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
  f(#)(c1-c2) = f(#)c1 - f(#)c2
  proof
    thus f(#)(c1-c2) = f(#)c1 + f(#)-c2 by Th2
    .= f(#)c1 - f(#)c2 by VALUED_2:24;
  end;
