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 no_Ik_in_first2 : forall xs ys zs k, NoDup (get_op_input_keys (xs ++ I k :: ys ++ O k :: zs)) -> forall k', In (I k') (xs ++ ys) -> k <> k'.