When one cites a theorem from a source in mathematics, the following problem usually arises: some assumptions/conditions of the theorem are written much earlier in the source, which do not appear in the statement of the theorem.
What are good strategies to solve this problem so that the writing could be more reader-friendly?
On the one hand, citing the theorem simply as "By theorem 3.1.4 in [Fang 2013] ..." means the reader may miss some of the conditions of theorem 3.1.4 if they appear earlier in the source.
On the other hand, yes, restating all the conditions of the theorem is considerably the "best" way. But if one has to cite a lot of hard theorems in a proof, restating everything may distract readers from the main issues.
Let me construct an example: if a chapter in a commutative ring theory book begins with "All rings in this chapter will be Noetherian", any theorem containing the word "ring" in this chapter would not include the word "Noetherian". If I cited one theorem in this chapter merely by its "number", a reader may be easily misguided if he/she directly read the theorem without reading the first sentence of this chapter.