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 Th64:
  for n being Ordinal, i being Nat, b, b1, b2 being bag of n st i
> 1 & i < len divisors b holds (divisors b)/.i <> EmptyBag n & (divisors b)/.i
  <> b
proof
  let n be Ordinal, i be Nat, b, b1, b2 be bag of n;
A1: 1 in dom divisors b & len divisors b in dom divisors b by FINSEQ_5:6;
A2: (divisors b)/.1 = EmptyBag n & (divisors b)/.len divisors b = b by Th63;
  assume
A3: i > 1 & i < len divisors b;
  then i in dom divisors b by FINSEQ_3:25;
  hence thesis by A2,A1,A3,PARTFUN2:10;
end;
