Before revision:  Specifically,  the rate-function attained by D-SSG for any fixed integer threshold b>0 , is no smaller than the maximum achievable rate-function by any scheduling policy for threshold b-1.
After revision:  Specifically, we show that the rate-function attained by D-SSG for any fixed integer threshold b>0 , is no smaller than the maximum achievable rate-function by any scheduling policy for threshold b-1.