Proof using.
unfold no_output_at_backup_trace, no_output_at_backup.
simpl. intros. intuition. subst. simpl in *. find_inversion. auto.
Qed.

(* Specifications: *)
Lemma NOABT_singleton_inr_read_response :
forall A h d,
@no_output_at_backup_trace A [(h, inr [ReadResponse d])].
Lemma NOABT_singleton_primary :
forall A out,
no_output_at_backup_trace [(Primary, @inr A _ out)].