Proof using.
unfold in_output_trace.
intuition.
break_exists. simpl in *. intuition.
find_inversion. auto.
Qed.

Lemma in_output_list_app_or :
forall c i o l1 l2,
in_output_list c i o (l1 ++ l2) ->
in_output_list c i o l1 \/
in_output_list c i o l2.