minor typo: “notational conventions that have been already been introduced in the argument” (“been” is repeated.)

Another issue:

“Also, it may end up that you (or someone else) will eventually find a simpler proof of that lemma, thus reducing the net simplicity of the paper markedly” (Is the simplicity reduced or increased?)

*[Corrected, thanks – T.]*

If the techniques used to prove the proposition are orthogonal to the techniques used in the rest of the paper, it may disrupt the flow of the paper to prove the proposition too early; one may then just state the proposition when it is first appropriate to do so, say something like “We will prove this proposition in Section 17, using techniques from theory X. Let us assume this proposition for now and continue the proof of Theorem 1.1…”, and then return to the proof later (in Section 17, in this case).

]]>If you have a bunch of auxiliary lemmas needed only for the proof of a main lemma, is it better to state and prove the auxiliary lemmas within the proof of the main lemma, or is it better to state and prove them outside the lemma — perhaps in a separate section?

Your advice above would seem to say that within the proof of the main lemma is better. But would you still do this even if including the proofs of all the auxiliary lemmas would stretch the proof of the main lemma to several pages? It’s also important to keep the proof of each lemma short, too, right (so the reader can keep it in his/her mind)? Thanks.

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