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

theorem Th9:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds (((x + y)` + z)` + (x + z)`)` = z
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  set X = (x + y)`, Y = z, Z = ((x + y)` + x)`;
  ((X + Y)` + ((Z + X)` + Y)`)` = Y by Th5;
  hence thesis by Th7;
end;
