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

theorem Th53:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds (x + y) + (x + z) = y + (x + z)
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  set Y = x, X = y;
  X`` + (Y + z) = (Y + X) + (Y + z) by Th52;
  hence thesis by Th23;
end;
