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

theorem Th10:
  for L being upper-bounded antisymmetric with_infima non empty
  RelStr holds Top L is irreducible
proof
  let L be upper-bounded with_infima antisymmetric non empty RelStr;
  let x,y be Element of L;
  assume x "/\" y = Top L;
  then
A1: x >= Top L & y >= Top L by YELLOW_0:23;
  x <= Top L or y <= Top L by YELLOW_0:45;
  hence thesis by A1,ORDERS_2:2;
end;
