There is no proof for deep sleep in your direct experience.
Now you might disagree and say something like: "I videotaped myself sleeping and watching it now, see, there's the proof! I even recorded the brainwaves indicating the deep sleep phases, another proof!"
But this is no proof. There is just the watching of a video tape right now and the interpretation of some brain wave records right now.
So, ultimately: There is no proof for deep sleep in your direct experience.