{u}} [self : ZFSet.Definable n f] (xs : Fin n → PSet.{u}),
ZFSet.mk (ZFSet.Definable.out f xs) = f fun x => ZFSet.mk (xs x) | true |
_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution.exists_minimal | Mathlib.NumberTheory.FLT.Three | ∀ {K : Type u_1} [inst : Field K] {ζ : K} {hζ : IsPrimitiveRoot ζ 3} (S : FermatLastTheoremForThreeGen.Solution✝ hζ),
∃ S₁, FermatLastTheoremForThreeGen.Solution.isMinimal✝ S₁ | true |
HasDerivWithinAt.inv | Mathlib.Analysis.Calculus.Deriv.Inv | ∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {c : 𝕜 → 𝕜} {c' : 𝕜},
HasDerivWithinAt c c' s x → c x ≠ 0 → HasDerivWithinAt c⁻¹ (-c' / c x ^ 2) s x | true |
MeasureTheory.AEFinStronglyMeasurable.const_smul | Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable | ∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace β]
{f : α → β} {𝕜 : Type u_5} [inst_1 : TopologicalSpace 𝕜] [inst_2 : Zero β] [inst_3 : SMulZeroClass 𝕜 β]
[ContinuousSMul 𝕜 β],
MeasureTheory.AEFinStronglyMeasurable f μ → ∀ (c : 𝕜), MeasureTheory.... | true |
Lean.Expr.appFn!'._sunfold | Lean.Expr | Lean.Expr → Lean.Expr | false |
Mathlib.Meta.NormNum.Result'.isNegNat.sizeOf_spec | Mathlib.Tactic.NormNum.Result | ∀ (inst lit proof : Lean.Expr),
sizeOf (Mathlib.Meta.NormNum.Result'.isNegNat inst lit proof) = 1 + sizeOf inst + sizeOf lit + sizeOf proof | true |
Std.DTreeMap.Internal.Impl.Const.isEmpty_alter_eq_isEmpty_erase | Std.Data.DTreeMap.Internal.Lemmas | ∀ {α : Type u} {instOrd : Ord α} {β : Type v} {t : Std.DTreeMap.Internal.Impl α fun x => β} [Std.TransOrd α] (h : t.WF)
{k : α} {f : Option β → Option β},
(Std.DTreeMap.Internal.Impl.Const.alter k f t ⋯).impl.isEmpty =
((Std.DTreeMap.Internal.Impl.erase k t ⋯).impl.isEmpty && (f (Std.DTreeMap.Internal.Impl.Cons... | true |
Part.right_dom_of_div_dom | Mathlib.Data.Part | ∀ {α : Type u_1} [inst : Div α] {a b : Part α}, (a / b).Dom → b.Dom | true |
_private.Mathlib.Analysis.InnerProductSpace.Coalgebra.0.InnerProductSpace.algebraOfCoalgebra._simp_1 | Mathlib.Analysis.InnerProductSpace.Coalgebra | ∀ {R : Type u_1} {R₂ : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring R₂] {σ₁₂ : R →+* R₂} {M : Type u_7}
{N : Type u_8} {M₂ : Type u_12} {N₂ : Type u_14} [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N]
[inst_4 : AddCommMonoid M₂] [inst_5 : AddCommMonoid N₂] [inst_6 : Module R M] [inst_7 : Module R ... | false |
Lean.Elab.Term.LVal.noConfusionType | Lean.Elab.Term.TermElabM | Sort u → Lean.Elab.Term.LVal → Lean.Elab.Term.LVal → Sort u | false |
RingCon.op._proof_1 | Mathlib.RingTheory.Congruence.Opposite | ∀ {R : Type u_1} [inst : Add R] [inst_1 : Mul R] (c : RingCon R) {w x y z : Rᵐᵒᵖ},
c.op.toSetoid w x → c.op.toSetoid y z → c.op (w * y) (x * z) | false |
Fintype.card_finsupp | Mathlib.Data.Finsupp.Fintype | ∀ (ι : Type u_1) (α : Type u_2) [inst : DecidableEq ι] [inst_1 : Fintype ι] [inst_2 : Zero α] [inst_3 : Fintype α],
