 reserve n,k for Nat;
 reserve L for comRing;
 reserve R for domRing;
 reserve x0 for positive Real;

theorem
  for f be Element of the carrier of Polynom-Ring F_Rat holds
    Product denomi-seq(f) is non zero
   proof
     let f be Element of the carrier of Polynom-Ring F_Rat;
     reconsider denomf = denomi-seq(f) as real-valued FinSequence;
A1:  for n being Nat st n in dom denomf holds denomf.n > 0
     proof
       let n be Nat;
       assume n in dom denomf; then
       (denomi-seq(f)).n in NAT & (denomi-seq(f)).n <> 0 by Lm10;
       hence thesis;
     end;
     reconsider denomf as positive-yielding real-valued FinSequence
       by A1,RVSUM_3:def 1;
     Product denomf is non zero;
     hence thesis;
   end;
