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I have a theorem that I want to break down into a theorem and a corollary to make my paper more readable. Can I use objects, e.g. a complicated set, that is introduced in the proof of the theorem in the proof of the corollary, or is this considered bad style? Alternatively, do I have to give a detailed definition of every concept I want to use in the corollary?

My thought is that a corollary and its theorem are understood to be closely related. Therefore, most readers of the proof of the corollary would also have read the proof of the main theorem first, so for the reader this would not present a problem.

user98563
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1 Answers1

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No, it is not considered bad style. A suggestion, though: if your complicated set is called, say, $S$, then, when you mention again the set $S$ in the context of the corollary, don't forget to write something like “where $S$ is the set that was defined within the proof of the previous theorem”.

José Carlos Santos
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