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

theorem Th52:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds x`` + (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))` = x` by Th43;
  hence thesis by Th51;
end;
