Corollary backward_simulation_same_safe_behavior:
  forall L1 L2, backward_simulation L1 L2 ->
  (forall beh, program_behaves L1 beh -> not_wrong beh) ->
  (forall beh, program_behaves L2 beh -> program_behaves L1 beh).Remark atomic_finish: forall s t, output_trace t -> Star (atomic L) (t, s) t (E0, s).

Lemma atomic_forward_simulation: forward_simulation L (atomic L).