Fintype.card (ι →₀ α) = Fintype.card α ^ Fintype.card ι | true |
CategoryTheory.Pseudofunctor.CoGrothendieck.compIso_hom_app | Mathlib.CategoryTheory.FiberedCategory.Grothendieck | ∀ {𝒮 : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} 𝒮]
(F : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮ᵒᵖ) CategoryTheory.Cat) (S : 𝒮)
(X : ↑(F.obj { as := Opposite.op S })),
(CategoryTheory.Pseudofunctor.CoGrothendieck.compIso F S).hom.app X = CategoryTheory.CategoryStruct.id S | true |
Std.DTreeMap.Raw.mem_diff_iff | Std.Data.DTreeMap.Raw.Lemmas | ∀ {α : Type u} {β : α → Type v} {cmp : α → α → Ordering} {t₁ t₂ : Std.DTreeMap.Raw α β cmp} [Std.TransCmp cmp],
t₁.WF → t₂.WF → ∀ {k : α}, k ∈ t₁ \ t₂ ↔ k ∈ t₁ ∧ k ∉ t₂ | true |
CommAlgCat.forget₂_commRingCat_obj | Mathlib.Algebra.Category.CommAlgCat.Basic | ∀ {R : Type u} [inst : CommRing R] (A : CommAlgCat R),
(CategoryTheory.forget₂ (CommAlgCat R) CommRingCat).obj A = CommRingCat.of ↑A | true |
_private.Lean.Meta.Tactic.Grind.EMatch.0.Lean.Meta.Grind.EMatch.ematchTheorem.tryAll._unsafe_rec | Lean.Meta.Tactic.Grind.EMatch | List Lean.Expr → List Lean.Meta.Grind.EMatch.Cnstr → Lean.Meta.Grind.EMatch.M Unit | false |
_private.Mathlib.LinearAlgebra.Dual.Lemmas.0.Subspace.dualAnnihilator_dualCoannihilator_eq._simp_1_2 | Mathlib.LinearAlgebra.Dual.Lemmas | ∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{Φ : Submodule R (Module.Dual R M)} (x : M), (x ∈ Φ.dualCoannihilator) = ∀ φ ∈ Φ, φ x = 0 | false |
Lean.Grind.LinarithConfig.mk.sizeOf_spec | Init.Grind.Config | ∀ (toNoopConfig : Lean.Grind.NoopConfig), sizeOf { toNoopConfig := toNoopConfig } = 1 + sizeOf toNoopConfig | true |
IsometryEquiv.dimH_image | Mathlib.Topology.MetricSpace.HausdorffDimension | ∀ {X : Type u_2} {Y : Type u_3} [inst : EMetricSpace X] [inst_1 : EMetricSpace Y] (e : X ≃ᵢ Y) (s : Set X),
dimH (⇑e '' s) = dimH s | true |
WeakDual.instBornology._aux_1 | Mathlib.Analysis.Normed.Module.WeakDual | {𝕜 : Type u_1} →
{E : Type u_2} →
[inst : NontriviallyNormedField 𝕜] →
[inst_1 : SeminormedAddCommGroup E] → [inst_2 : NormedSpace 𝕜 E] → Filter (WeakDual 𝕜 E) | false |
AddSubgroup.multiset_sum_mem | Mathlib.Algebra.Group.Subgroup.Finite | ∀ {G : Type u_3} [inst : AddCommGroup G] (K : AddSubgroup G) (g : Multiset G), (∀ a ∈ g, a ∈ K) → g.sum ∈ K | true |
DyckWord.nest_insidePart_add_outsidePart | Mathlib.Combinatorics.Enumerative.DyckWord | ∀ {p : DyckWord}, p ≠ 0 → p.insidePart.nest + p.outsidePart = p | true |
CategoryTheory.Bicategory.Adjunction.homEquiv₁._proof_2 | Mathlib.CategoryTheory.Bicategory.Adjunction.Mate | ∀ {B : Type u_3} [inst : CategoryTheory.Bicategory B] {b c d : B} {l : b ⟶ c} {r : c ⟶ b}
(adj : CategoryTheory.Bicategory.Adjunction l r) {g : b ⟶ d} {h : c ⟶ d}
(γ : g ⟶ CategoryTheory.CategoryStruct.comp l h),
CategoryTheory.bicategoricalComp (CategoryTheory.CategoryStruct.id g)
