apply funext
α : Type u_1
inst✝ : Coding α Memory
N : ℕ
g : (Fin (N + 1) → Bool) → α
⊢ (fun g_1 =>
      match g_1 0 with
      | false => g (Fin.cons false (Fin.tail g_1))
      | true => g (Fin.cons true (Fin.tail g_1))) =
    g
case h
α : Type u_1
inst✝ : Coding α Memory
N : ℕ
g : (Fin (N + 1) → Bool) → α
⊢ ∀ (x : Fin (N + 1) → Bool),
    (match x 0 with
      | false => g (Fin.cons false (Fin.tail x))
      | true => g (Fin.cons true (Fin.tail x))) =
      g x