Proof using.
eauto using deduplicate_log'_app.
Qed.

(* Specifications: *)
Lemma in_output_trace_not_nil :
in_output_trace client id out [] -> False.
Lemma output_correct_monotonic :
forall c i o xs ys,
output_correct c i o xs ->
output_correct c i o (xs ++ ys).