name stringlengths 2 347 | module stringlengths 6 90 | type stringlengths 1 5.42M |
|---|---|---|
Std.IterM.length_map | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | ∀ {α β β' : Type w} {m : Type w → Type w'} [inst : Std.Iterator α m β] [inst_1 : Monad m]
[inst_2 : Std.IteratorLoop α m m] [Std.Iterators.Finite α m] [LawfulMonad m] [Std.LawfulIteratorLoop α m m]
{it : Std.IterM m β} {f : β → β'}, (Std.IterM.map f it).length = it.length |
Ideal.gc_map_comap | Mathlib.RingTheory.Ideal.Maps | ∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
[inst_3 : RingHomClass F R S], GaloisConnection (Ideal.map f) (Ideal.comap f) |
exists_mem_nhds_ball_subset_of_mem_nhds | Mathlib.Topology.UniformSpace.Defs | ∀ {α : Type ua} [inst : UniformSpace α] {a : α} {U : Set α},
U ∈ nhds a → ∃ V ∈ nhds a, ∃ t ∈ uniformity α, ∀ a' ∈ V, UniformSpace.ball a' t ⊆ U |
AddEquiv.addSubgroupCongr.eq_1 | Mathlib.Algebra.Group.Subgroup.Map | ∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G} (h : H = K),
AddEquiv.addSubgroupCongr h = { toEquiv := Equiv.setCongr ⋯, map_add' := ⋯ } |
_private.Init.Data.BitVec.Lemmas.0.BitVec.setWidth_setWidth_succ_eq_setWidth_setWidth_of_getLsbD_false._proof_1_1 | Init.Data.BitVec.Lemmas | ∀ {w : ℕ} {i : ℕ} (k : ℕ), ¬i = k → k < i + 1 → ¬k < i → False |
_private.Mathlib.RingTheory.Binomial.0.Ring.smeval_ascPochhammer_int_ofNat._simp_1_3 | Mathlib.RingTheory.Binomial | ∀ {R : Type u} [inst : Semiring R] (n : ℕ), ↑n = Polynomial.C ↑n |
Std.DTreeMap.Internal.Impl.balanceL!.match_5.congr_eq_1 | Std.Data.DTreeMap.Internal.Balancing | ∀ {α : Type u_1} {β : α → Type u_2} (motive : Std.DTreeMap.Internal.Impl α β → Sort u_3)
(l : Std.DTreeMap.Internal.Impl α β) (h_1 : Unit → motive Std.DTreeMap.Internal.Impl.leaf)
(h_2 :
(ls : ℕ) →
(lk : α) →
(lv : β lk) →
(ll lr : Std.DTreeMap.Internal.Impl α β) → motive (Std.DTreeMap.Internal.Impl.inner ls lk lv ll lr)),
l = Std.DTreeMap.Internal.Impl.leaf →
(match l with
| Std.DTreeMap.Internal.Impl.leaf => h_1 ()
| Std.DTreeMap.Internal.Impl.inner ls lk lv ll lr => h_2 ls lk lv ll lr) ≍
h_1 () |
MeasureTheory.IsHahnDecomposition.le_on | Mathlib.MeasureTheory.Measure.Decomposition.Hahn | ∀ {α : Type u_1} {mα : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} {s : Set α},
MeasureTheory.IsHahnDecomposition μ ν s → μ.restrict s ≤ ν.restrict s |
FractionRing.algEquiv | Mathlib.RingTheory.Localization.FractionRing | (A : Type u_4) →
[inst : CommRing A] →
(K : Type u_6) → [inst_1 : CommRing K] → [inst_2 : Algebra A K] → [IsFractionRing A K] → FractionRing A ≃ₐ[A] K |
Subgroup.mem_smul_pointwise_iff_exists | Mathlib.Algebra.Group.Subgroup.Pointwise | ∀ {α : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : Monoid α] [inst_2 : MulDistribMulAction α G] (m : G) (a : α)
(S : Subgroup G), m ∈ a • S ↔ ∃ s ∈ S, a • s = m |
BddDistLat._sizeOf_inst | Mathlib.Order.Category.BddDistLat | SizeOf BddDistLat |
WithCStarModule.uniformEquiv._proof_1 | Mathlib.Analysis.CStarAlgebra.Module.Synonym | ∀ {A : Type u_2} {E : Type u_1} [inst : UniformSpace E], IsUniformInducing ⇑(WithCStarModule.equiv A E) |
CompactlySupportedContinuousMap.toRealLinearMap._proof_6 | Mathlib.Topology.ContinuousMap.CompactlySupported | ContinuousConstSMul ℝ ℝ |
Metric.infEDist_union | Mathlib.Topology.MetricSpace.HausdorffDistance | ∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {s t : Set α},
Metric.infEDist x (s ∪ t) = min (Metric.infEDist x s) (Metric.infEDist x t) |
_private.Lean.Meta.IndPredBelow.0.Lean.Meta.IndPredBelow.NewDecl.motive | Lean.Meta.IndPredBelow | Lean.LocalDecl → ℕ → Array Lean.FVarId → Lean.Meta.IndPredBelow.NewDecl✝ |
AlgebraicGeometry.Scheme.Modules.pseudofunctor_associativity_assoc | Mathlib.AlgebraicGeometry.Modules.Sheaf | ∀ {X Y Z T : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) (h : Z ⟶ T)
{Z_1 : CategoryTheory.Functor T.Modules X.Modules}
(h_1 :
AlgebraicGeometry.Scheme.Modules.pullback
(CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.comp f g) h) ⟶
Z_1),
CategoryTheory.CategoryStruct.comp
(AlgebraicGeometry.Scheme.Modules.pullbackComp f (CategoryTheory.CategoryStruct.comp g h)).inv
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.Functor.whiskerRight (AlgebraicGeometry.Scheme.Modules.pullbackComp g h).inv
