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

theorem Th17:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y being
  Element of L holds (((x + y)` + x)` + y)` = (y + y)`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y be Element of L;
  set X = (x + y)`;
  (X + ((X + x)` + y)`)` = y by Th5;
  hence thesis by Th16;
end;
