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| module FinVector-cons (T : Set) where | |
| data Nat : Set where | |
| zero : Nat | |
| suc : Nat → Nat | |
| data Fin : Nat → Set where | |
| zero : ∀ {n} → Fin (suc n) | |
| suc : ∀ {n} → Fin n → Fin (suc n) | |
| data _≡_ {A : Set} (x : A) : A → Set where | |
| refl : x ≡ x | |
| postulate | |
| funext : {A B : Set} → {f g : A → B} → (∀ x → f x ≡ g x) → f ≡ g | |
| B : Nat → Set | |
| B n = Fin n → T | |
| cons : ∀ {n} (t : T) → B n → B (suc n) | |
| cons x xs zero = x | |
| cons x xs (suc z) = xs z | |
| head : ∀ {n} → B (suc n) → T | |
| head xs = xs zero | |
| tail : ∀ {n} → B (suc n) → B n | |
| tail xs n = xs (suc n) | |
| cons-ok : ∀ {n} → (b : B (suc n)) → ∀ n → cons (head b) (tail b) n ≡ b n | |
| cons-ok b zero = refl | |
| cons-ok b (suc n) = refl | |
| cons-ok-ext : ∀ {n} → (b : B (suc n)) → cons (head b) (tail b) ≡ b | |
| cons-ok-ext b = funext (cons-ok b) |
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