It is not difficult to prove (see “Counter-examples about funcoids and reloids” in the book) that (where is the cofinite filter). But the result is counterintuitive: meet of two binary relations is not a binary relation.
After proving this I always felt that there is some “mystery” about meet of funcoids: It behaves in a weird way and what it is in general (not this one special counterexample case) is not known.
Today I noted a simple formula which decomposes : for every funcoids and and more generally for a set of funcoids. (It follows from that is an upper adjoint and that for every funcoid .) This way it looks much more clear and less counterintuitive.
So now it looks more clear, but I have not yet found particular implications of these formulas leading to interesting results.