End SIMULATION_STAR.
(** Simulation when one transition in the first program corresponds to one or several transitions in the second program. *)
Section SIMULATION_PLUS.
Hypothesis simulation:
forall s1 t s1', Step L1 s1 t s1' ->
forall s2, match_states s1 s2 ->
exists s2', Plus L2 s2 t s2' /\ match_states s1' s2'.

Lemma forward_simulation_plus: forward_simulation L1 L2.