(AlgebraicGeometry.Scheme.Modules.pullback f))
(CategoryTheory.CategoryStruct.comp
((AlgebraicGeometry.Scheme.Modules.pullback h).associator (AlgebraicGeometry.Scheme.Modules.pullback g)
(AlgebraicGeometry.Scheme.Modules.pullback f)).hom
(CategoryTheory.CategoryStruct.comp
((AlgebraicGeometry.Scheme.Modules.pullback h).whiskerLeft
(AlgebraicGeometry.Scheme.Modules.pullbackComp f g).hom)
(CategoryTheory.CategoryStruct.comp
(AlgebraicGeometry.Scheme.Modules.pullbackComp (CategoryTheory.CategoryStruct.comp f g) h).hom h_1)))) =
CategoryTheory.CategoryStruct.comp (CategoryTheory.eqToHom ⋯) h_1 |
_private.Lean.Compiler.LCNF.Renaming.0.Lean.Compiler.LCNF.Param.applyRenaming.match_1 | Lean.Compiler.LCNF.Renaming | (motive : Option Lean.Name → Sort u_1) →
(x : Option Lean.Name) →
((binderName : Lean.Name) → motive (some binderName)) → ((x : Option Lean.Name) → motive x) → motive x |
ContinuousMultilinearMap.norm_ofSubsingleton_id_le | Mathlib.Analysis.Normed.Module.Multilinear.Basic | ∀ (𝕜 : Type u) {ι : Type v} (G : Type wG) [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedAddCommGroup G]
[inst_2 : NormedSpace 𝕜 G] [inst_3 : Fintype ι] [inst_4 : Subsingleton ι] (i : ι),
‖(ContinuousMultilinearMap.ofSubsingleton 𝕜 G G i) (ContinuousLinearMap.id 𝕜 G)‖ ≤ 1 |
Std.Time.TimeZone.Transition.localTimeType | Std.Time.Zoned.ZoneRules | Std.Time.TimeZone.Transition → Std.Time.TimeZone.LocalTimeType |
CategoryTheory.categoryOfEnrichedCategoryType._proof_1 | Mathlib.CategoryTheory.Enriched.Basic | ∀ (C : Type u_2) [𝒞 : CategoryTheory.EnrichedCategory (Type u_1) C] {X Y : C} (f : X ⟶[Type u_1] Y),
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.leftUnitor (X ⟶[Type u_1] Y)).inv
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.eId (Type u_1) X) (X ⟶[Type u_1] Y))
(CategoryTheory.eComp (Type u_1) X X Y))
f =
CategoryTheory.CategoryStruct.id (X ⟶[Type u_1] Y) f |
Lean.IR.IRType._sizeOf_1 | Lean.Compiler.IR.Basic | Lean.IR.IRType → ℕ |
CategoryTheory.StructuredArrow.commaMapEquivalenceCounitIso._proof_4 | Mathlib.CategoryTheory.Comma.StructuredArrow.CommaMap | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_1, u_4} C] {D : Type u_6}
[inst_1 : CategoryTheory.Category.{u_2, u_6} D] {T : Type u_8} [inst_2 : CategoryTheory.Category.{u_3, u_8} T]
{L : CategoryTheory.Functor C T} {R : CategoryTheory.Functor D T} {C' : Type u_10}
[inst_3 : CategoryTheory.Category.{u_5, u_10} C'] {D' : Type u_11} [inst_4 : CategoryTheory.Category.{u_7, u_11} D']
{T' : Type u_12} [inst_5 : CategoryTheory.Category.{u_9, u_12} T'] {L' : CategoryTheory.Functor C' T'}
{R' : CategoryTheory.Functor D' T'} {F₁ : CategoryTheory.Functor C C'} {F₂ : CategoryTheory.Functor D D'}
{F : CategoryTheory.Functor T T'} (α : F₁.comp L' ⟶ L.comp F) (β : R.comp F ⟶ F₂.comp R')
[inst_6 : CategoryTheory.IsIso β] (X : CategoryTheory.Comma L' R')
{X_1 Y :
CategoryTheory.Comma (CategoryTheory.StructuredArrow.map₂ (CategoryTheory.CategoryStruct.id (L'.obj X.left)) α)
(CategoryTheory.StructuredArrow.map₂ X.hom (CategoryTheory.inv β))}
(f : X_1 ⟶ Y),
CategoryTheory.CategoryStruct.comp
(((CategoryTheory.StructuredArrow.commaMapEquivalenceInverse α β X).comp
(CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor α β X)).map
f)
((fun x =>
CategoryTheory.Comma.isoMk
(CategoryTheory.Iso.refl
(((CategoryTheory.StructuredArrow.commaMapEquivalenceInverse α β X).comp
(CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor α β X)).obj
x).left)
(CategoryTheory.Iso.refl
(((CategoryTheory.StructuredArrow.commaMapEquivalenceInverse α β X).comp
(CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor α β X)).obj
x).right)
⋯)
Y).hom =
CategoryTheory.CategoryStruct.comp
((fun x =>
CategoryTheory.Comma.isoMk
(CategoryTheory.Iso.refl
(((CategoryTheory.StructuredArrow.commaMapEquivalenceInverse α β X).comp
(CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor α β X)).obj
x).left)
(CategoryTheory.Iso.refl
(((CategoryTheory.StructuredArrow.commaMapEquivalenceInverse α β X).comp
(CategoryTheory.StructuredArrow.commaMapEquivalenceFunctor α β X)).obj
x).right)
⋯)
X_1).hom
((CategoryTheory.Functor.id
(CategoryTheory.Comma