(CategoryTheory.bicategor... | false |
Lean.Elab.Tactic.evalUnknown._regBuiltin.Lean.Elab.Tactic.evalUnknown_1 | Lean.Elab.Tactic.BuiltinTactic | IO Unit | false |
Num.land_eq_and | Mathlib.Data.Num.Bitwise | ∀ (p q : Num), p.land q = p &&& q | true |
CPolynomialAt.comp | Mathlib.Analysis.Analytic.Composition | ∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
[inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
[inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {g : F → G} {f : E → F} {x : E},
CP... | true |
CategoryTheory.CategoryOfElements.toStructuredArrow | Mathlib.CategoryTheory.Elements | {C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
(F : CategoryTheory.Functor C (Type w)) →
CategoryTheory.Functor F.Elements (CategoryTheory.StructuredArrow PUnit.{w + 1} F) | true |
MeasureTheory.AECover | Mathlib.MeasureTheory.Integral.IntegralEqImproper | {α : Type u_1} → {ι : Type u_2} → [inst : MeasurableSpace α] → MeasureTheory.Measure α → Filter ι → (ι → Set α) → Prop | true |
CategoryTheory.Localization.hasSmallLocalizedHom_of_isLocalization | Mathlib.CategoryTheory.Localization.SmallHom | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (W : CategoryTheory.MorphismProperty C) {D : Type u₂}
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] (L : CategoryTheory.Functor C D) [L.IsLocalization W] {X Y : C},
CategoryTheory.Localization.HasSmallLocalizedHom W X Y | true |
CategoryTheory.MonoidalCoherence.whiskerRight_iso | Mathlib.Tactic.CategoryTheory.MonoidalComp | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C] (X Y Z : C)
[inst_2 : CategoryTheory.MonoidalCoherence X Y],
CategoryTheory.MonoidalCoherence.iso =
CategoryTheory.MonoidalCategory.whiskerRightIso CategoryTheory.MonoidalCoherence.iso Z | true |
Quiver.emptyQuiver | Mathlib.Combinatorics.Quiver.Basic | (V : Type u) → Quiver (Quiver.Empty V) | true |
UInt8.ofNat_sub | Init.Data.UInt.Lemmas | ∀ {a b : ℕ}, b ≤ a → UInt8.ofNat (a - b) = UInt8.ofNat a - UInt8.ofNat b | true |
Disjoint.inf_left | Mathlib.Order.Disjoint | ∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] {a b : α} (c : α), Disjoint a b → Disjoint (a ⊓ c) b | true |
Hyperreal.InfiniteNeg.neg | Mathlib.Analysis.Real.Hyperreal | ∀ {x : ℝ*}, x.InfiniteNeg → (-x).InfinitePos | true |
_private.Batteries.Data.Char.Basic.0.Char.of_all_eq_true_aux._proof_1_11 | Batteries.Data.Char.Basic | ∀ (n : ℕ) (hn : n < 55296), ↑⟨n, ⋯⟩ < 55296 ∨ 57343 < ↑⟨n, ⋯⟩ ∧ ↑⟨n, ⋯⟩ < 1114112 | false |
CategoryTheory.MorphismProperty.Comma.id_hom | Mathlib.CategoryTheory.MorphismProperty.Comma | ∀ {A : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} A] {B : Type u_2}
[inst_1 : CategoryTheory.Category.{v_2, u_2} B] {T : Type u_3} [inst_2 : CategoryTheory.Category.{v_3, u_3} T]
{L : CategoryTheory.Functor A T} {R : CategoryTheory.Functor B T} {P : CategoryTheory.MorphismProperty T}
{Q : CategoryTheory... | true |
