lemma 3.11.3
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@ -401,17 +401,23 @@ module lemma3∙11∙3 where
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iii : {A : Set} → A ≃ 𝟙 → properties A
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iii : {A : Set} → A ≃ 𝟙 → properties A
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iii Aeqv @ (f , mkIsEquiv g g* h h*) = mkProperties p1 p2 p3
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iii Aeqv @ (f , mkIsEquiv g g* h h*) = mkProperties p1 p2 p3
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where
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where
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p1 = g tt , λ x → {! ap g ? !}
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alltt : (a b : 𝟙) → a ≡ b
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p2 = g tt , λ x y → {! !}
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alltt tt tt = refl
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p3 = Aeqv
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p1 = h tt , λ x → ap h (alltt tt (f x)) ∙ h* x
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p2 = h tt , λ x y → sym (h* x) ∙ ap h (alltt (f x) (f y)) ∙ h* y
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p3 = Aeqv
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```
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```
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### Lemma 3.11.6
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### Lemma 3.11.6
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```
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```
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lemma3∙11∙6 : {A : Set} {P : A → Set} → ((a : A) → isContr (P a)) → isContr ((x : A) → P x)
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lemma3∙11∙6 : {A : Set} {P : A → Set} → ((a : A) → isContr (P a)) → isContr ((x : A) → P x)
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lemma3∙11∙6 {A} {P} allContr = {! !}
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lemma3∙11∙6 {A} {P} allContr =
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let
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Pa-isProp : isProp ((x : A) → P x)
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Pa-isProp = example3∙6∙2 λ x → Σ.snd (lemma3∙11∙3.properties.ii (lemma3∙11∙3.i (allContr x)))
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in {! !} , {! !}
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```
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```
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### Lemma 3.11.8
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### Lemma 3.11.8
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