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 NoDup_get_op_output_keys_In_O : forall xs ys k, NoDup (get_op_output_keys (xs ++ O k :: ys)) -> In (O k) (xs ++ ys) -> False.