
theorem Th22:
  for L being antisymmetric with_suprema RelStr for a,b,c being
Element of L holds c = a"\/"b iff c >= a & c >= b & for d being Element of L st
  d >= a & d >= b holds c <= d
proof
  let A be antisymmetric with_suprema RelStr;
  let a,b be Element of A;
  ex x being Element of A st a <= x & b <= x & for c being Element of A st
  a <= c & b <= c holds x <= c by LATTICE3:def 10;
  hence thesis by LATTICE3:def 13;
end;
