Proof using.
intros.
rewrite get_op_output_keys_app in *.
rewrite get_op_output_keys_defn in *.
do_in_app.
intuition; eapply NoDup_remove_2; eauto using get_op_output_keys_complete, in_or_app.
Qed.

Lemma NoDup_get_op_output_keys_In_2_3 :
forall xs ys zs k,
NoDup (get_op_output_keys (xs ++ I k :: ys ++ O k :: zs)) ->
In (O k) (xs ++ ys ++ zs) ->
False.