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

theorem Th3:
  for L being satisfying_DN_1 non empty ComplLLattStr, x being
  Element of L holds ((x + x`)` + x)` = x`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x be Element of L;
  set y = the Element of L;
  set V = (x + y)`;
  ((x + x`)` + (((x`` + y)` + x)` + (x`` + (x` + V)`)`)`)` = x` by Th1;
  hence thesis by Def1;
end;
