End SIMULATION_STAR_WF.
Section SIMULATION_STAR.
(** We now consider the case where we have a nonnegative integer measure associated with states of the first semantics.  It must decrease when we take a stuttering step. *)
Variable measure: state L1 -> nat.
Hypothesis simulation:
forall s1 t s1', Step L1 s1 t s1' ->
forall s2, match_states s1 s2 ->
(exists s2', Plus L2 s2 t s2' /\ match_states s1' s2')
\/ (measure s1' < measure s1 /\ t = E0 /\ match_states s1' s2)%nat.

Lemma fsim_properties_star:
fsim_properties L1 L2 _ (ltof _ measure)
(fun (idx s1 : state L1) (s2 : state L2) => idx = s1 /\ match_states s1 s2).