End FACTOR_BACKWARD_SIMULATION.

(* Specifications: *)
Theorem factor_backward_simulation:
forall L1 L2,
backward_simulation L1 L2 -> single_events L1 -> well_behaved_traces L2 ->
backward_simulation L1 (atomic L2).
Lemma atomic_initial: forall L s,
initial_state L s ->  initial_state (atomic L) (E0, s).
Theorem factor_backward_simulation:
forall L1 L2,
backward_simulation L1 L2 -> single_events L1 -> well_behaved_traces L2 ->
backward_simulation L1 (atomic L2).