lemma 3.11.3

This commit is contained in:
Michael Zhang 2024-07-11 00:29:39 -05:00
parent 83c80001e5
commit 3807a5759a

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@ -401,17 +401,23 @@ module lemma3∙11∙3 where
iii : {A : Set} → A ≃ 𝟙 → properties A
iii Aeqv @ (f , mkIsEquiv g g* h h*) = mkProperties p1 p2 p3
where
p1 = g tt , λ x → {! ap g ? !}
p2 = g tt , λ x y → {! !}
p3 = Aeqv
alltt : (a b : 𝟙) → a ≡ b
alltt tt tt = refl
p1 = h tt , λ x → ap h (alltt tt (f x)) ∙ h* x
p2 = h tt , λ x y → sym (h* x) ∙ ap h (alltt (f x) (f y)) ∙ h* y
p3 = Aeqv
```
### Lemma 3.11.6
```
lemma3∙11∙6 : {A : Set} {P : A → Set} → ((a : A) → isContr (P a)) → isContr ((x : A) → P x)
lemma3∙11∙6 {A} {P} allContr = {! !}
lemma3∙11∙6 {A} {P} allContr =
let
Pa-isProp : isProp ((x : A) → P x)
Pa-isProp = example3∙6∙2 λ x → Σ.snd (lemma3∙11∙3.properties.ii (lemma3∙11∙3.i (allContr x)))
in {! !} , {! !}
```
### Lemma 3.11.8