FormalMultilinearSeries.instAddCommGroup._aux_6 | Mathlib.Analysis.Calculus.FormalMultilinearSeries | {𝕜 : Type u_1} →
{E : Type u_2} →
{F : Type u_3} →
[inst : Ring 𝕜] →
[inst_1 : AddCommGroup E] →
[inst_2 : Module 𝕜 E] →
[inst_3 : TopologicalSpace E] →
[inst_4 : IsTopologicalAddGroup E] →
[inst_5 : ContinuousConstSMul 𝕜 E] →
... | false |
Lean.Parser.ParserAttributeHook.mk.sizeOf_spec | Lean.Parser.Extension | ∀ (postAdd : Lean.Name → Lean.Name → Bool → Lean.AttrM Unit), sizeOf { postAdd := postAdd } = 1 | true |
Submodule.smul_mem_iff''._simp_1 | Mathlib.Algebra.Module.Submodule.Defs | ∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] {module_M : Module R M} (p : Submodule R M)
{r : R} {x : M} [Invertible r], (r • x ∈ p) = (x ∈ p) | false |
WittVector.IsPoly.instInhabitedId | Mathlib.RingTheory.WittVector.IsPoly | (p : ℕ) → Inhabited (WittVector.IsPoly p fun x x_1 => id) | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_707 | Mathlib.GroupTheory.Perm.Cycle.Type | ∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w w_1 : α)
(h_5 : 2 ≤ List.count w_1 [g a, g (g a)]),
(List.findIdxs (fun x => decide (x = w_1)) [g a, g (g a)])[[].length] + 1 ≤
(List.findIdxs (fun x => decide (x = w_1)) [g a, g (g a)]).length →
(List.findIdxs (fun x => decide (x = w... | false |
instConditionallyCompleteLinearOrderTropical._proof_1 | Mathlib.Algebra.Tropical.Lattice | ∀ {R : Type u_1} [inst : ConditionallyCompleteLinearOrder R] (a b : Tropical R), a ≤ b ∨ b ≤ a | false |
Bundle.TotalSpace.isManifold | Mathlib.Geometry.Manifold.VectorBundle.Basic | ∀ {n : WithTop ℕ∞} {𝕜 : Type u_1} {B : Type u_2} (F : Type u_4) (E : B → Type u_6) [inst : NontriviallyNormedField 𝕜]
{EB : Type u_7} [inst_1 : NormedAddCommGroup EB] [inst_2 : NormedSpace 𝕜 EB] {HB : Type u_8}
[inst_3 : TopologicalSpace HB] {IB : ModelWithCorners 𝕜 EB HB} [inst_4 : TopologicalSpace B]
[inst_... | true |
Diffeomorph.ext_iff | Mathlib.Geometry.Manifold.Diffeomorph | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {E' : Type u_3} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {H : Type u_5}
[inst_5 : TopologicalSpace H] {H' : Type u_6} [inst_6 : TopologicalSpace H'] {I : ModelWithCor... | true |
Aesop.RappData | Aesop.Tree.Data | Type → Type → Type | true |
SeparationQuotient.instCommMagma | Mathlib.Topology.Algebra.SeparationQuotient.Basic | {M : Type u_1} →
[inst : TopologicalSpace M] → [inst_1 : CommMagma M] → [ContinuousMul M] → CommMagma (SeparationQuotient M) | true |
_private.Mathlib.Analysis.SpecialFunctions.Stirling.0.Stirling.factorial_isEquivalent_stirling._simp_1_7 | Mathlib.Analysis.SpecialFunctions.Stirling | ∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {a : G₀} (n : ℤ), a ≠ 0 → (a ^ n = 0) = False | false |
Real.exp_artanh | Mathlib.Analysis.SpecialFunctions.Artanh | ∀ {x : ℝ}, x ∈ Set.Ioo (-1) 1 → Real.exp (Real.artanh x) = √((1 + x) / (1 - x)) | true |
