Just for the sake of completion, the authoritative answer is here: "The proximity position of a member of a node-set with respect to an axis is defined to be the position of the node in the node-set ordered in document order if the axis is a forward axis and ordered in reverse document order if the axis is a reverse axis. The first position is 1."

Ah, okay. I didn't catch that you wanted "the nearest ancestor with a
particular name." In that case then I think you are golden. If there
is a chance that the element itself is a div1 element, then you will
want to use ancestor-or-self instead, but otherwise I think you have
it right.
​
Hopefully, I will never have to find the nearest div for a div in this collection, the objective was to locate the smallest container for an infringing non-container (ie, not a div) element. So I think I'm done here.

Thanks!
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entia non sunt multiplicanda praeter necessitatem