
theorem Th4:
  for X being set, S being finite Subset of X, n being Element of
  NAT, i being set st i in S holds (S, n)-bag.i = n
proof
  let X be set, S be finite Subset of X, n be Element of NAT, i be set such
  that
A1: i in S;
  dom (S --> n) = S by FUNCOP_1:13;
  hence (S, n)-bag.i = (S --> n).i by A1,FUNCT_4:13
    .= n by A1,FUNCOP_1:7;
end;