UniformContinuousOn.comp | Mathlib.Topology.UniformSpace.Basic | ∀ {α : Type ua} {β : Type ub} {γ : Type uc} [inst : UniformSpace α] [inst_1 : UniformSpace β] [inst_2 : UniformSpace γ]
{f : α → β} {s : Set α} {g : β → γ} {t : Set β},
UniformContinuousOn g t → UniformContinuousOn f s → Set.MapsTo f s t → UniformContinuousOn (g ∘ f) s | true |
_private.Std.Sat.CNF.Basic.0.Std.Sat.CNF.Internal.any_not_isEmpty_iff_exists_mem._simp_1_2 | Std.Sat.CNF.Basic | ∀ {α : Type u_1} {xs : List α}, (xs.isEmpty = false) = ∃ x, x ∈ xs | false |
_private.Mathlib.Tactic.NormNum.Basic.0.Mathlib.Meta.NormNum.evalIntOfNat.match_3 | Mathlib.Tactic.NormNum.Basic | (motive : Lean.Expr → Sort u_1) →
(__discr : Lean.Expr) →
((us : List Lean.Level) → (n : Q(ℕ)) → motive ((Lean.Expr.const `Int.ofNat us).app n)) →
((x : Lean.Expr) → motive x) → motive __discr | false |
HahnSeries.SummableFamily.hsum_smulFamily | Mathlib.RingTheory.HahnSeries.Summable | ∀ {Γ : Type u_1} {R : Type u_3} {V : Type u_4} {α : Type u_5} [inst : PartialOrder Γ] [inst_1 : AddCommMonoid R]
[inst_2 : AddCommMonoid V] [inst_3 : SMulWithZero R V] (f : α → R) (s : HahnSeries.SummableFamily Γ V α) (g : Γ),
(HahnSeries.SummableFamily.smulFamily f s).hsum.coeff g = ∑ᶠ (i : α), f i • (s i).coeff g | true |
LinearMap.isNilRegular_iff_coeff_polyCharpoly_nilRank_ne_zero | Mathlib.Algebra.Module.LinearMap.Polynomial | ∀ {R : Type u_1} {L : Type u_2} {M : Type u_3} {ι : Type u_5} [inst : CommRing R] [inst_1 : AddCommGroup L]
[inst_2 : Module R L] [inst_3 : AddCommGroup M] [inst_4 : Module R M] (φ : L →ₗ[R] Module.End R M)
[inst_5 : Fintype ι] [inst_6 : DecidableEq ι] [inst_7 : Module.Free R M] [inst_8 : Module.Finite R M]
(b : ... | true |
MulEquiv.coprodPUnit._proof_2 | Mathlib.GroupTheory.Coprod.Basic | ∀ (M : Type u_1) [inst : Monoid M], Monoid.Coprod.fst.comp Monoid.Coprod.inl = MonoidHom.id M | false |
CategoryTheory.IsAddMonHom.mk | Mathlib.CategoryTheory.Monoidal.Mon_ | ∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {M' N' : C}
[inst_2 : CategoryTheory.AddMonObj M'] [inst_3 : CategoryTheory.AddMonObj N'] {f : M' ⟶ N'},
autoParam (CategoryTheory.CategoryStruct.comp CategoryTheory.AddMonObj.zero f = CategoryTheory.AddMonObj.z... | true |
DirectSum.lid_symm_apply | Mathlib.Algebra.DirectSum.Module | ∀ (R : Type u) [inst : Semiring R] {M : Type v} {ι : Type u_1} [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : Unique ι] (x : M), (DirectSum.lid R M ι).symm x = (DirectSum.lof R ι (fun i => M) default) x | true |
Matrix.PosSemidef.transpose | Mathlib.LinearAlgebra.Matrix.PosDef | ∀ {n : Type u_2} {R' : Type u_4} [inst : CommRing R'] [inst_1 : PartialOrder R'] [inst_2 : StarRing R']
{M : Matrix n n R'}, M.PosSemidef → M.transpose.PosSemidef | true |
CategoryTheory.Functor.OplaxRightLinear.mk._flat_ctor | Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | {D : Type u_1} →
