[Om] Multistep "equation" symbol?

[Professor James Davenport]

On Mon, May 11, 2009 6:38 pm, Bruce Miller wrote:
> Lars Hellström wrote:
>> Is there an established OM symbol for "multistep equations" (see
>> example below)? If not, would it make sense as part of some official
>> content dictionary?
>
> When I've asked such questions in the past,
> I generally got James' (essentially correct) response,
> that it is equivalent to a conjunction of relations.
Thanks fro the compliment.
> I shared your concern that such a multi-something
> is easily converted to the conjunction form, but
There is a legitimate concern here. But I think if one is really handling
such a beast, one wants the ability to mix, e.g. a < b <= c < d.
I also like the abilito to annotate that Lars is asking for.
> less reliably converted back.  Perhaps <OMR> would be
> useful here?
agreed.
>
> As James points out, your case seems to
> be sort of a proof, or derivation. Each
> rhs follows from, can be derived from, is implied
> by, is the asymptotic expansion of, ...
> it's associated rhs.  The set of
> relation(-like) operators, and their sensible
> sequences is tricky, and in general there isn't
> a trivial transitivity.
>
> The same notation is used as, eg. a < b = c <= d << e,
> where there is (seemingly) less hidden semantic,
> just a shorthand.
>
> I suspect there are cases where there other
> hidden semantics.
>
> My main point being, if one _were_ to define
> such a symbol, it would seem that more than one
> "Multi<something>" would be called for.
I suspect, rather, one multi-purpose "reasoning chain" object: the example
above could be recast in terms of \subset, or \subgroup or ...

James Davenport
Visiting Full Professor, University of Waterloo
Otherwise:
Hebron & Medlock Professor of Information Technology and
Chairman, Powerful Computing WP, University of Bath
OpenMath Content Dictionary Editor and Programme Chair, OpenMath 2009
IMU Committee on Electronic Information and Communication