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_input_keys_In_I : forall xs ys k, NoDup (get_op_input_keys (xs ++ I k :: ys)) -> In (I k) (xs ++ ys) -> False.