To Thierry: it [~df-chn] is what I need, indeed! Amazing coincidence.

I'd then

   - move your chain definition to main, somewhere between "5.7 Words over 
   a set" and "17.3.1 Walks" (in "GRAPH THEORY" part)
   so probably to a new section "9.7 Chains" (in "BASIC ORDER THEORY" part)
   *Note: there is something in your htmldef that makes it render "( < 
   Chain𝐴)" with a missing space* ;
   - move your chain theorems to main too;
   - remove ~cupword, ~df-upword which are my definitions for the same;
   - port those of my 'UpWord' (chain) theorems which are not obsolete, to 
   main;
   - add a few equality and subset theorems to that same section in main.

Is that a valid way to move forward?
Additionally, when proving subsequent theorems, would I place them in my 
mathbox or in that section?


To Matthew and to David: sounds reasonable! I'll probably stick to 
surrounding newly defined classes with parens if they need any arguments.


Best wishes,
Ender

четверг, 15 января 2026 г. в 20:15:36 UTC+3, Thierry Arnoux: 

> In the mean time I have proposed df-chn 
> <https://us.metamath.org/mpeuni/df-chn.html> in my Mathbox, which I 
> believe is exactly what you need: a chain in the sense of order theory 
> <https://en.wikipedia.org/wiki/Total_order#Chains>.
>
>
> If there was to be a rule, I'd say parentheses are used for classes, and 
> left away for wffs.
>
> For example: `( A + B )` (df-ov) is a class and has parentheses, while `A 
> < B` is a (df-br) is a wff and does not.
>
> Same for example for df-fv, df-dif, df-un, df-in (classes, parentheses), 
> and df-clel, df-ne, df-ss, df-po, (wff, no parentheses), etc.
>
> BR,
> _
> Thierry
>
>
> On 15/01/2026 17:27, Matthew House wrote:
>
> metamath-knife -g is pretty helpful for testing the grammar for 
> ambiguities. In this case, it has no complaints if I add $c AdjRelWord $. 
>  cadjrelword $a class AdjRelWord S R $. to set.mm, so it's presumably 
> fine. And as you mention, its syntax is analogous to cdc 
> <https://us.metamath.org/mpeuni/cdc.html> in any case.
>
> (Though conventionally, when I see "class functions" in main set.mm 
> taking multiple arguments, they're written with full ( , ) particles, 
> e.g., if ( ph , A , B ); Pred ( R , A , X ); frecs ( R , A , F ); wrecs ( 
> R , A , F ); rec ( F , I ); seqom ( F , I ); sup ( A , B , R ); inf ( A , 
> B , R ); and OrdIso ( R , A ). Odd ones include seq M ( .+ , F ) and seq_s 
> M ( .+ , F ).)
>
> On Thu, Jan 15, 2026 at 7:43 AM Ender Ting <[email protected]> wrote:
>
>> I'm considering to generalize my definition UpWord S (for strictly 
>> increasing words on alphabet S) to AdjRelWord S R (which would have R 
>> instead of hard-coded <, and so could be used on other partial orders).
>>
>> I do not quite get if I need to put parentheses like ( AdjRelWord S R ); 
>> the decimal constructor ~cdc has none, the sum syntax ~csu has nothing 
>> between its two classes too, while ~cpred wraps its arguments in 
>> parentheses. In theory, the classes should already be unambiguously 
>> decodable as a prefix code, but I am not certain.
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