{D' : Type u_2} →
[inst : CategoryTheory.Category.{v_1, u_1} D] →
[inst_1 : CategoryTheory.Category.{v_2, u_2} D'] →
{F : CategoryTheory.Functor D D'} →
{C : Type u_3} →
[inst_2 : CategoryTheory.Category.{v_3, u_3} C] →
[inst_3 : CategoryTheory.Mo... | false |
_private.Mathlib.GroupTheory.SpecificGroups.Dihedral.0.instDecidableEqDihedralGroup.decEq.match_1.eq_3 | Mathlib.GroupTheory.SpecificGroups.Dihedral | ∀ {n : ℕ} (motive : DihedralGroup n → DihedralGroup n → Sort u_1) (a a_1 : ZMod n)
(h_1 : (a b : ZMod n) → motive (DihedralGroup.r a) (DihedralGroup.r b))
(h_2 : (a a_2 : ZMod n) → motive (DihedralGroup.r a) (DihedralGroup.sr a_2))
(h_3 : (a a_2 : ZMod n) → motive (DihedralGroup.sr a) (DihedralGroup.r a_2))
(h_... | true |
Lean.JsonRpc.instHashableRequestID.hash | Lean.Data.JsonRpc | Lean.JsonRpc.RequestID → UInt64 | true |
SSet.Truncated.ev12₂._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | 0 ≤ 1 | false |
Lean.RecursorVal.numParams | Lean.Declaration | Lean.RecursorVal → ℕ | true |
_private.Init.Data.List.Lemmas.0.List.getLast?_eq_some_getLast.match_1_1 | Init.Data.List.Lemmas | ∀ {α : Type u_1} (motive : (x : List α) → x ≠ [] → Prop) (x : List α) (x_1 : x ≠ []),
(∀ (head : α) (tail : List α) (x : head :: tail ≠ []), motive (head :: tail) x) → motive x x_1 | false |
SimpleGraph.Copy.topEmbedding._proof_2 | Mathlib.Combinatorics.SimpleGraph.Copy | ∀ {V : Type u_1} {α : Type u_2} {G : SimpleGraph V} (f : ⊤.Copy G) {v w : α},
G.Adj (f.toEmbedding v) (f.toEmbedding w) ↔ ⊤.Adj v w | false |
NonemptyInterval.sub_mem_sub | Mathlib.Algebra.Order.Interval.Basic | ∀ {α : Type u_2} [inst : Preorder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [inst_3 : OrderedSub α]
[inst_4 : AddLeftMono α] (s t : NonemptyInterval α) {a b : α}, a ∈ s → b ∈ t → a - b ∈ s - t | true |
_private.Lean.Widget.Diff.0.Lean.Widget.ExprDiff.recOn | Lean.Widget.Diff | {motive : Lean.Widget.ExprDiff✝ → Sort u} →
(t : Lean.Widget.ExprDiff✝¹) →
((changesBefore changesAfter : Lean.SubExpr.PosMap Lean.Widget.ExprDiffTag✝) →
motive { changesBefore := changesBefore, changesAfter := changesAfter }) →
motive t | false |
Std.Internal.UV.System.RUsage.isRSS | Std.Internal.UV.System | Std.Internal.UV.System.RUsage → UInt64 | true |
Lean.Compiler.CSimp.Entry._sizeOf_1 | Lean.Compiler.CSimpAttr | Lean.Compiler.CSimp.Entry → ℕ | false |
WeierstrassCurve.toShortNFOfCharThree_spec | Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms | ∀ {R : Type u_1} [inst : CommRing R] (W : WeierstrassCurve R) [inst_1 : CharP R 3],
W.b₂ = 0 → (W.toShortNFOfCharThree • W).IsShortNF | true |
_private.Init.System.Uri.0.System.Uri.UriEscape.decodeUri._sparseCasesOn_1 | Init.System.Uri | {α : Type u} →
{motive : Option α → Sort u_1} →
(t : Option α) → ((val : α) → motive (some val)) → (Nat.hasNotBit 2 t.ctorIdx → motive t) → motive t | false |
