Is there a way to prove that winner has hid the game in his library?

Try to use his SteamDB page. If he had play time in the game, it will be recorded there. Also, if the game has achievements and he unlocked any, those are permanently saved as well.

Since you can see the history of a profile on steamrep, I assume that you can see the games he previously owned that way.
EDIT: Nevermind, you can't. :P

Maybe family sharing, I'm sharing with 2. But this is most often broken, their games keep disappearing (Achievements, playtime etc. also count for shared games.)

Maybe they\ve bought it, realized that they've won it and refunded the game.