(** * 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'.