(CategoryTheory.StructuredArrow.map₂ (CategoryTheory.CategoryStruct.id (L'.obj X.left)) α)
(CategoryTheory.StructuredArrow.map₂ X.hom (CategoryTheory.inv β)))).map
f) |
Homotopy.mkInductiveAux₁._sunfold | Mathlib.Algebra.Homology.Homotopy | {V : Type u} →
[inst : CategoryTheory.Category.{v, u} V] →
[inst_1 : CategoryTheory.Preadditive V] →
{P Q : ChainComplex V ℕ} →
(e : P ⟶ Q) →
(zero : P.X 0 ⟶ Q.X 1) →
(one : P.X 1 ⟶ Q.X 2) →
e.f 1 =
CategoryTheory.CategoryStruct.comp (P.d 1 0) zero + CategoryTheory.CategoryStruct.comp one (Q.d 2 1) →
((n : ℕ) →
(p :
(f : P.X n ⟶ Q.X (n + 1)) ×'
(f' : P.X (n + 1) ⟶ Q.X (n + 2)) ×'
e.f (n + 1) =
CategoryTheory.CategoryStruct.comp (P.d (n + 1) n) f +
CategoryTheory.CategoryStruct.comp f' (Q.d (n + 2) (n + 1))) →
(f'' : P.X (n + 2) ⟶ Q.X (n + 3)) ×'
e.f (n + 2) =
CategoryTheory.CategoryStruct.comp (P.d (n + 2) (n + 1)) p.snd.fst +
CategoryTheory.CategoryStruct.comp f'' (Q.d (n + 3) (n + 2))) →
(n : ℕ) →
(f : P.X n ⟶ Q.X (n + 1)) ×'
(f' : P.X (n + 1) ⟶ Q.X (n + 2)) ×'
e.f (n + 1) =
CategoryTheory.CategoryStruct.comp (P.d (n + 1) n) f +
CategoryTheory.CategoryStruct.comp f' (Q.d (n + 2) (n + 1)) |
Cardinal.toNat_congr | Mathlib.SetTheory.Cardinal.ToNat | ∀ {α : Type u} {β : Type v} (e : α ≃ β), Cardinal.toNat (Cardinal.mk α) = Cardinal.toNat (Cardinal.mk β) |
AddZero.toZero | Mathlib.Algebra.Group.Defs | {M : Type u_2} → [self : AddZero M] → Zero M |
_private.Lean.Meta.Tactic.FunIndInfo.0.Lean.Meta.getFunInduct?._sparseCasesOn_1 | Lean.Meta.Tactic.FunIndInfo | {motive : Lean.ConstantInfo → Sort u} →
(t : Lean.ConstantInfo) →
((val : Lean.DefinitionVal) → motive (Lean.ConstantInfo.defnInfo val)) →
(Nat.hasNotBit 2 t.ctorIdx → motive t) → motive t |
CategoryTheory.Functor.RepresentableBy.recOn | Mathlib.CategoryTheory.Yoneda | {C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{F : CategoryTheory.Functor Cᵒᵖ (Type v)} →
{Y : C} →
{motive : F.RepresentableBy Y → Sort u} →
(t : F.RepresentableBy Y) →
((homEquiv : {X : C} → (X ⟶ Y) ≃ F.obj (Opposite.op X)) →
(homEquiv_comp :
∀ {X X' : C} (f : X ⟶ X') (g : X' ⟶ Y),
homEquiv (CategoryTheory.CategoryStruct.comp f g) = F.map f.op (homEquiv g)) →
motive { homEquiv := homEquiv, homEquiv_comp := homEquiv_comp }) →
motive t |
Aesop.Script.TacticState._sizeOf_inst | Aesop.Script.TacticState | SizeOf Aesop.Script.TacticState |
IsEvenlyCovered.homeomorph_comp | Mathlib.Topology.Covering.Basic | ∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X} {I : Type u_3}
[inst_2 : TopologicalSpace I] {x : X},
IsEvenlyCovered f x I → ∀ {Y : Type u_4} [inst_3 : TopologicalSpace Y] (g : X ≃ₜ Y), IsEvenlyCovered (⇑g ∘ f) (g x) I |
Unitary.mapEquiv_trans | Mathlib.Algebra.Star.Unitary | ∀ {R : Type u_2} {S : Type u_3} {T : Type u_4} [inst : Monoid R] [inst_1 : StarMul R] [inst_2 : Monoid S]
[inst_3 : StarMul S] [inst_4 : Monoid T] [inst_5 : StarMul T] (f : R ≃⋆* S) (g : S ≃⋆* T),
Unitary.mapEquiv (f.trans g) = (Unitary.mapEquiv f).trans (Unitary.mapEquiv g) |
Lean.Widget.DiffTag.wasDeleted.sizeOf_spec | Lean.Widget.InteractiveCode | sizeOf Lean.Widget.DiffTag.wasDeleted = 1 |
_private.Std.Data.DHashMap.Internal.RawLemmas.0.Std.DHashMap.Internal.Raw₀.Equiv.diff_right._simp_1_1 | Std.Data.DHashMap.Internal.RawLemmas | ∀ {α : Type u} {β : α → Type v} {m₁ m₂ : Std.DHashMap.Raw α β},
m₁.Equiv m₂ = (Std.DHashMap.Internal.toListModel m₁.buckets).Perm (Std.DHashMap.Internal.toListModel m₂.buckets) |
_private.Batteries.Data.List.Lemmas.0.List.getElem_idxOf_eq_idxOfNth_add._proof_1_32 | Batteries.Data.List.Lemmas | ∀ {α : Type u_1} {x : α} [inst : BEq α] (head : α) (tail : List α),
1 ≤ (List.filter (fun x_1 => x_1 == x) (head :: tail)).length →
0 < (List.findIdxs (fun x_1 => x_1 == x) (head :: tail)).length |
SimpleGraph.Walk.boxProdRight.eq_1 | Mathlib.Combinatorics.SimpleGraph.Prod | ∀ {α : Type u_1} {β : Type u_2} (G : SimpleGraph α) {H : SimpleGraph β} {b₁ b₂ : β} (a : α),
SimpleGraph.Walk.boxProdRight G a = SimpleGraph.Walk.map (G.boxProdRight H a).toHom |
Equidecomp.trans_toPartialEquiv | Mathlib.Algebra.Group.Action.Equidecomp | ∀ {X : Type u_1} {G : Type u_2} [inst : Monoid G] [inst_1 : MulAction G X] (f g : Equidecomp X G),
(f.trans g).toPartialEquiv = f.trans g.toPartialEquiv |
