Open zwang123 opened 3 weeks ago
I fully agree with @zwang123's proposal. This would result in a clearer and more comprehensible structure. And it could help to shorten proofs, as indicated by the "editorial" in the comment of ~df-odu.
The definition of Toset and the related theorems could be moved into a new section 9.2.2 (the current section 9.2.2 Lattices becomes 9.2.3).
I agree. The new TOC could be:
9. Order theory
9.1. Dual of an order structure
9.2. Preordered sets
9.2. Directed sets
9.3. Partially ordered sets
9.4. Totally ordered sets
9.5. Lattices
9.5.1. Lattices
9.5.2. Distributive lattices
9.5.3. The distributive lattice of sets under inclusion
9.6. Posets, directed sets, and lattices as relations
(This treatment predates our systematic use of extensible structures;
TODO: see to what extent we keep it, merge it, update it to use the
extensible structures framework.)
Aftrer #4298 was merged, I had a look at the HTML pages. Here my remarks:
0.
and 1.
(currently in subsection 9.4 "Totally ordered sets (tosets)") should be moved to subsection 9.3 "Partially ordered sets (posets)".Finally, which proofs will benefit from the availability of ODual now? Are there already some applications? Since this was the original motivation for the new structure, (at least some) applications of it should be provided (maybe "the theorems proved for lub could potentially be reused by glb", as mentioned above), before this issue is closed.
An immediate benefit is to move the first few theorems in the old distributive lattice section to their right places, the lattice section. (Already done) A quick benefit is to enable moving my theorems to main because some of them depend on dual.
I suggest moving things from codu to odubas to the beginning of part 9 (potentially making it a new 9.1), and the remaining of “9.2.3 The dual of an ordered set” to (potentially the beginning of) their corresponding sections (poset/meet/join/glb/lub to the poset section; lat to lat section; clat to clat section)
The benefit is multiple (or even significant, tbh):
I confirmed that these theorems (codu to odubas) have no dependency on any theorems in part 9 so it should be safe to move.
P.S. The toset part worth a new section IMO especially after me moving some of TA's theorems to main.