[mmq]

I don't think that memorizing is the perfect approach to learn mathematical proofs. Generally, you should be able to try the proof based on your understanding of the concepts, and hence if you can't proof them, it only means that you didn't get the concept well. When I used to be in the CPGE [1], we had one exam after two years intensive courses of maths, physics philosophy and engineering sciences. And we had pretty much everything demonstrated. The only way we, other students and I, dealt with it is by understanding the concept very well, rereading the courses and going through problems. It's been 6 years now that I left CPGE, And I am still able to proof the Bolzano-weirstrass theorem, and I am sure that most of the other students could also.

[1]I don't know if you are familiar with the french educational system, and specifically the CPGE( classes préparatoires aux grandes écoles). It consists of two very intensive years of mathematics, physics, philosophy and engineering science.