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

Lemma bsim_E0_star:
forall s2 s2', Star L2 s2 E0 s2' ->
forall i s1, match_states i s1 s2 -> safe L1 s1 ->
exists i', exists s1', Star L1 s1 E0 s1' /\ match_states i' s1' s2'.