an odd ambiguity

We've mentioned how ambiguous "|" can be, but I don't remember seeing
anyone mentioning this example:
{ x   ∣ x  ∣ 10}
The set of all x such that x divides 10.

In one expression are both the low priority separator "such that" and the
medium priority relational operator "divides" (both are infix). There are
two characters that *could *be used: vertical bar (U+007C) and divides
(U+2223).  The Unicode Standard indicates that both should be U+2223 (I'm
not sure that equivalence is correct)

In TeX, there seems to be agreement that the first bar is be \mid.
However, there
seems to be disagreement for what to use for the second bar.
<https://tex.stackexchange.com/questions/498/mid-vertical-bar-vert-lvert-rvert-divides>
Some people suggest \mid, others "|", and still others \divides (which only
exists in the MnSymbol package AFAIK). There are spacing differences and
maybe height differences. Using different macros means there is a potential
semantic distinction if the author actually uses them as opposed to using
the ASCII "|". A reason TeX distinguishes them is that the spacing around
the vertical bar differs a little. Someone will surely correct me on this
if I'm wrong, but the spacing of these two uses is opposite their
contextual meaning. TeX considers \mid to be a relational operator, but
relational operators return boolean values -- \mid is really a
separator/punctuation. On the other hand, \divides really is a relation (m
divides n is either true or false), but it is spaced as a binary operator
(at least in this context). Typographically, this is what is supposed to
happen, but it seems counter-intuitive. Very strange.

What does this mean for MathML? One thing is that in practice, software
can't be sure the correct symbol is used in MathML (I leave it to someone
else to report what TeX, ASCIIMath, and WYSIWYG editors use). The other
issue is what the operator dictionary should say about the spacing and
priority for these two symbols. Currently they both have the same spacing
and priority, but that seems wrong.

Thoughts?

    Neil