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

theorem Th18:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y being
  Element of L holds (x` + (y + x)`)` = x
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y be Element of L;
  set X = (y + x)`;
  (X + ((x` + y)` + (x` + X)`)`)` = x by Th13;
  hence thesis by Th10;
end;
