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

theorem
  for L being lower-bounded antisymmetric non empty RelStr holds Bottom
  L is co-prime
proof
  let L be lower-bounded antisymmetric non empty RelStr;
  Top (L~) is prime by Th20;
  hence (Bottom L)~ is prime by YELLOW_7:33;
end;
