(** * Useful properties of registers *)

(** [important_preg] extends [data_preg] by tracking the LR register as well.
    It is used to state that a code sequence modifies no data registers
    and does not modify LR either. *)

Definition important_preg (r: preg) : bool :=
  match r with
  | IR GPR0 => false
  | PC => false    | CTR => false
  | CR0_0 => false | CR0_1 => false | CR0_2 => false | CR0_3 => false
  | CARRY => false
  | _ => true
  end.

Lemma important_diff: forall r r', important_preg r = true -> important_preg r' = false -> r <> r'.