Intersecting families in (l[m]) ∨ (k[n])

Let m, n, l and k be positive integers with l not equal k, n > 2k, m < 2l and n = max{m, n} >= l + k. If F is an intersecting family in (([m])(l)) boolean OR (([n])(k)), then vertical bar F vertical bar <= max{((m)(l)), ((m - 1)(l -1)) + ((n - 1)(k - 1))}. Unless n = l + k >= m, equality holds if and only if ((m-1)(l)) >= ((n - 1)(k - 1)) and F = (([m])(l)) or ((m-1)(l)) <= ((n - 1)(k - 1)) and F consists of all members of (([m])(l)) boolean OR (([n])(k)) that contain a fixed element of [m] boolean AND [n].