(** * 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 ireg_of_not_GPR0: forall m r, ireg_of m = OK r -> IR r <> IR GPR0.