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

theorem Th20:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y being
  Element of L holds (x + (y + x`)`)` = x`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y be Element of L;
  set Z = x`, X = y, Y = x;
  (((X + Y)` + Z)` + (X + Z)`)` = Z by Th9;
  hence thesis by Th19;
end;
