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

(* Specifications: *)
Lemma NOABT_singleton_inl :
forall A h r,
@no_output_at_backup_trace A [(h, inl r)].