_private.Lean.Compiler.LCNF.ToMono.0.Lean.Compiler.LCNF.argsToMonoWithFnType.match_1 | Lean.Compiler.LCNF.ToMono | (motive : Option Lean.Expr → Sort u_1) →
(remainingType : Option Lean.Expr) →
((binderName : Lean.Name) →
(d b : Lean.Expr) →
(binderInfo : Lean.BinderInfo) → motive (some (Lean.Expr.forallE binderName d b binderInfo))) →
((x : Option Lean.Expr) → motive x) → motive remainingType |
HasStrictDerivAt.hasStrictFDerivAt_equiv | Mathlib.Analysis.Calculus.Deriv.Inverse | ∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {f : 𝕜 → 𝕜} {f' x : 𝕜},
HasStrictDerivAt f f' x →
∀ (hf' : f' ≠ 0), HasStrictFDerivAt f (↑((ContinuousLinearEquiv.unitsEquivAut 𝕜) (Units.mk0 f' hf'))) x |
Std.ExtTreeSet.contains_insert | Std.Data.ExtTreeSet.Lemmas | ∀ {α : Type u} {cmp : α → α → Ordering} {t : Std.ExtTreeSet α cmp} [inst : Std.TransCmp cmp] {k a : α},
(t.insert k).contains a = (cmp k a == Ordering.eq || t.contains a) |
CategoryTheory.Limits.Multicofork.ofSigmaCofork._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | ∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_4} C] {J : CategoryTheory.Limits.MultispanShape}
{I : CategoryTheory.Limits.MultispanIndex J C} {c : CategoryTheory.Limits.Cofan I.left}
{hc : CategoryTheory.Limits.IsColimit c} {d : CategoryTheory.Limits.Cofan I.right}
(a : CategoryTheory.Limits.Cofork (I.fstSigmaMapOfIsColimit d hc) (I.sndSigmaMapOfIsColimit d hc))
⦃X Y : CategoryTheory.Limits.WalkingMultispan J⦄ (f : X ⟶ Y),
CategoryTheory.CategoryStruct.comp (I.multispan.map f)
(match Y with
| CategoryTheory.Limits.WalkingMultispan.left a_1 =>
CategoryTheory.CategoryStruct.comp (c.inj a_1)
(CategoryTheory.CategoryStruct.comp (I.fstSigmaMapOfIsColimit d hc) a.π)
| CategoryTheory.Limits.WalkingMultispan.right a_1 => CategoryTheory.CategoryStruct.comp (d.inj a_1) a.π) =
CategoryTheory.CategoryStruct.comp
(match X with
| CategoryTheory.Limits.WalkingMultispan.left a_1 =>
CategoryTheory.CategoryStruct.comp (c.inj a_1)
(CategoryTheory.CategoryStruct.comp (I.fstSigmaMapOfIsColimit d hc) a.π)
| CategoryTheory.Limits.WalkingMultispan.right a_1 => CategoryTheory.CategoryStruct.comp (d.inj a_1) a.π)
(((CategoryTheory.Functor.const (CategoryTheory.Limits.WalkingMultispan J)).obj a.pt).map f) |
List.splitOnP_nil | Mathlib.Data.List.SplitOn | ∀ {α : Type u_1} (p : α → Bool), List.splitOnP p [] = [[]] |
List.permutationsAux2._sunfold | Mathlib.Data.List.Defs | {α : Type u_1} → {β : Type u_2} → α → List α → List β → List α → (List α → β) → List α × List β |
_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum.basicOpen_eq_bot_iff._simp_1_6 | Mathlib.RingTheory.Spectrum.Prime.Topology | ∀ {A : Type u_1} {B : Type u_2} [i : SetLike A B] {p : A} {x : B}, (x ∈ ↑p) = (x ∈ p) |
Std.Iterators.HetT.property_liftInner | Std.Data.Iterators.Lemmas.Equivalence.HetT | ∀ {α : Type u_1} {m : Type w → Type w'} {n : Type w → Type w''} [inst : MonadLiftT m n] {x : Std.Iterators.HetT m α},
(Std.Iterators.HetT.liftInner n x).Property = x.Property |
BoundedContinuousFunction | Mathlib.Topology.ContinuousMap.Bounded.Basic | (α : Type u) → (β : Type v) → [TopologicalSpace α] → [PseudoMetricSpace β] → Type (max u v) |
_private.Mathlib.Algebra.Algebra.Spectrum.Basic.0.spectrum.smul_mem_smul_iff._simp_1_3 | Mathlib.Algebra.Algebra.Spectrum.Basic | ∀ {α : Type u_5} {β : Type u_6} [inst : Group α] [inst_1 : Monoid β] [inst_2 : MulAction α β] [SMulCommClass α β β]
[IsScalarTower α β β] (g : α) (m : β), IsUnit (g • m) = IsUnit m |
Std.DHashMap.Raw.WF.inter₀ | Std.Data.DHashMap.Raw | ∀ {α : Type u} {β : α → Type v} [inst : BEq α] [inst_1 : Hashable α] {m₁ m₂ : Std.DHashMap.Raw α β}
{h₁ : 0 < m₁.buckets.size} {h₂ : 0 < m₂.buckets.size},
m₁.WF → m₂.WF → (↑(Std.DHashMap.Internal.Raw₀.inter ⟨m₁, h₁⟩ ⟨m₂, h₂⟩)).WF |
AddSubmonoid.single_mem_pi._simp_1 | Mathlib.Algebra.Group.Submonoid.Operations | ∀ {ι : Type u_4} {M : ι → Type u_5} [inst : (i : ι) → AddZeroClass (M i)] [inst_1 : DecidableEq ι] {I : Set ι}
{S : (i : ι) → AddSubmonoid (M i)} (i : ι) (x : M i), (Pi.single i x ∈ AddSubmonoid.pi I S) = (i ∈ I → x ∈ S i) |
List.instLE | Init.Data.List.Basic | {α : Type u} → [LT α] → LE (List α) |
Asymptotics.isLittleOTVS_sup | Mathlib.Analysis.Asymptotics.TVS | ∀ {α : Type u_1} {𝕜 : Type u_3} {E : Type u_4} {F : Type u_5} [inst : NontriviallyNormedField 𝕜]
