Sometimes, in a math paper, we read something like "Although a priori this statement could be true, it is in fact false, as proven by this theorem". But aren't all mathematical statements a priori? So why include that misleading bit of language in the beginning?
In my experience as a mathematician, the mathematical usage of a priori corresponds more to the traditional definition of prima facie: it is applied for “conclusions we can draw fairly easily based on our current definitions/assumptions (together with previously acquired background knowledge)”, typically contrasted with “things that take some new non-trivial work to deduce”. A couple of examples:
Constructively this approach does not work, because it is not a priori evident that such a function exists. Once the mapping function is known to exist, it can easily be shown to be such a function.
— Foundations of Constructive Analysis, Errett Bishop, 1967
…we don't know how to embed H*SF(n+1) as a sub-algebra of an algebra which we know a priori is commutative (if n is odd)…
— The homology of iterated loop spaces, Peter May, 1976
This works if we can specify the degree a priori. If we cannot, or do not wish to, then it is more convenient to use binary forms.
— Combinatorics the Rota way, Kung, Rota, Yan, 2009
As the question points out, this does not quite match the accepted philosophical sense(s) of a priori. I strongly doubt this is due to any intentional distinction — rather, it’s just the usual divergence between colloquial and technical usages of a term.