Often times, when we dream of something that's "going to happen" or do dream of something that later comes true. We dream these things, because we have thought about them previously, and there is always a chance they may appear in your dream, diving further, and becoming a symbolic message.
For example, if you heard yesterday or even a few days ago that your friend's dog was sick, and you dreamed about him dieing...and he did die the following day, well there isn't much to it but your subconscious bringing out the worst possibility.
Also Nys, you say you remember your dreams, but you are aware that people experience multiple dreams throughout the night and generally come to remember only one right?
I do remember having a dream about an econ class the semester before I took it....When that class happened, I got the déja vu and could tell what my professor was going to say next.
How exactly would they prove premonition dreams to be false, anyway?
It's already been proven that everyone dreams. There's also been a general consensus that events making you feel a deja vu or "woah I saw this coming" vibe are courtesy of your subconscious gathering lil bits here and there from your life and answering the question in your dreams. When it happens in real life, you get that deja vu feeling. Basically, you thought it up in your dreams, but you don't remember it until it happens in real life.
Also, unless you believe in ESP and psychic powers...then dreams predicting the future is utterly false. If you do believe in that stuff, then I can't argue with that unless you change your mind.