reserve L for satisfying_DN_1 non empty ComplLLattStr;
reserve x, y, z for Element of L;

theorem Th14:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y being
  Element of L holds (x + y)` = (y + x)`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y be Element of L;
  set Z = y, X = x, Y = (y + x)`;
  ((Y + Z)` + (Z + X)`)` = y by Th7;
  hence thesis by Th12;
end;
