reserve a, b, n for Nat,
  r for Real,
  f for FinSequence of REAL;
reserve p for Prime;

theorem Th39:
  pfexp 1 = EmptyBag SetPrimes
proof
  set f = pfexp 1;
  for z being object st z in dom f holds f.z = 0
  proof
    let z be object;
    assume z in dom f;
    then reconsider z as Prime by Th33;
A1: z <> 1 by INT_2:def 4;
    f.z = z |-count 1 by Def8
      .= 0 by A1,Th21;
    hence thesis;
  end;
  then
A2:  f = (dom f) --> 0 by FUNCOP_1:11;
   dom f = SetPrimes by PARTFUN1:def 2;
  hence thesis by A2;
end;
