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 subseq_get_op_output_keys : forall xs ys, subseq xs ys -> subseq (get_op_output_keys xs) (get_op_output_keys ys).