A Proof of Theorem 3.1

In this section, we prove Theorem 3.1, which says that it suffices to the augmented state space First, we have the following lemma. Lemma A.2. W e have D Now, we prove Theorem 3.1. By Lemma A.2, we have F Theorem 3.1 follows straightforwardly from this result. Consider the same setup as in Lemma B.1. Lemma B.1, we have F Consider the same setup as in Lemma B.1.