End FORWARD_SIMU_DIAGRAMS.
(** ** Forward simulation of transition sequences *)
Section SIMULATION_SEQUENCES.
Context L1 L2 index order match_states (S: fsim_properties L1 L2 index order match_states).

(* Specifications: *)
Lemma simulation_star:
forall s1 t s1', Star L1 s1 t s1' ->
forall i s2, match_states i s1 s2 ->
exists i', exists s2', Star L2 s2 t s2' /\ match_states i' s1' s2'.
Lemma simulation_plus:
forall s1 t s1', Plus L1 s1 t s1' ->
forall i s2, match_states i s1 s2 ->
(exists i', exists s2', Plus L2 s2 t s2' /\ match_states i' s1' s2')
\/ (exists i', clos_trans _ order i' i /\ t = E0 /\ match_states i' s1' s2).
Lemma simulation_forever_silent:
forall i s1 s2,
Forever_silent L1 s1 -> match_states i s1 s2 ->
Forever_silent L2 s2.
Lemma simulation_forever_reactive:
forall i s1 s2 T,
Forever_reactive L1 s1 T -> match_states i s1 s2 ->
Forever_reactive L2 s2 T.