Proof using.
unfold good_op_move. intros.
destruct x as [k|k], y as [k'|k']; exists k, k'; intuition.
- right. right. intuition. subst. eauto.
- exfalso. eauto.
Qed.

Lemma acknowledged_op_I_cons_reduce :
forall k k' l,
acknowledged_op k (I k' :: l) ->
acknowledged_op k l.