Section SIMULATION_STAR_WF.
(** [order] is a well-founded ordering associated with states of the first semantics.  Stuttering steps must correspond to states that decrease w.r.t. [order]. *)
Variable order: state L1 -> state L1 -> Prop.
Hypothesis order_wf: well_founded order.
Hypothesis simulation:
forall s1 t s1', Step L1 s1 t s1' ->
forall s2, match_states s1 s2 ->
exists s2',
(Plus L2 s2 t s2' \/ (Star L2 s2 t s2' /\ order s1' s1))
/\ match_states s1' s2'.
Notation match_states':=
(fun (idx s1 : state L1) (s2 : state L2) => idx = s1 /\ match_states s1 s2).

Lemma fsim_properties_star_wf:
fsim_properties L1 L2 _ order match_states'.