Proof using.
unfold no_output_at_backup_trace, no_output_at_backup.
simpl. intuition. subst. simpl in *. discriminate.
Qed.

Theorem pbj_NOABT :
forall net tr,
step_async_star (params:=PB_multi_params) step_async_init net tr ->
no_output_at_backup_trace tr.