In the following sentence (which I took from a random article): "A robust but puzzling fact about the way people trade, a fact known as the 'disposition effect'", I would like to know what grammatical rule dictates the the article should appear before the noun ("fact") referring to another noun previously mentioned. I know this is the correct usage, I just need the terminology in order to show someone else this is right. Thanks!
Just from looking at the extract, it's clear that you have cited the compound subject of a sentence, but no predicate:
'A robust but puzzling fact about the way people trade' + predicate [is ...]
[implied correlative conjunction 'and']
a fact known as the 'disposition effect' + predicate [is ...]
Now I don't know whether this has a specific grammatical name, but I think you'll find that the 'put 'a' first, then subsequently refer to the substantive using 'the'' rule works across two separate sentences or clauses.*
Rhetorically, in the context of the full sentence in which it appears, the second part is a parenthesis, a form of hyperbaton (a word, phrase, or sentence inserted as an aside in a sentence complete in itself) [Richard A Lanham, A Handlist of Rhetorical Terms, Berkeley & LA, CA, University of California Press, 1991, 2nd Ed, p 108]. Lanham cites the following synonyms for the device: insertour, interclusio, interjectio, interpositio, parathesis, paremptosis.
You could, rhetorically, again, make it into a series of three, or tricolon (with a twist), although the contrast implied by 'yet' doesn't support the treatment, here's an example:
There is a fact about the way people trade.
It is a robust fact, yet a puzzling fact, a fact known as the 'disposition effect'.
It is a fact I know nothing at all about.
*Incidentally, this works differently in titles of fables. The title introduces the fable as a whole. We first meet the characters at the start of the telling.
As an example, from one of my versified versions of Aesopic fables from 'Aesop the Storyteller, London: Aladdins Cave Publishing, 2008', which serves to illustrate both points discussed here:
The Fox and the Grapes
In a time beyond our time,
In a land beyond our land,
A brown fox,
A young fox,
A young, brown fox,
A naughty fox -
A fox who was used to getting what he wanted
And getting what he wanted exactly when he wanted it,
A fox who was used to taking what he wanted,
Whether others wanted him to or not
(Usually they didn't) - is sniffing the air.
This fox -
This young, brown fox -
This naughty fox -