reserve x,y for object, X for set;

theorem
  for p be bag of SetPrimes, n be non zero Nat st p is
  prime-factorization-like & n = Product p holds (ppf n) = p
proof
  let p be bag of SetPrimes, n be non zero Nat;
  assume that
A1: p is prime-factorization-like and
A2: n=Product p;
  Product ppf n = Product p by A2,NAT_3:61;
  hence thesis by A1,Th15;
end;
