diff --git a/src/CubicalHott/Lemma3-11-4.agda b/src/CubicalHott/Lemma3-11-4.agda index 4ac0334..65e8af2 100644 --- a/src/CubicalHott/Lemma3-11-4.agda +++ b/src/CubicalHott/Lemma3-11-4.agda @@ -7,13 +7,29 @@ open import CubicalHott.Example3-6-2 renaming (example to example3-6-2) lemma : {A : Type} → isProp (isContr A) lemma {A} A-contr-x @ (x , px) (y , py) i = - let A-is-set = isProp→isSet (isContr→isProp A-contr-x) in px y i , goal i where + A-is-set = isProp→isSet (isContr→isProp A-contr-x) + + helper2 : px y i ≡ y + helper2 = sym (py (px y i)) + helper1 : isProp ((z : A) → px y i ≡ z) - helper1 = example3-6-2 (λ x → isContr→isProp {! !}) + helper1 = example3-6-2 (λ z → isContr→isProp (helper2 ∙ py z , λ q → A-is-set (px y i) z (helper2 ∙ py z) q)) + + wtf : (z : A) → sym (px z) ∙∙ px y ∙∙ py z ≡ refl {x = z} + wtf z = A-is-set z z (sym (px z) ∙∙ px y ∙∙ py z) refl + + helper3 : (z : A) → PathP (λ i → px z i ≡ py z i) (px y) (sym (px z) ∙∙ px y ∙∙ py z) + helper3 z = doubleCompPath-filler (sym (px z)) (px y) (py z) + + helper5 : (z : A) → PathP (λ i → px z i ≡ py z i) (px y) (refl {x = z}) + helper5 z = helper3 z ▷ wtf z + + goal2 : (z : A) → PathP (λ i → px y i ≡ z) (px z) (py z) + goal2 z i j = helper5 z j i goal : PathP (λ i → (z : A) → px y i ≡ z) px py - goal i z = {! helper1 !} + goal i z j = funExt (λ z → goal2 z i) j z - -- λ y' j → isProp→isSet (isContr→isProp A-contr-x) (px y i) y' {! !} {! !} j i \ No newline at end of file + -- λ y' j → isProp→isSet (isContr→isProp A-contr-x) (px y i) y' {! !} {! !} j i \ No newline at end of file