
theorem
  for L being antisymmetric reflexive with_suprema RelStr for a,b being
  Element of L holds a = a"\/"b iff a >= b
proof
  let L be antisymmetric reflexive with_suprema RelStr;
  let a,b be Element of L;
  a <= a & for d being Element of L st d >= a & d >= b holds a <= d;
  hence thesis by Th22;
end;
