fix(library/init/core): show
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1 changed files with 5 additions and 5 deletions
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@ -268,7 +268,7 @@ infix ≅ := Heq
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theorem eqOfHeq {α : Sort u} {a a' : α} (h : a ≅ a') : a = a' :=
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have ∀ (α' : Sort u) (a' : α') (h₁ : @Heq α a α' a') (h₂ : α = α'), (Eq.recOn h₂ a : α') = a' :=
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fun (α' : Sort u) (a' : α') (h₁ : @Heq α a α' a') => Heq.recOn h₁ (fun h₂ : α = α => rfl);
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show (Eq.ndrecOn (Eq.refl α) a : α) = a', from
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show (Eq.ndrecOn (Eq.refl α) a : α) = a' from
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this α a' h (Eq.refl α)
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inductive Sum (α : Type u) (β : Type v)
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@ -1653,7 +1653,7 @@ Quot.liftOn f
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(fun f₁ f₂ h => h x)
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theorem funext {f₁ f₂ : Π x : α, β x} (h : ∀ x, f₁ x = f₂ x) : f₁ = f₂ :=
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show extfunApp ⟦f₁⟧ = extfunApp ⟦f₂⟧, from
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show extfunApp ⟦f₁⟧ = extfunApp ⟦f₂⟧ from
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congrArg extfunApp (sound h)
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end
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@ -1728,11 +1728,11 @@ have pImpliesUv : p → u = v from
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fun a => Or.inr hp;
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have hr : (x = False ∨ p) → (x = True ∨ p) from
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fun a => Or.inr hp;
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show (x = True ∨ p) = (x = False ∨ p), from
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show (x = True ∨ p) = (x = False ∨ p) from
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propext (Iff.intro hl hr);
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have h₀ : ∀ exU exV, @choose _ U exU = @choose _ V exV from
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hpred ▸ fun exU exV => rfl;
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show u = v, from h₀ _ _;
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show u = v from h₀ _ _;
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Or.elim notUvOrP
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(fun (hne : u ≠ v) => Or.inr (mt pImpliesUv hne))
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Or.inl
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@ -1768,7 +1768,7 @@ noncomputable def strongIndefiniteDescription {α : Sort u} (p : α → Prop)
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(h : Nonempty α) : {x : α // Exists (fun y : α => p y) → p x} :=
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@dite (Exists (fun x : α => p x)) (propDecidable _) _
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(fun hp : Exists (fun x : α => p x) =>
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show {x : α // Exists (fun y : α => p y) → p x}, from
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show {x : α // Exists (fun y : α => p y) → p x} from
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let xp := indefiniteDescription _ hp;
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⟨xp.val, fun h' => xp.property⟩)
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(fun hp => ⟨choice h, fun h => absurd h hp⟩)
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