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 get_op_input_keys_app : forall xs ys, get_op_input_keys (xs ++ ys) = get_op_input_keys xs ++ get_op_input_keys ys.