
theorem
  for L being complete antisymmetric non empty RelStr for a being
Element of L, X being set holds a = "\/"(X,L) iff a is_>=_than X & for b being
  Element of L st b is_>=_than X holds a <= b
proof
  let L be complete antisymmetric non empty RelStr;
  let a be Element of L, X be set;
  ex_sup_of X,L by Th17;
  hence thesis by Th30;
end;
