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

theorem Th15:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds (((x + y)` + (y + z)`)` + z)` = (y + z)`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  set Y = ((x + y)` + (y + z)`)`;
  (z + Y)` = (Y + z)` by Th14;
  hence thesis by Th12;
end;
