Would you really want to prove it? What would that accomplish?
You're probably going to be depressed either way: either your parallel life is worse or your parallel life is better. If it's worse then you have to witness it and (I assume) can't do anything about it. If it's better then it's not really you that gets to enjoy it, and is nothing more than an existential cocktease.
I guess if you're really lucky parallel-universe-you might have invented something world-changing and you figure out how it works and bring that information back to your universe. But if it's anything like most of my dreams it's mostly just uncanny anxiety-inducing quasi-nightmares.