diff --git a/src/CubicalHott/Example3-6-2.agda b/src/CubicalHott/Example3-6-2.agda index 06e1467..94954c2 100644 --- a/src/CubicalHott/Example3-6-2.agda +++ b/src/CubicalHott/Example3-6-2.agda @@ -7,4 +7,4 @@ open import Cubical.Foundations.Prelude example : {A : Type} → {B : A → Type} → ((x : A) → isProp (B x)) → isProp ((x : A) → B x) -example B-x-prop x y = λ i z → B-x-prop {! !} {! !} {! !} i \ No newline at end of file +example B-x-prop fx fy = λ i z → B-x-prop z (B-x-prop z (fx z) (fy z) i) (B-x-prop z (fx z) (fy z) i) i \ No newline at end of file diff --git a/src/CubicalHott/Lemma3-11-3.agda b/src/CubicalHott/Lemma3-11-3.agda index 9468305..a078336 100644 --- a/src/CubicalHott/Lemma3-11-3.agda +++ b/src/CubicalHott/Lemma3-11-3.agda @@ -2,4 +2,4 @@ module CubicalHott.Lemma3-11-3 where -open import Cubical.Foundations.Prelude \ No newline at end of file +open import Cubical.Foundations.Prelude diff --git a/src/CubicalHott/Lemma3-11-4.agda b/src/CubicalHott/Lemma3-11-4.agda index d6ec615..4ac0334 100644 --- a/src/CubicalHott/Lemma3-11-4.agda +++ b/src/CubicalHott/Lemma3-11-4.agda @@ -3,13 +3,17 @@ module CubicalHott.Lemma3-11-4 where open import Cubical.Foundations.Prelude +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 ≡ z - -- ———— Boundary (wanted) ————————————————————————————————————— - -- i = i0 ⊢ px z - -- i = i1 ⊢ py z - px y i , λ z j → {! !} + px y i , goal i where + helper1 : isProp ((z : A) → px y i ≡ z) + helper1 = example3-6-2 (λ x → isContr→isProp {! !}) + + goal : PathP (λ i → (z : A) → px y i ≡ z) px py + goal i z = {! helper1 !} + + -- λ y' j → isProp→isSet (isContr→isProp A-contr-x) (px y i) y' {! !} {! !} j i \ No newline at end of file diff --git a/src/CubicalHott/Theorem7-1-10.agda b/src/CubicalHott/Theorem7-1-10.agda index 3e5a00d..a3bd843 100644 --- a/src/CubicalHott/Theorem7-1-10.agda +++ b/src/CubicalHott/Theorem7-1-10.agda @@ -9,6 +9,6 @@ open import Cubical.Data.Nat z = isContr theorem : {X : Type} → (n : ℕ) → isProp (isOfHLevel n X) -theorem zero x y i = snd x (fst y) i , {! !} +theorem zero = {! !} theorem (suc zero) x y = {! !} theorem (suc (suc n)) x y = {! !} \ No newline at end of file