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Michael Zhang 2024-07-24 21:18:10 -05:00
parent acbb85481f
commit a2dbafb324
2 changed files with 6 additions and 2 deletions
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6
src/HottBook/Chapter8.lagda.md
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@ -86,10 +86,14 @@ module lemma8∙1∙2 where
open definition8∙1∙1 open definition8∙1∙1
open axiom2∙10∙3 open axiom2∙10∙3
open ≡-Reasoning open ≡-Reasoning
open S¹
lifted-loop : {l : Level} → lift base ≡ lift base
lifted-loop {l} = ap (lift {l = l}) loop
i : {l : Level} → (x : Int {l}) → (transport code loop x) ≡ int-suc x i : {l : Level} → (x : Int {l}) → (transport code loop x) ≡ int-suc x
i x = begin i x = begin
(transport code loop x) ≡⟨ lemma2∙3∙10 {! id !} code loop x ⟩ (transport code loop x) ≡⟨ lemma2∙3∙10 id code {! lifted-loop !} x ⟩
(transport id (ap code loop) x) ≡⟨ {! !} ⟩ (transport id (ap code loop) x) ≡⟨ {! !} ⟩
-- (transport id (ua int-suc) x) ≡⟨ {! !} ⟩ -- (transport id (ua int-suc) x) ≡⟨ {! !} ⟩
int-suc x ∎ int-suc x ∎

2
src/HottBook/CoreUtil.agda
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@ -4,6 +4,6 @@ module HottBook.CoreUtil where
open import Agda.Primitive open import Agda.Primitive
record Lift {a ℓ} (A : Set a) : Set (a ⊔ ℓ) where record Lift {a l} (A : Set a) : Set (a ⊔ l) where
constructor lift constructor lift
field lower : A field lower : A