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

theorem Th51:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
being Element of L holds (x` + ((y + x) + (y + z))`)` + (y + z) = (y + x) + (y
  + z)
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  (x` + ((y + x) + (y + z))`)` + (y + z) = (y + x)`` + (y + z) by Th50;
  hence thesis by Th23;
end;
