reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th65:
  for n being Ordinal holds divisors EmptyBag n = <* EmptyBag n *>
proof
  let n be Ordinal;
  consider S being non empty finite Subset of Bags n such that
A1: divisors EmptyBag n = SgmX(BagOrder n, S) and
A2: for p being bag of n holds p in S iff p divides EmptyBag n by Def15;
A3: S c= { EmptyBag n}
  proof
    let x be object;
    assume
A4: x in S;
    then reconsider b = x as bag of n;
    b divides EmptyBag n by A2,A4;
    then b = EmptyBag n;
    hence thesis by TARSKI:def 1;
  end;
A5: BagOrder n linearly_orders S by Lm4,ORDERS_1:38;
  EmptyBag n in S by A2;
  then { EmptyBag n } c= S by ZFMISC_1:31;
  then S = { EmptyBag n} by A3;
  then
A6: rng divisors EmptyBag n = {EmptyBag n} by A1,A5,Def2;
  len divisors EmptyBag n = card rng divisors EmptyBag n by Th18
    .= 1 by A6,CARD_1:30;
  hence thesis by A6,FINSEQ_1:39;
end;
