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 good_op_move_good_move_IO : forall k k', good_op_move (I k) (O k') -> good_move (IRI k) (IRO k').