I'm afraid it's just practice. Lots and lots of solving problems until the definitions, methods, and techniques are burned into your mind. Once you have the ba

I'm afraid it's just practice. Lots and lots of solving problems until the definitions, methods, and techniques are burned into your mind. Once you have the background knowledge, everything is a lot simpler. Learn whether each theorem has an easy proof or a hard proof. If it has an easy proof, you can forget it (deriving it when you need to; an example is the contraction mapping theorem [1]). If it has a hard proof, you can forget it and look it up when you need to. [1]: https://www.patrickstevens.co.uk/how-to-discover-the-contraction-mapping-theorem/ https://www.patrickstevens.co.uk/how-to-discover-the-contrac...