reserve x for set;

theorem Th5:
  for L being antisymmetric reflexive with_infima with_suprema
  RelStr for a,b being Element of L holds a"/\"b = b iff a"\/"b = a
proof
  let L be antisymmetric reflexive with_infima with_suprema RelStr;
  let a,b be Element of L;
  thus a"/\"b = b implies a"\/"b = a
  proof
    assume a"/\"b = b;
    then b <= a by YELLOW_0:23;
    hence thesis by YELLOW_0:24;
  end;
  assume a"\/"b = a;
  then b <= a by YELLOW_0:22;
  hence thesis by YELLOW_0:25;
end;
