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

theorem Th42:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds x + ((y + x`) + z)` = x
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  (((y + x`) + z)` + x)`` = x by Th41;
  hence thesis by Th25;
end;
