Including proofs of known theorems in master's thesis I am currently writing my master's thesis in computer science. In my topic, I had a lot of papers to read and my main result relies also heavily on some theorems from especially one paper.

In the common literature there are some standard theorems for which the proofs are usually omitted bescause it is common knowledge or radically shortened as in "an easy application of the KKT theorem" and the authors do not want to waste any space for that.

In a master's thesis, however, I would assume that it is good practice to write down those proofs more extensively, since it also shows that you really understand your topic in-depth.

My question is: Would you agree on that and would a citation as in

Proposition 3.14 (see [5]). A nice theorem.
Proof. My extended proof.

be sufficient?

I checked out When should one include the proof of known results in a mathematical PhD thesis? already where the answers suggest that my intuition is right here (for a PhD thesis). My thesis advisor also agrees (which is probably most important), however, I am unsure to what degree this is appropriate.
It would be a good idea to make it slightly more conspicuous that the theorem (and proof) are not original, e.g.:


  The following theorem is due to [5]; for the clarity of our exposition we give a more detailed version of the succinct proof in [5].


This leaves no doubt in the reader's mind that the work is not original, and also explains why you chose to include the proof.