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

theorem Th55:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds x + (y + z) = z + (y + x)
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  (y + x) + (y + z) = z + (y + x) by Th53;
  hence thesis by Th53;
end;
