 reserve n,i for Nat;
 reserve p for Prime;

theorem Matsu0:
  for f being bag of SetPrimes
    ex g being FinSequence of NAT st
    Product f = Product g & g = f*canFS(support f)
  proof
    let f be bag of SetPrimes;
    consider g being FinSequence of COMPLEX such that
A2: Product f = Product g & g = f*canFS(support f) by NAT_3:def 5;
    rng g c= NAT by A2,VALUED_0:def 6; then
    g is FinSequence of NAT by FINSEQ_1:def 4;
    hence thesis by A2;
end;
