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

Lemma star_non_E0_split:
forall s2 t s2', Star L2 s2 t s2' -> (length t = 1)%nat ->
exists s2x, exists s2y, Star L2 s2 E0 s2x /\ Step L2 s2x t s2y /\ Star L2 s2y E0 s2'.