
theorem Th5:
  for S being non empty antisymmetric RelStr st ex_inf_of {},S
  holds S is upper-bounded
proof
  let S be non empty antisymmetric RelStr;
  assume
A1: ex_inf_of {},S;
  take Top S;
  let x be Element of S;
  {} is_>=_than x;
  hence thesis by A1,YELLOW_0:31;
end;