[inst_1 : AddCommGroup E] [inst_2 : TopologicalSpace E] [inst_3 : Module 𝕜 E] [inst_4 : AddCommGroup F]
[inst_5 : TopologicalSpace F] [inst_6 : Module 𝕜 F] {l₁ l₂ : Filter α} {f : α → E} {g : α → F},
f =o[𝕜; l₁ ⊔ l₂] g ↔ f =o[𝕜; l₁] g ∧ f =o[𝕜; l₂] g |
_private.Mathlib.SetTheory.Ordinal.Arithmetic.0.Ordinal.add_le_add_iff_right.match_1_1 | Mathlib.SetTheory.Ordinal.Arithmetic | ∀ (motive : ℕ → Prop) (x : ℕ), (∀ (a : Unit), motive 0) → (∀ (n : ℕ), motive n.succ) → motive x |
Lean.PrettyPrinter.OneLine.State.column._default | Lean.PrettyPrinter.Formatter | ℕ |
groupHomology.boundaries₁ | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {k G : Type u} → [inst : CommRing k] → [inst_1 : Group G] → (A : Rep k G) → Submodule k (G →₀ ↑A.V) |
CategoryTheory.MorphismProperty.limitsOfShape_le | Mathlib.CategoryTheory.MorphismProperty.Limits | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {W : CategoryTheory.MorphismProperty C} {J : Type u_1}
[inst_1 : CategoryTheory.Category.{v_1, u_1} J] [W.IsStableUnderLimitsOfShape J], W.limitsOfShape J ≤ W |
Complex.ofReal_inv._simp_1 | Mathlib.Data.Complex.Basic | ∀ (r : ℝ), (↑r)⁻¹ = ↑r⁻¹ |
_private.Mathlib.Algebra.Homology.SpectralObject.Page.0.CategoryTheory.Abelian.SpectralObject.isIso_map._proof_11 | Mathlib.Algebra.Homology.SpectralObject.Page | 1 ≤ 3 |
SchwartzMap.toLpCLM._proof_3 | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | ∀ (𝕜 : Type u_3) {E : Type u_1} (F : Type u_2) [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
[inst_2 : NormedAddCommGroup F] [inst_3 : NormedSpace ℝ F] [inst_4 : MeasurableSpace E]
[inst_5 : OpensMeasurableSpace E] [inst_6 : NormedField 𝕜] [inst_7 : NormedSpace 𝕜 F] [inst_8 : SMulCommClass ℝ 𝕜 F]
[inst_9 : SecondCountableTopologyEither E F] (p : ENNReal) (μ : MeasureTheory.Measure E) [hμ : μ.HasTemperateGrowth]
(x : 𝕜) (x_1 : SchwartzMap E F), (x • x_1).toLp p μ = (x • x_1).toLp p μ |
_private.Mathlib.RingTheory.Norm.Transitivity.0.Algebra.Norm.Transitivity.eval_zero_comp_det._simp_1_7 | Mathlib.RingTheory.Norm.Transitivity | ∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} {x : NonAssocSemiring α} {x_1 : NonAssocSemiring β}
{x_2 : NonAssocSemiring γ} {δ : Type u_5} {x_3 : NonAssocSemiring δ} (f : α →+* β) (g : β →+* γ) (h : γ →+* δ),
h.comp (g.comp f) = (h.comp g).comp f |
_private.Mathlib.Analysis.Convex.DoublyStochasticMatrix.0.convex_doublyStochastic._simp_1_2 | Mathlib.Analysis.Convex.DoublyStochasticMatrix | ∀ {R : Type u_1} {n : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : Semiring R]
[inst_3 : PartialOrder R] [inst_4 : IsOrderedRing R] {M : Matrix n n R},
(M ∈ doublyStochastic R n) = ((∀ (i j : n), 0 ≤ M i j) ∧ (∀ (i : n), ∑ j, M i j = 1) ∧ ∀ (j : n), ∑ i, M i j = 1) |
Lean.Elab.Term.mkCalcStepViews | Lean.Elab.Calc | Lean.TSyntax `Lean.calcSteps → Lean.Elab.TermElabM (Array Lean.Elab.Term.CalcStepView) |
Lean.SourceInfo.fromRef | Init.Prelude | Lean.Syntax → optParam Bool false → Lean.SourceInfo |
_private.Mathlib.Data.Seq.Basic.0.Stream'.Seq.all_cons._simp_1_1 | Mathlib.Data.Seq.Basic | ∀ {α : Type u} {a b : α} {s : Stream'.Seq α}, (a ∈ Stream'.Seq.cons b s) = (a = b ∨ a ∈ s) |
AnalyticAtWithin.compContinuousLinearMap | Mathlib.Analysis.Analytic.Constructions | ∀ {𝕜 : Type u_2} [inst : NontriviallyNormedField 𝕜] {E : Type u_3} {F : Type u_4} {G : Type u_5}
[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] {u : E →L[𝕜] F} {f : F → G} {s : Set F} {x : E},
AnalyticWithinAt 𝕜 f s (u x) → AnalyticWithinAt 𝕜 (f ∘ ⇑u) (⇑u ⁻¹' s) x |
LinearMap.rTensor_comp | Mathlib.LinearAlgebra.TensorProduct.Map | ∀ {R : Type u_1} [inst : CommSemiring R] (M : Type u_7) {N : Type u_8} {P : Type u_9} {Q : Type u_10}
[inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid P] [inst_4 : AddCommMonoid Q]
[inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : Module R P] [inst_8 : Module R Q] (g : P →ₗ[R] Q)
(f : N →ₗ[R] P), LinearMap.rTensor M (g ∘ₗ f) = LinearMap.rTensor M g ∘ₗ LinearMap.rTensor M f |
Filter.Tendsto.val_inv_units | Mathlib.Topology.Algebra.Monoid | ∀ {ι : Type u_1} {N : Type u_4} [inst : TopologicalSpace N] [inst_1 : Monoid N] [inst_2 : ContinuousMul N]