_private.Mathlib.Analysis.Complex.Hadamard.0.Complex.HadamardThreeLines.norm_mul_invInterpStrip_le_one_of_mem_verticalClosedStrip._simp_1_4 | Mathlib.Analysis.Complex.Hadamard | ∀ {a b c : Prop}, (a ∧ b → c) = (a → b → c) | false |
finite_compl_fixedBy_swap | Mathlib.GroupTheory.Perm.ClosureSwap | ∀ {α : Type u_2} [inst : DecidableEq α] {x y : α}, (MulAction.fixedBy α (Equiv.swap x y))ᶜ.Finite | true |
_private.Mathlib.NumberTheory.LSeries.HurwitzZetaEven.0.HurwitzZeta.hasSum_int_evenKernel₀._simp_1_6 | Mathlib.NumberTheory.LSeries.HurwitzZetaEven | ∀ {G : Type u_3} [inst : AddGroup G] {a b : G}, (-a = b) = (a + b = 0) | false |
HomotopicalAlgebra.PathObject.noConfusion | Mathlib.AlgebraicTopology.ModelCategory.PathObject | {P : Sort u_1} →
{C : Type u} →
{inst : CategoryTheory.Category.{v, u} C} →
{inst_1 : HomotopicalAlgebra.CategoryWithWeakEquivalences C} →
{A : C} →
{t : HomotopicalAlgebra.PathObject A} →
{C' : Type u} →
{inst' : CategoryTheory.Category.{v, u} C'} →
... | false |
Order.not_isSuccLimit_of_noMax | Mathlib.Order.SuccPred.Limit | ∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : SuccOrder α] [IsSuccArchimedean α] [NoMaxOrder α],
¬Order.IsSuccLimit a | true |
Lean.Elab.Tactic.Conv.evalReduce._regBuiltin.Lean.Elab.Tactic.Conv.evalReduce.declRange_3 | Lean.Elab.Tactic.Conv.Basic | IO Unit | false |
ENNReal.top_ne_coe._simp_1 | Mathlib.Data.ENNReal.Basic | ∀ {r : NNReal}, (⊤ = ↑r) = False | false |
TopCat.Presheaf.IsSheaf.isSheafUniqueGluing | Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {FC : C → C → Type u_2} {CC : C → Type u_3}
[inst_1 : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)] [inst_2 : CategoryTheory.ConcreteCategory C FC]
[CategoryTheory.Limits.HasLimitsOfSize.{x, x, v_1, u_1} C] [(CategoryTheory.forget C).ReflectsIsomorphisms]... | true |
MultilinearMap.instDistribMulActionOfSMulCommClass._proof_4 | Mathlib.LinearAlgebra.Multilinear.Basic | ∀ {R : Type u_1} {S : Type u_5} {ι : Type u_2} {M₁ : ι → Type u_3} {M₂ : Type u_4} [inst : Semiring R]
[inst_1 : (i : ι) → AddCommMonoid (M₁ i)] [inst_2 : (i : ι) → Module R (M₁ i)] [inst_3 : AddCommMonoid M₂]
[inst_4 : Module R M₂] [inst_5 : Monoid S] [inst_6 : DistribMulAction S M₂] [inst_7 : SMulCommClass R S M₂... | false |
_private.Mathlib.Algebra.Module.ZMod.0.QuotientAddGroup.zmodModule._simp_2 | Mathlib.Algebra.Module.ZMod | ∀ {G : Type u_1} [inst : AddGroup G] (N : AddSubgroup G) [nN : N.Normal] (a : G) (n : ℕ), n • ↑a = ↑(n • a) | false |
Asymptotics.IsTheta.of_norm_left | Mathlib.Analysis.Asymptotics.Theta | ∀ {α : Type u_1} {F : Type u_4} {E' : Type u_6} [inst : Norm F] [inst_1 : SeminormedAddCommGroup E'] {g : α → F}
{f' : α → E'} {l : Filter α}, (fun x => ‖f' x‖) =Θ[l] g → f' =Θ[l] g | true |
Set.multiset_prod_singleton | Mathlib.Algebra.Group.Pointwise.Set.BigOperators | ∀ {M : Type u_5} [inst : CommMonoid M] (s : Multiset M), (Multiset.map (fun i => {i}) s).prod = {s.prod} | true |
