How do you prove you're real?

[Minyatur]

I disagree with a notion that an illusion can believe it is real, an awareness can believe it is something within illusion and define wrongly what it is.

Exactly.  The experiencer cannot be the experience.  The creator is the backdrop of the created.  Awareness is the creator.

Or like it is described in quantum mechanics, the observer that makes reality remain coherent. Each of us is an observer, but ultimately we all are the very same Observer.

I tend to call the OIC, the One Infinite Dreamer because of this notion. We are not fake, we are dreaming of our reality.