reserve a,b for object, I,J for set;

theorem Th21:
  Sum (<*>Bags I) = EmptyBag I
  proof set f = <*>Bags I;
    consider F being Function of NAT, Bags I such that
A1: Sum f = F.len f and
A2: F.0 = EmptyBag I and
    for i being Nat
    for b being bag of I
    st i < len f & b = f.(i + 1)
    holds F.(i + 1) = F.i + b by SUM;
    thus thesis by A1,A2;
  end;
