fix: disambiguate duplicate Verso labels in Section 5.4

[Chessing234]

proposition 5.4.4 alone had seven declarations sharing one docstring label, so the rendered book repeats the same heading seven times in a row.

lettered the clusters the text leaves unlettered (examples 5.4.2, proposition 5.4.4) and added a short descriptor where the text already supplies a letter (definitions 5.4.1 / 5.4.5 / 5.4.6, proposition 5.4.7(a) and (e)).

comment-only, no statements or proofs touched.

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Generated by Claude Code

[teorth]

Almost all of this is good — the descriptive qualifiers on Definition 5.4.1 (positive)/(negative), Definition 5.4.5 (positive case)/…, Definition 5.4.6, and the sub-qualifiers on Proposition 5.4.7(a)/(e) are exactly the right technique, and I would take those as-is.

The one hunk to change is Proposition 5.4.4, which this labels (a) through (g). In the text those letters are already taken, and they mean something different (ch5.tex):

Proposition [Basic properties of positive reals]. For every real number x, exactly one of the following three statements is true: (a)x is zero; (b)x is positive; (c)x is negative. A real number x is negative if and only if -x is positive. If x and y are positive, then so are x+y and xy.

So (a)/(b)/(c) label the three alternatives of the trichotomy, not three separate results — and there is no (d)–(g) at all. Under this PR, Real.not_zero_pos : ¬(x = 0 ∧ x.IsPos) becomes "Proposition 5.4.4(b)", but a reader who looks that up finds "(b) x is positive".

Descriptive qualifiers of the kind you already use elsewhere in this very PR would fit well, e.g.

Proposition 5.4.4 (trichotomy, at least one) / Exercise 5.4.1 -- Real.trichotomous
Proposition 5.4.4 (trichotomy, zero/positive exclusive) -- Real.not_zero_pos
Proposition 5.4.4 (trichotomy, zero/negative exclusive) -- Real.not_zero_neg
Proposition 5.4.4 (trichotomy, positive/negative exclusive) -- Real.not_pos_neg
Proposition 5.4.4 (negation) -- Real.neg_iff_pos_of_neg
Proposition 5.4.4 (sum) -- Real.pos_add
Proposition 5.4.4 (product) -- Real.pos_mul

Any equivalent wording is fine — the point is just not to reuse (a)/(b)/(c) for a different decomposition.

Worth flagging that #616 has the same issue elsewhere in this file: it labels Exercise 5.4.9 (a)–(f), where the text gives that exercise parts (i)–(iv) (it is one of the few exercises Tao numbers with romans). If you are touching Section_5_4.lean anyway, folding that correction in here would be welcome.

For reference, #639 is the model — it keeps the book’s real letters for Proposition 4.3.3(a)/(c)/(d)/(e)/(g) and adds descriptive qualifiers only to separate declarations sharing a letter. I merged that one, along with 14 others today.

[Chessing234]

done — prop 5.4.4 now uses the descriptive trichotomy/negation/sum/product labels, and 5.4.9 is (i)–(iv) with descriptors so it matches the book's roman parts. examples 5.4.2 got the same treatment (the text doesn't number those either).