Letterman asked about the critics who say Armstrong is a cheater and said, "They will say, 'Oh, he's doing well four years later because he's using some mysterious chemical.' Are you prepared for that?"
Armstrong replied, "Oh, yeah, very. That's been a big part of my life. I've dealt with it for the last decade."
Armstrong then added that he can "prove" that he's clean.
I don't think he's ever going to have the "proof" to convince everyone that he's clean, but he wants to convince as many people as he can.