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-- Agda program using the Iowa Agda library
open import bool
module PROOF-appendAddLengths
(Choice : Set)
(choose : Choice → 𝔹)
(lchoice : Choice → Choice)
(rchoice : Choice → Choice)
where
open import eq
open import nat
open import list
open import maybe
---------------------------------------------------------------------------
-- Translated Curry operations:
++ : {a : Set} → 𝕃 a → 𝕃 a → 𝕃 a
++ [] x = x
++ (y :: z) u = y :: (++ z u)
append : {a : Set} → 𝕃 a → 𝕃 a → 𝕃 a
append x y = ++ x y
---------------------------------------------------------------------------
appendAddLengths : {a : Set} → (x : 𝕃 a) → (y : 𝕃 a)
→ ((length x) + (length y)) ≡ (length (append x y))
appendAddLengths [] y = refl
appendAddLengths (x :: xs) y rewrite appendAddLengths xs y = refl
---------------------------------------------------------------------------
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