This was cool, thanks!
I always had no idea what to do, as I never really learned proofs. "Prove that x = y" My first thought was always "wtf does that mean, I can't PROVE it, it just will" and then I'd move terms around or whatever until x = y. (This is first year general math stuff).
Only problem i have with this (in general) is the law of excluded middles, which I'm not really a fan of.
http://en.wikipedia.org/wiki/Intuitionism