How to Reference a Long Breakdown of a Mathematical Model from Another Thesis?
It sounds to me like your thesis just got about 15% shorter.  

Rather than developing the material yourself, you need to instead put a review of the key results of the prior work as they relate to the rest of your thesis.  Presumably you needed to do this analysis because you were going to put its results to use elsewhere.  Well, you no longer need to do the analysis.  Instead, you can cite the other paper and explicitly say that you're going to review the key results that your work builds upon, e.g.,


  A detailed analysis of the X algorithm has already been conducted in [cite].  Further parts of this thesis build upon some of the results of that analysis, which we summarize here for the convenience of the reader.


Then you put in your paraphrased summary of the results you will use and the important intuitions with respect to the rest of your work.  You almost certainly do not need a reader to be familiar with every detail of the other proofs.  Likely some of their lemmas/sub-results don't need to be stated and there may be side-results / corollaries that are irrelevant to your use of the materials as well.  As such, your summary should be able to be much more terse than the original, and can be completely in your own words.  Renumbering and re-organizing material is OK as well.  You also don't need to put citations in everywhere continuously: as long as you write the prose in your own words and make it clear up front that everything in that collection of material is a summary of the material you are citing, the attribution should be quite clear to a reader.