(* 
  Find the list of booleans associated with an element,
  return the empty list if the element does not exists
*)
Fixpoint find_code (a : A) (l : code) {struct l} : list bool :=
  match l with
  | nil => nil
  | (b, c) :: l1 =>
      match eqA_dec a b with
      | left _ => c
      | right _ => find_code a l1
      end
  end.

Theorem find_code_permutation : forall (a : A) (c1 c2 : code), permutation c1 c2 -> unique_prefix c1 -> find_code a c1 = find_code a c2.