[inst_3 : T2Space N] {f : ι → Nˣ} {r₁ r₂ : N} {l : Filter ι} [inst_4 : l.NeBot]
(h₁ : Filter.Tendsto (fun x => ↑(f x)) l (nhds r₁)) (h₂ : Filter.Tendsto (fun x => ↑(f x)⁻¹) l (nhds r₂)),
↑(h₁.units h₂)⁻¹ = r₂ |
pointedToBipointedSndBipointedToPointedSndAdjunction._proof_7 | Mathlib.CategoryTheory.Category.Bipointed | ∀ (X : Pointed) (Y : Bipointed) (f : X ⟶ bipointedToPointedSnd.obj Y),
f.toFun X.point = (bipointedToPointedSnd.obj Y).point |
CategoryTheory.StrictPseudofunctorPreCore.ctorIdx | Mathlib.CategoryTheory.Bicategory.Functor.StrictPseudofunctor | {B : Type u₁} →
{inst : CategoryTheory.Bicategory B} →
{C : Type u₂} → {inst_1 : CategoryTheory.Bicategory C} → CategoryTheory.StrictPseudofunctorPreCore B C → ℕ |
SaturatedSubmonoid.instCompleteLattice._proof_3 | Mathlib.Algebra.Group.Submonoid.Saturation | ∀ (M : Type u_1) [inst : MulOneClass M] (a b c : SaturatedSubmonoid M), a ≤ c → b ≤ c → SemilatticeSup.sup a b ≤ c |
Lean.Widget.RpcEncodablePacket.strict.«_@».Lean.Widget.InteractiveDiagnostic.2157017296._hygCtx._hyg.1.noConfusion | Lean.Widget.InteractiveDiagnostic | {P : Sort u} →
{a a' : Lean.Json} →
Lean.Widget.RpcEncodablePacket.strict✝ a = Lean.Widget.RpcEncodablePacket.strict✝ a' → (a = a' → P) → P |
Lean.Meta.instReprSimpCongrTheorems.repr | Lean.Meta.Tactic.Simp.SimpCongrTheorems | Lean.Meta.SimpCongrTheorems → ℕ → Std.Format |
ModuleCat.extendScalars_assoc' | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | ∀ {R₁ R₂ R₃ R₄ : Type u₁} [inst : CommRing R₁] [inst_1 : CommRing R₂] [inst_2 : CommRing R₃] [inst_3 : CommRing R₄]
(f₁₂ : R₁ →+* R₂) (f₂₃ : R₂ →+* R₃) (f₃₄ : R₃ →+* R₄),
CategoryTheory.CategoryStruct.comp (ModuleCat.extendScalarsComp (f₂₃.comp f₁₂) f₃₄).hom
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.Functor.whiskerRight (ModuleCat.extendScalarsComp f₁₂ f₂₃).hom (ModuleCat.extendScalars f₃₄))
(CategoryTheory.CategoryStruct.comp
((ModuleCat.extendScalars f₁₂).associator (ModuleCat.extendScalars f₂₃) (ModuleCat.extendScalars f₃₄)).hom
(CategoryTheory.CategoryStruct.comp
((ModuleCat.extendScalars f₁₂).whiskerLeft (ModuleCat.extendScalarsComp f₂₃ f₃₄).inv)
(ModuleCat.extendScalarsComp f₁₂ (f₃₄.comp f₂₃)).inv))) =
CategoryTheory.CategoryStruct.id (ModuleCat.extendScalars (f₃₄.comp (f₂₃.comp f₁₂))) |
measurableEmbedding_mulLeft₀ | Mathlib.MeasureTheory.Group.MeasurableEquiv | ∀ {G₀ : Type u_2} [inst : GroupWithZero G₀] [inst_1 : MeasurableSpace G₀] [MeasurableMul G₀] {g : G₀},
g ≠ 0 → MeasurableEmbedding fun x => g * x |
Qq.Impl.PatVarDecl.fvar | Qq.MatchImpl | (decl : Qq.Impl.PatVarDecl) →
have a := decl.fvarTy;
Q(«$a») |
_private.Mathlib.Combinatorics.SimpleGraph.Matching.0.SimpleGraph.Subgraph.IsMatching.iSup._simp_1_1 | Mathlib.Combinatorics.SimpleGraph.Matching | ∀ {α : Type u} {s t : Set α}, Disjoint s t = ∀ ⦃a : α⦄, a ∈ s → a ∉ t |
Cardinal.lift_eq_aleph1 | Mathlib.SetTheory.Cardinal.Aleph | ∀ {c : Cardinal.{u}}, Cardinal.lift.{v, u} c = Cardinal.aleph 1 ↔ c = Cardinal.aleph 1 |
List.forIn'.loop._proof_1 | Init.Data.List.Control | ∀ {α : Type u_1} (as : List α) (a : α) (as' : List α), (∃ bs, bs ++ a :: as' = as) → ∃ bs, bs ++ as' = as |
groupHomology.isBoundary₁_of_mem_boundaries₁ | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | ∀ {k G A : Type u} [inst : CommRing k] [inst_1 : Group G] [inst_2 : AddCommGroup A] [inst_3 : Module k A]
[inst_4 : DistribMulAction G A] [inst_5 : SMulCommClass G k A],
∀ x ∈ groupHomology.boundaries₁ (Rep.ofDistribMulAction k G A), groupHomology.IsBoundary₁ x |
CategoryTheory.FreeBicategory.Hom₂.whisker_left.sizeOf_spec | Mathlib.CategoryTheory.Bicategory.Free | ∀ {B : Type u} [inst : Quiver B] [inst_1 : SizeOf B] {a b c : CategoryTheory.FreeBicategory B} (f : a ⟶ b) {g h : b ⟶ c}
(η : CategoryTheory.FreeBicategory.Hom₂ g h),
sizeOf (CategoryTheory.FreeBicategory.Hom₂.whisker_left f η) =
1 + sizeOf a + sizeOf b + sizeOf c + sizeOf f + sizeOf g + sizeOf h + sizeOf η |
UInt32.toFin_mul | Init.Data.UInt.Lemmas | ∀ (a b : UInt32), (a * b).toFin = a.toFin * b.toFin |
AlgebraicGeometry.Scheme.Pullback.t_fst_snd | Mathlib.AlgebraicGeometry.Pullbacks | ∀ {X Y Z : AlgebraicGeometry.Scheme} (𝒰 : X.OpenCover) (f : X ⟶ Z) (g : Y ⟶ Z)
[inst : ∀ (i : 𝒰.I₀), CategoryTheory.Limits.HasPullback (CategoryTheory.CategoryStruct.comp (𝒰.f i) f) g]
