Section BACKWARD_SIMULATION_SEQUENCES.
Context L1 L2 index order match_states (S: bsim_properties L1 L2 index order match_states).

Lemma bsim_E0_plus:
forall s2 t s2', Plus L2 s2 t s2' -> t = E0 ->
forall i s1, match_states i s1 s2 -> safe L1 s1 ->
(exists i', exists s1', Plus L1 s1 E0 s1' /\ match_states i' s1' s2')
\/ (exists i', clos_trans _ order i' i /\ match_states i' s1 s2').