End SIMULATION_PLUS.
(** Lock-step simulation: each transition in the first semantics corresponds to exactly one transition in the second semantics. *)
Section SIMULATION_STEP.
Hypothesis simulation:
forall s1 t s1', Step L1 s1 t s1' ->
forall s2, match_states s1 s2 ->
exists s2', Step L2 s2 t s2' /\ match_states s1' s2'.

Lemma forward_simulation_step: forward_simulation L1 L2.