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_AAOF_IR_equiv : forall xs ys, op_equivalent xs ys -> forall l, IR_equivalent (acknowledge_all_ops_func xs l) (acknowledge_all_ops_func ys l).