From 7dfdab1973dbc7e0c4f592803430c89061267aff Mon Sep 17 00:00:00 2001 From: Michael Zhang Date: Mon, 22 Apr 2024 03:28:04 +0000 Subject: [PATCH] auto gitdoc commit --- src/HottBook/Chapter2.lagda.md | 24 ++---------------------- 1 file changed, 2 insertions(+), 22 deletions(-) diff --git a/src/HottBook/Chapter2.lagda.md b/src/HottBook/Chapter2.lagda.md index 2b98fc7..46cb581 100644 --- a/src/HottBook/Chapter2.lagda.md +++ b/src/HottBook/Chapter2.lagda.md @@ -259,28 +259,8 @@ A ≃ B = Σ[ f ∈ (A → B) ] isequiv f ### Theorem 2.8.1 ``` --- open import Function.HalfAdjointEquivalence --- _is-⋆ : (x : 𝟙) → x ≡ ⋆ --- ⋆ is-⋆ = refl --- --- theorem281-helper2 : {x : 𝟙} → (p : x ≡ x) → p ≡ refl --- theorem281-helper2 {x} p = --- let a = sym (x is-⋆) ∙ p ∙ (x is-⋆) in --- J (λ the what → p ≡ the) ? ? --- --- theorem281-helper : {x y : 𝟙} → (p : x ≡ y) → (x is-⋆) ∙ sym (y is-⋆) ≡ p --- theorem281-helper {x} p = --- J (λ the what → (x is-⋆) ∙ sym (the is-⋆) ≡ what) p (theorem281-helper2 _) --- --- theorem281 : (x y : 𝟙) → (x ≡ y) ≃ 𝟙 --- theorem281 x y = record --- { to = λ _ → ⋆ --- ; from = λ _ → (x is-⋆) ∙ sym (y is-⋆) --- ; left-inverse-of = theorem281-helper --- -- λ z → J (λ the what → (x is-⋆) ∙ sym (the is-⋆) ≡ what) z ? --- ; right-inverse-of = λ z → sym (z is-⋆) --- ; left-right = ? --- } +theorem2∙8∙1 : (x y : 𝟙) → (x ≡ y) ≃ 𝟙 +theorem2∙8∙1 = {! !} ``` ## 2.9 Π-types and the function extensionality axiom