fix(library/init/core): show

This commit is contained in:
Leonardo de Moura 2019-07-02 17:27:03 -07:00
parent 0bee94886e
commit f74f5bc33a

View file

@ -268,7 +268,7 @@ infix ≅ := Heq
theorem eqOfHeq {α : Sort u} {a a' : α} (h : a ≅ a') : a = a' :=
have ∀ (α' : Sort u) (a' : α') (h₁ : @Heq α a α' a') (h₂ : α = α'), (Eq.recOn h₂ a : α') = a' :=
fun (α' : Sort u) (a' : α') (h₁ : @Heq α a α' a') => Heq.recOn h₁ (fun h₂ : α = α => rfl);
show (Eq.ndrecOn (Eq.refl α) a : α) = a', from
show (Eq.ndrecOn (Eq.refl α) a : α) = a' from
this α a' h (Eq.refl α)
inductive Sum (α : Type u) (β : Type v)
@ -1653,7 +1653,7 @@ Quot.liftOn f
(fun f₁ f₂ h => h x)
theorem funext {f₁ f₂ : Π x : α, β x} (h : ∀ x, f₁ x = f₂ x) : f₁ = f₂ :=
show extfunApp ⟦f₁⟧ = extfunApp ⟦f₂⟧, from
show extfunApp ⟦f₁⟧ = extfunApp ⟦f₂⟧ from
congrArg extfunApp (sound h)
end
@ -1728,11 +1728,11 @@ have pImpliesUv : p → u = v from
fun a => Or.inr hp;
have hr : (x = False p) → (x = True p) from
fun a => Or.inr hp;
show (x = True p) = (x = False p), from
show (x = True p) = (x = False p) from
propext (Iff.intro hl hr);
have h₀ : ∀ exU exV, @choose _ U exU = @choose _ V exV from
hpred ▸ fun exU exV => rfl;
show u = v, from h₀ _ _;
show u = v from h₀ _ _;
Or.elim notUvOrP
(fun (hne : u ≠ v) => Or.inr (mt pImpliesUv hne))
Or.inl
@ -1768,7 +1768,7 @@ noncomputable def strongIndefiniteDescription {α : Sort u} (p : α → Prop)
(h : Nonempty α) : {x : α // Exists (fun y : α => p y) → p x} :=
@dite (Exists (fun x : α => p x)) (propDecidable _) _
(fun hp : Exists (fun x : α => p x) =>
show {x : α // Exists (fun y : α => p y) → p x}, from
show {x : α // Exists (fun y : α => p y) → p x} from
let xp := indefiniteDescription _ hp;
⟨xp.val, fun h' => xp.property⟩)
(fun hp => ⟨choice h, fun h => absurd h hp⟩)