reserve x,y for object, X for set;

theorem Th15:
  for p,q be bag of SetPrimes st p is prime-factorization-like &q
  is prime-factorization-like& Product p = Product q holds p=q
proof
  let p,q be bag of SetPrimes;
  assume that
A1: p is prime-factorization-like and
A2: q is prime-factorization-like and
A3: Product p = Product q;
  reconsider n=Product p as Element of NAT;
  n <=2|^n by NEWTON:86;
  hence thesis by A1,A2,A3,Lm11;
end;
