While my question topic is that of mathematical writing of papers, which is a broad subject, the particular question is specific.
I am writing a paper, in which we have a section called "Outline of Proof". (It's Section 2.) The outline is fairly informal, and we omit some technical details, making approximations. Among these approximations, should we state (and label) important definitions and results (lemmas, equations, etc), with the intent of, later in the paper, referencing thes?
This raises the point of redundencies: some people don't like things being stated twice precisely (including in the outline), so wouldn't want anything explained/stated (even in the outline) re-explained/stated.
This seems ill-advised to me. When I read a paper, I rarely carefully read the outline: I just read it, and try to get an overview (or 'outline') of the proof; if there are parts that I don't really understand, I don't get hung up on them, trusting that with the more rigorous explanation later I'll be able to make sense of what the authors are saying.
So my question is this:
(a) is it standard to read an outline of a proof carefully?
(b) is it standard (or at least not discouraged) to state in the outline precisely important, even key, results/definitions that will be referred back to in the main body of the paper when giving proofs?