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_IR_output_keys_complete_U : forall xs k, In (IRU k) xs -> In k (get_IR_output_keys xs).