diff --git a/library/init/core.lean b/library/init/core.lean index b7a569f8aa..2f5cd4be55 100644 --- a/library/init/core.lean +++ b/library/init/core.lean @@ -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⟩)