theorem
  for V being add-associative right_zeroed
  right_complementable non empty addLoopStr, v,u being Element of V
  holds v + u - u = v
  proof
    let V be add-associative right_zeroed
    right_complementable non empty addLoopStr, v,u be Element of V;
    thus v + u - u = v + (u-u) by RLVECT_1:28
    .= v + 0.V by RLVECT_1:5
    .= v;
  end;
