Show that the best response correspondence B(a) = B1(a-1) B2(a-2) ... Bn (a-n) of a supermodular

Question:

Show that the best response correspondence B(a) = B1(a-1) × B2(a-2) ×...× Bn (a-n)
of a supermodular game satisfies the conditions of Zhou's theorem (corollary 2.4.2). Therefore the set of Nash equilibria of a supermodular game is a complete lattice.