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

theorem Th32:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y being
  Element of L holds (x + y)` + (y + y`)` = (x + y)`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y be Element of L;
  set X = (x + y)`, Y = y`;
  X + ((Y + X)` + Y)` = X by Th28;
  hence thesis by Th18;
end;
