A Missing Proofs

For adversary's strategy defined in This is the desired result in the lemma. Rearranging the above inequality will yield us desired result. On the other hand, we can also upper bound the above conditional mutual information. Putting together the pieces yields our result. We first prove the result for point error, the result of function error can be achieved by a Jensen's inequality (please see the end of the proof). Convexity is maintained by the maximum operator over two convex functions.