reserve
  x for object, X for set,
  i, n, m for Nat,
  r, s for Real,
  c, c1, c2, d for Complex,
  f, g for complex-valued Function,
  g1 for n-element complex-valued FinSequence,
  f1 for n-element real-valued FinSequence,
  T for non empty TopSpace,
  p for Element of TOP-REAL n;

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;
