
theorem Th3:
  for X being set, S being finite Subset of X, n being Element of
  NAT, i being object st not i in S holds (S, n)-bag.i = 0
proof
  let X be set, S be finite Subset of X, n be Element of NAT,
      i be object such that
A1: not i in S;
  dom (S --> n) = S by FUNCOP_1:13;
  hence (S, n)-bag.i = (EmptyBag X).i by A1,FUNCT_4:11
    .= 0 by PBOOLE:5;
end;
