(** We need to show that, in the simulation diagram, we cannot take infinitely many Mach transitions that correspond to zero transitions on the Asm side.  Actually, all Mach transitions correspond to at least one Asm transition, except the transition from [Machsem.Returnstate] to [Machsem.State]. So, the following integer measure will suffice to rule out the unwanted behaviour. *)
Definition measure (s: Mach.state) : nat :=
match s with
| Mach.State _ _ _ _ _ _ => 0%nat
| Mach.Callstate _ _ _ _ => 0%nat
| Mach.Returnstate _ _ _ => 1%nat
end.
Remark preg_of_not_X30: forall r, negb (mreg_eq r R30) = true -> IR X30 <> preg_of r.
(** This is the simulation diagram.  We prove it by case analysis on the Mach transition. *)

Lemma transf_final_states:
forall st1 st2 r,
match_states st1 st2 -> Mach.final_state st1 r -> Asm.final_state st2 r.