(** We need to show that, in the simulation diagram, we cannot
  take infinitely many Mach transitions that correspond to zero
  transitions on the PPC side.  Actually, all Mach transitions
  correspond to at least one Asm transition, except the
  transition from [Mach.Returnstate] to [Mach.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.

Lemma transf_initial_states: forall st1, Mach.initial_state prog st1 -> exists st2, Asm.initial_state tprog st2 /\ match_states st1 st2.