Proof using.
unfold no_output_at_backup_trace, no_output_at_backup.
simpl. intuition.
Qed.

(* Specifications: *)
Lemma NOABT_app :
forall A xs ys,
@no_output_at_backup_trace A xs ->
no_output_at_backup_trace ys ->
no_output_at_backup_trace (xs ++ ys).