An inequality for generalized quadrangles

Let $\mathcal{S}$ be a generalized quadrangle of order (s, t). Let X and Y be disjoint sets of pairwise noncollinear points of $\mathcal{S}$ such that each point of X is collinear with each point of Y. If $m = \vert X\vert$ and $n = \vert Y\vert$, then $(m - 1)(n - 1) \leqslant {s^2}$ . When equality holds, severe restrictions are placed on m, n, s, and t.