Include proof in bsc thesis that I couldn't do fully myself I'm writing my BSc thesis in computer science right now, for which I'm implementing Fast Fourier Transforms. Now a really important paper on the topic is making a proof which I think I got what they are doing, but I probably could not replicate myself. Now I was wondering if there is a go-to way to cite the proof and especially use the result of the proof, without having to re-write it all by myself because going into all of the math would be beyond the scope of my thesis since it is more about the implementation, even so confirmed by my assistant. 
The way I would go about it is to describe how they proof what in words, with a citation to the paper, e.g. like that:

"In [xy], yz show that equation a can be solved by doing ..."

Any hints are appreciated.
I don't see an issue here for an undergraduate thesis. If the "important paper" is new and the work overlapped with your own, you should be able to get credit for your work independently of the other. If it is a classic paper that you should have known about, but didn't, then you may have a more serious issue and a reason to re-write. 

But citing the other work, just as in your example, seems right, including the main conclusions you draw from the paper. 

But the professor to whom you are responsible (maybe not just the assistant) is the best source for an answer to this question. 

If there is any serious issue raised by the professor, then you need, first, to think about what if anything is unique about your solution. It may be that a relatively minor re-write will do the trick if you just stress what is new/unique about it. 

I'd also suggest some perspective. The fact that, as an undergraduate, you can "follow" but not "replicate" the work in another paper may be good or bad depending on the other paper. We normally expect that students at this level are students and thus can't know or do everything. Even experts can struggle with some deep ideas and intricate proofs. 

I'll note that it would be a more serious issue for a doctoral dissertation. There is a fairly recent case, two people known to me, who had their doctorates delayed for a year because they each did a piece of nearly identical work without knowledge of the other. They didn't need to re-do any work, but it took a year for the (Computer Science) community to determine that this was just parallel work and no collusion nor plagiarism was involved. Sticky, but both are now highly regarded.