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.
However, among these approximations, my co-author wants to state (and label) *important* definitions and results (lemmas, equations, etc). He then wants to, later in the paper when we are doing the corresponding part carefully and rigorously, refer back to these (say, "by equation (2.4)", or "by Lemma 2.2"). Moreover, he is very against redundancies, so does not like things being stated twice precisely (including in the outline) -- once precisely in the text and once approximately in the outline is fine.

This seems ill-advised to me. When I read a paper, I never 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.
*However*, I'm a pretty junior author -- 2nd year of PhD -- while he is a postdoc, who has collaborated with lots of top people; he is a lot more experienced than me.

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 outlineprecisely important, even key, results/definitions that will be referred back to in the main body of the paper when giving proofs?

Just as some extra comments... I'm not here to try to get people to tell me that I'm right and my co-author is wrong! I'm here to learn :-) please have no qualms about giving criticism! (assume that it's constructive, of course)