_private.Mathlib.CategoryTheory.Sites.Descent.Precoverage.0.CategoryTheory.Pseudofunctor.DescentData.full_pullFunctor.familyOfElements._proof_1 | Mathlib.CategoryTheory.Sites.Descent.Precoverage | ∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {ι : Type u_3} {X : ι → C} (i : ι)
(Z : CategoryTheory.Over (X i)),
CategoryTheory.CategoryStruct.comp Z.hom (CategoryTheory.Over.mk (CategoryTheory.CategoryStruct.id X i)).hom = Z.hom | false |
Lean.Grind.Linarith.Expr.denoteN.eq_6 | Init.Grind.Module.NatModuleNorm | ∀ {α : Type u_1} [inst : Lean.Grind.NatModule α] (ctx : Lean.Grind.Linarith.Context α) (a b : Lean.Grind.Linarith.Expr),
Lean.Grind.Linarith.Expr.denoteN ctx (a.add b) =
Lean.Grind.Linarith.Expr.denoteN ctx a + Lean.Grind.Linarith.Expr.denoteN ctx b | true |
_private.Mathlib.Geometry.Manifold.Notation.0.Manifold.Elab.findModelFiber? | Mathlib.Geometry.Manifold.Notation | Lean.Expr → Lean.MetaM (Option Lean.Expr) | true |
ModelWithCorners.continuousAt | Mathlib.Geometry.Manifold.IsManifold.Basic | ∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) {x : H},
ContinuousAt (↑I) x | true |
CategoryTheory.Triangulated.TStructure.eTruncLT_map_app_eTruncLTι_app | Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | ∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.HasShift C ℤ]
[inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
(t : CategoryT... | true |
TopCat.ofHom_hom | Mathlib.Topology.Category.TopCat.Basic | ∀ {X Y : TopCat} (f : X ⟶ Y), TopCat.ofHom (TopCat.Hom.hom f) = f | true |
isOpen_prod_iff' | Mathlib.Topology.Constructions.SumProd | ∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {s : Set X} {t : Set Y},
IsOpen (s ×ˢ t) ↔ IsOpen s ∧ IsOpen t ∨ s = ∅ ∨ t = ∅ | true |
Std.Iter.findSome?_eq_findSome?_toIterM | Init.Data.Iterators.Lemmas.Consumers.Loop | ∀ {α β γ : Type w} [inst : Std.Iterator α Id β] [inst_1 : Std.IteratorLoop α Id Id] [Std.Iterators.Finite α Id]
{it : Std.Iter β} {f : β → Option γ}, it.findSome? f = (it.toIterM.findSome? f).run | true |
AddChar.mul_apply | Mathlib.Algebra.Group.AddChar | ∀ {A : Type u_2} {M : Type u_3} [inst : AddMonoid A] [inst_1 : CommMonoid M] (ψ φ : AddChar A M) (a : A),
(ψ * φ) a = ψ a * φ a | true |
Lean.Parser.Level.paren._regBuiltin.Lean.Parser.Level.paren_1 | Lean.Parser.Level | IO Unit | false |
subset_interior_sub_right | Mathlib.Topology.Algebra.Group.Pointwise | ∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [IsTopologicalAddGroup G] {s t : Set G},
s - interior t ⊆ interior (s - t) | true |
Dynamics.netMaxcard_infinite_iff | Mathlib.Dynamics.TopologicalEntropy.NetEntropy | ∀ {X : Type u_1} (T : X → X) (F : Set X) (U : SetRel X X) (n : ℕ),
Dynamics.netMaxcard T F U n = ⊤ ↔ ∀ (k : ℕ), ∃ s, Dynamics.IsDynNetIn T F U n ↑s ∧ k ≤ s.card | true |
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