In the paper 'Double Thompson Sampling for Dueling Bandits', the authors claim that the proof for their Lemma 1. ('Under D-TS, for an arbitrary constant \epsilon > 0 and one pair (i, j) with pji < 1/2, ......',) could be even simpler than another paper because under D-TS, arm j with pji < 1/2 is competing with arm i with pii = 1/2, which is known and fixed. You've read that another paper before. Provide the full name of that paper.