(i j : 𝒰.I₀),
CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Pullback.t 𝒰 f g i j)
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.Limits.pullback.fst
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.Limits.pullback.fst (CategoryTheory.CategoryStruct.comp (𝒰.f j) f) g) (𝒰.f j))
(𝒰.f i))
(CategoryTheory.Limits.pullback.snd (CategoryTheory.CategoryStruct.comp (𝒰.f j) f) g)) =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.Limits.pullback.fst
(CategoryTheory.CategoryStruct.comp
(CategoryTheory.Limits.pullback.fst (CategoryTheory.CategoryStruct.comp (𝒰.f i) f) g) (𝒰.f i))
(𝒰.f j))
(CategoryTheory.Limits.pullback.snd (CategoryTheory.CategoryStruct.comp (𝒰.f i) f) g) |
Lean.Elab.Term.elabProp._regBuiltin.Lean.Elab.Term.elabProp.declRange_3 | Lean.Elab.BuiltinTerm | IO Unit |
_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.CollectDerivedValInfo.State._sizeOf_1 | Lean.Compiler.LCNF.ExplicitRC | Lean.Compiler.LCNF.CollectDerivedValInfo.State✝ → ℕ |
Lean.Meta.Grind.CheckResult.closed.elim | Lean.Meta.Tactic.Grind.CheckResult | {motive : Lean.Meta.Grind.CheckResult → Sort u} →
(t : Lean.Meta.Grind.CheckResult) → t.ctorIdx = 3 → motive Lean.Meta.Grind.CheckResult.closed → motive t |
_private.Mathlib.Algebra.Category.Ring.Colimits.0.RingCat.Colimits.descFunLift.match_1.eq_4 | Mathlib.Algebra.Category.Ring.Colimits | ∀ {J : Type u_1} [inst : CategoryTheory.SmallCategory J] (F : CategoryTheory.Functor J RingCat)
(motive : RingCat.Colimits.Prequotient F → Sort u_2) (x : RingCat.Colimits.Prequotient F)
(h_1 : (j : J) → (x : ↑(F.obj j)) → motive (RingCat.Colimits.Prequotient.of j x))
(h_2 : Unit → motive RingCat.Colimits.Prequotient.zero) (h_3 : Unit → motive RingCat.Colimits.Prequotient.one)
(h_4 : (x : RingCat.Colimits.Prequotient F) → motive x.neg)
(h_5 : (x y : RingCat.Colimits.Prequotient F) → motive (x.add y))
(h_6 : (x y : RingCat.Colimits.Prequotient F) → motive (x.mul y)),
(match x.neg with
| RingCat.Colimits.Prequotient.of j x => h_1 j x
| RingCat.Colimits.Prequotient.zero => h_2 ()
| RingCat.Colimits.Prequotient.one => h_3 ()
| x.neg => h_4 x
| x.add y => h_5 x y
| x.mul y => h_6 x y) =
h_4 x |
instReprUInt64 | Init.Data.Repr | Repr UInt64 |
CharP.orderOf_eq_two_iff | Mathlib.GroupTheory.OrderOfElement | ∀ {R : Type u_6} [inst : Ring R] [Nontrivial R] [NoZeroDivisors R] (p : ℕ),
p ≠ 2 → ∀ [CharP R p] {x : R}, orderOf x = 2 ↔ x = -1 |
Polynomial.aeval_conj | Mathlib.Analysis.RCLike.Lemmas | ∀ {K : Type u_1} [inst : RCLike K] (p : Polynomial ℝ) (z : K),
(Polynomial.aeval ((starRingEnd K) z)) p = (starRingEnd K) ((Polynomial.aeval z) p) |
MulOpposite.instCommCStarAlgebra._proof_3 | Mathlib.Analysis.CStarAlgebra.Classes | ∀ {A : Type u_1} [inst : CommCStarAlgebra A], StarModule ℂ Aᵐᵒᵖ |
CategoryTheory.GrothendieckTopology.Subcanonical.of_le | Mathlib.CategoryTheory.Sites.Canonical | ∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J K : CategoryTheory.GrothendieckTopology C},
J ≤ K → ∀ [K.Subcanonical], J.Subcanonical |
ZNum.rec | Mathlib.Data.Num.Basic | {motive : ZNum → Sort u} →
motive ZNum.zero → ((a : PosNum) → motive (ZNum.pos a)) → ((a : PosNum) → motive (ZNum.neg a)) → (t : ZNum) → motive t |
CategoryTheory.LocalizerMorphism.RightResolution.Hom.noConfusion | Mathlib.CategoryTheory.Localization.Resolution | {P : Sort u} →
{C₁ : Type u_1} →
{C₂ : Type u_2} →
{inst : CategoryTheory.Category.{v_1, u_1} C₁} →
{inst_1 : CategoryTheory.Category.{v_2, u_2} C₂} →
{W₁ : CategoryTheory.MorphismProperty C₁} →
{W₂ : CategoryTheory.MorphismProperty C₂} →
{Φ : CategoryTheory.LocalizerMorphism W₁ W₂} →
{X₂ : C₂} →
{R R' : Φ.RightResolution X₂} →
{t : R.Hom R'} →
{C₁' : Type u_1} →
{C₂' : Type u_2} →
{inst' : CategoryTheory.Category.{v_1, u_1} C₁'} →
{inst'_1 : CategoryTheory.Category.{v_2, u_2} C₂'} →
{W₁' : CategoryTheory.MorphismProperty C₁'} →
{W₂' : CategoryTheory.MorphismProperty C₂'} →
{Φ' : CategoryTheory.LocalizerMorphism W₁' W₂'} →
{X₂' : C₂'} →
{R'_1 R'' : Φ'.RightResolution X₂'} →
{t' : R'_1.Hom R''} →
C₁ = C₁' →
C₂ = C₂' →
inst ≍ inst' →
inst_1 ≍ inst'_1 →
W₁ ≍ W₁' →
W₂ ≍ W₂' →
Φ ≍ Φ' →
X₂ ≍ X₂' →
R ≍ R'_1 →
R' ≍ R'' →
t ≍ t' →
