reserve L for Lattice,
  p,q,r for Element of L,
  p9,q9,r9 for Element of L.:,
  x, y for set;

theorem
  p"/\"q = p.:"\/"q.: & p"\/"q = p.:"/\"q.: & p9"/\"q9 = .:p9"\/".: q9 &
  p9"\/"q9 = .:p9 "/\".:q9;
