reserve x,y,Y,Z for set,
  L for LATTICE,
  l for Element of L;

theorem
  for L be lower-bounded continuous LATTICE, x be Element of L holds (
  wayabove x) is Open
proof
  let L be lower-bounded continuous LATTICE, x be Element of L;
  for l be Element of L st l in (wayabove x) ex y be Element of L st y in
  (wayabove x) & y << l
  proof
    let l be Element of L;
    assume l in (wayabove x);
    then x << l by WAYBEL_3:8;
    then consider y be Element of L such that
A1: x << y & y << l by WAYBEL_4:52;
    take y;
    thus thesis by A1,WAYBEL_3:8;
  end;
  hence thesis;
end;
