Definition good_op_move (x y : op) : Prop :=
    (forall k k', ~ (x = O k /\ y = I k')) /\
    (forall k, ~ (x = I k /\ y = O k)).

Lemma op_equiv_ack_op_lr : forall xs ys, op_equivalent xs ys -> forall k, acknowledged_op k xs -> acknowledged_op k ys.