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 O_IRO_preserved_IU : forall xs ys k' ir, (forall k, In (O k) (xs ++ I k' :: ys) -> In (IRO k) (IRI k' :: IRU k' :: ir)) -> forall k, In (O k) (xs ++ ys) -> In (IRO k) ir.