auto gitdoc commit

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Michael Zhang 2024-04-22 02:28:00 +00:00
parent 88fcab2a06
commit e5ab040c54

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@ -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)