Remove commented code
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@ -9,14 +9,6 @@ open import Cat.Category
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open IsCategory
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open IsCategory
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-- data Path {ℓ : Level} {A : Set ℓ} : (a b : A) → Set ℓ where
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-- emptyPath : {a : A} → Path a a
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-- concatenate : {a b c : A} → Path a b → Path b c → Path a b
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-- import Data.List
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-- P : (a b : Object ℂ) → Set (ℓ ⊔ ℓ')
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-- P = {!Data.List.List ?!}
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-- Generalized paths:
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data Path {ℓ ℓ' : Level} {A : Set ℓ} (R : A → A → Set ℓ') : (a b : A) → Set (ℓ ⊔ ℓ') where
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data Path {ℓ ℓ' : Level} {A : Set ℓ} (R : A → A → Set ℓ') : (a b : A) → Set (ℓ ⊔ ℓ') where
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empty : {a : A} → Path R a a
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empty : {a : A} → Path R a a
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cons : {a b c : A} → R b c → Path R a b → Path R a c
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cons : {a b c : A} → R b c → Path R a b → Path R a c
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@ -20,28 +20,3 @@ module Equality where
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Σ≡ : a ≡ b
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Σ≡ : a ≡ b
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proj₁ (Σ≡ i) = proj₁≡ i
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proj₁ (Σ≡ i) = proj₁≡ i
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proj₂ (Σ≡ i) = proj₂≡ i
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proj₂ (Σ≡ i) = proj₂≡ i
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-- Remark 2.7.1: This theorem:
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--
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-- (x , u) ≡ (x , v) → u ≡ v
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--
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-- does *not* hold! We can only conclude that there *exists* `p : x ≡ x`
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-- such that
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--
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-- p* u ≡ v
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-- thm : isSet A → (∀ {a} → isSet (B a)) → isSet (Σ A B)
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-- thm sA sB (x , y) (x' , y') p q = res
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-- where
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-- x≡x'0 : x ≡ x'
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-- x≡x'0 = λ i → proj₁ (p i)
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-- x≡x'1 : x ≡ x'
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-- x≡x'1 = λ i → proj₁ (q i)
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-- someP : x ≡ x'
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-- someP = {!!}
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-- tricky : {!y!} ≡ y'
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-- tricky = {!!}
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-- -- res' : (λ _ → Σ A B) [ (x , y) ≡ (x' , y') ]
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-- res' : ({!!} , {!!}) ≡ ({!!} , {!!})
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-- res' = {!!}
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-- res : p ≡ q
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-- res i = {!res'!}
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