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

theorem Th12:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds (x + ((y + z)` + (z + x)`)`)` = (z + x)`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  set Y = z, Z = ((y + x)` + (y + z)`)`;
  (x + ((Y + Z)` + (Y + x)`)`)` = (Y + x)` by Th10;
  hence thesis by Th10;
end;
