
theorem Th6:
  for S being non empty antisymmetric RelStr st ex_sup_of {},S
  holds S is lower-bounded
proof
  let S be non empty antisymmetric RelStr;
  assume
A1: ex_sup_of {},S;
  take Bottom S;
  let x be Element of S;
  {} is_<=_than x;
  hence thesis by A1,YELLOW_0:30;
end;
