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 Th66:
  for n being Ordinal, i being Element of NAT, b being bag of n st
i in dom decomp b ex b1, b2 being bag of n st (decomp b)/.i = <*b1, b2*> & b =
  b1+b2
proof
  let n be Ordinal, i be Element of NAT, b be bag of n;
  reconsider p = (divisors b)/.i as bag of n;
  assume
A1: i in dom decomp b;
  take p, b-'p;
  thus (decomp b)/.i = <*p,b-'p*> by A1,Def16;
  i in dom divisors b by A1,Def16;
  hence thesis by Th46,Th62;
end;