CategoryTheory.LocalizerMorphism.RightResolution.Hom.noConfusionType
P t t' |
Nat.le_sub_of_add_le' | Init.Data.Nat.Lemmas | ∀ {n k m : ℕ}, m + n ≤ k → n ≤ k - m |
Mathlib.Tactic.Translate.TranslateData.mk.noConfusion | Mathlib.Tactic.Translate.Core | {P : Sort u} →
{ignoreArgsAttr : Lean.NameMapExtension (List ℕ)} →
{doTranslateAttr : Lean.NameMapExtension Bool} →
{unfoldBoundaries? : Option Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaryExt} →
{translations : Lean.NameMapExtension Mathlib.Tactic.Translate.TranslationInfo} →
{attrName : Lean.Name} →
{changeNumeral isDual : Bool} →
{guessNameData : Mathlib.Tactic.GuessName.GuessNameData} →
{ignoreArgsAttr' : Lean.NameMapExtension (List ℕ)} →
{doTranslateAttr' : Lean.NameMapExtension Bool} →
{unfoldBoundaries?' : Option Mathlib.Tactic.UnfoldBoundary.UnfoldBoundaryExt} →
{translations' : Lean.NameMapExtension Mathlib.Tactic.Translate.TranslationInfo} →
{attrName' : Lean.Name} →
{changeNumeral' isDual' : Bool} →
{guessNameData' : Mathlib.Tactic.GuessName.GuessNameData} →
{ ignoreArgsAttr := ignoreArgsAttr, doTranslateAttr := doTranslateAttr,
unfoldBoundaries? := unfoldBoundaries?, translations := translations,
attrName := attrName, changeNumeral := changeNumeral, isDual := isDual,
guessNameData := guessNameData } =
{ ignoreArgsAttr := ignoreArgsAttr', doTranslateAttr := doTranslateAttr',
unfoldBoundaries? := unfoldBoundaries?', translations := translations',
attrName := attrName', changeNumeral := changeNumeral', isDual := isDual',
guessNameData := guessNameData' } →
(ignoreArgsAttr = ignoreArgsAttr' →
doTranslateAttr = doTranslateAttr' →
unfoldBoundaries? = unfoldBoundaries?' →
translations = translations' →
attrName = attrName' →
changeNumeral = changeNumeral' →
isDual = isDual' → guessNameData = guessNameData' → P) →
P |
Action.instMonoidalForget._proof_2 | Mathlib.CategoryTheory.Action.Monoidal | ∀ (V : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} V] (G : Type u_3) [inst_1 : Monoid G]
[inst_2 : CategoryTheory.MonoidalCategory V] {X Y : Action V G} (f : X ⟶ Y) (X' : Action V G),
CategoryTheory.CategoryStruct.comp
(CategoryTheory.MonoidalCategoryStruct.whiskerRight ((Action.forget V G).map f) ((Action.forget V G).obj X'))
(CategoryTheory.Iso.refl
(CategoryTheory.MonoidalCategoryStruct.tensorObj ((Action.forget V G).obj Y)
((Action.forget V G).obj X'))).hom =
CategoryTheory.CategoryStruct.comp
(CategoryTheory.Iso.refl
(CategoryTheory.MonoidalCategoryStruct.tensorObj ((Action.forget V G).obj X)
((Action.forget V G).obj X'))).hom
((Action.forget V G).map (CategoryTheory.MonoidalCategoryStruct.whiskerRight f X')) |
AlgebraicIndependent.to_subtype_range | Mathlib.RingTheory.AlgebraicIndependent.Basic | ∀ {ι : Type u} {R : Type u_2} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A],
AlgebraicIndependent R x → AlgebraicIndependent R Subtype.val |
Decidable.decide.congr_simp | Init.SimpLemmas | ∀ (p p_1 : Prop), p = p_1 → ∀ {h : Decidable p} [h_1 : Decidable p_1], decide p = decide p_1 |
IsLocalization.map_units | Mathlib.RingTheory.Localization.Defs | ∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} (S : Type u_2) [inst_1 : CommSemiring S]
[inst_2 : Algebra R S] [IsLocalization M S] (y : ↥M), IsUnit ((algebraMap R S) ↑y) |
MvPFunctor.B | Mathlib.Data.PFunctor.Multivariate.Basic | {n : ℕ} → (self : MvPFunctor.{u} n) → self.A → TypeVec.{u} n |
Real.cos_sub_two_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | ∀ (x : ℝ), Real.cos (x - 2 * Real.pi) = Real.cos x |
AlgebraicGeometry.Scheme.Hom.asFiberHom._proof_1 | Mathlib.AlgebraicGeometry.Fiber | ∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (x : ↥X),
CategoryTheory.Limits.HasPullback f (Y.fromSpecResidueField (f x)) |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_536 | Mathlib.GroupTheory.Perm.Cycle.Type | ∀ {α : Type u_1} [inst_1 : DecidableEq α] {g : Equiv.Perm α} {a : α} (w : α)
(h :
List.findIdxNth (fun x => decide (x = w)) [g (g a)] (List.idxOfNth w [g (g a)] 1) + 1 ≤
(List.filter (fun x => decide (x = w)) []).length),
(List.findIdxs (fun x => decide (x = w))
[])[List.findIdxNth (fun x => decide (x = w)) [g (g a)] (List.idxOfNth w [g (g a)] 1)] <
[].length |
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