(* 
  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_correct1 : forall (c : code) (a : A) (b : bool) (l : list bool), find_code a c = b :: l -> In (a, b :: l) c.