End SIMULATION_OPT.
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).

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).