From e5ab040c544b881997b9faf89128abc23d03abe5 Mon Sep 17 00:00:00 2001 From: Michael Zhang Date: Mon, 22 Apr 2024 02:28:00 +0000 Subject: [PATCH] auto gitdoc commit --- src/HottBook/Chapter2.lagda.md | 25 +++++++++++++++++-------- 1 file changed, 17 insertions(+), 8 deletions(-) diff --git a/src/HottBook/Chapter2.lagda.md b/src/HottBook/Chapter2.lagda.md index c1ad14a..50ce83f 100644 --- a/src/HottBook/Chapter2.lagda.md +++ b/src/HottBook/Chapter2.lagda.md @@ -149,12 +149,12 @@ lemma2∙3∙8 {l} {A} {B} f {x} {y} p = ### Lemma 2.3.11 ``` -lemma2∙3∙11 : {A : Set} {P Q : A → Set} - → (f : (x : A) → P x → Q x) - → {x y : A} (p : x ≡ y) → (u : P x) - → transport Q p (f x u) ≡ f y (transport P p u) -lemma2∙3∙11 {A} {P} {Q} f {x} {y} p u = - J (λ a b p → transport Q p (f a {! !}) ≡ f b (transport P p {! !})) (λ a → {! !}) x y p +-- lemma2∙3∙11 : {A : Set} {P Q : A → Set} +-- → (f : (x : A) → P x → Q x) +-- → {x y : A} (p : x ≡ y) → (u : P x) +-- → transport Q p (f x u) ≡ f y (transport P p u) +-- lemma2∙3∙11 {A} {P} {Q} f {x} {y} p u = +-- J (λ a b p → transport Q p (f a {! !}) ≡ f b (transport P p {! !})) (λ a → {! !}) x y p -- J (λ the what → transport Q what (f x u) ≡ f the (transport P what u)) p refl ``` @@ -295,8 +295,17 @@ postulate ### Lemma 2.10.1 ``` --- idToEquiv : {A B : Set} → (A ≡ B) → A ≃ B --- idToEquiv p = ? , ? +idToEquiv : {A B : Set} + → (A ≡ B) + → A ≃ B +idToEquiv {A} {B} p = {! !} , equiv + where + equiv = record + { g = {! !} + ; g-id = {! !} + ; h = {! !} + ; h-id = {! !} + } ``` ### Axiom 2.10.3 (Univalence)