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

theorem Th31:
  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`)`;
  X + ((y + X)` + y)` = X by Th28;
  hence thesis by Th20;
end;
