Definition if_preg (r: preg) : bool :=
  match r with
  | IR _ => true
  | FR _ => true
  | CR _ => false
  | PC   => false
  end.

(* Specifications: *)
Lemma data_if_preg: forall r, data_preg r = true -> if_preg r = true.
Lemma if_preg_not_PC: forall r, if_preg r = true -> r <> PC.