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

theorem Th45:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y being
  Element of L holds (x + (x + y`)`)` = (x + y)`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y be Element of L;
  (x + ((x + y)` + x)`)` = (x + y)` by Th8;
  hence thesis by Th44;
end;
