 reserve R for domRing;
 reserve p for odd prime Nat, m for positive Nat;
 reserve g for non zero Polynomial of INT.Ring;
 reserve f for Element of the carrier of Polynom-Ring INT.Ring;
 reserve z0 for non zero Element of F_Real;

theorem Th46:  :: F_Rat version of LIOUVIL2:19
  for f being INT -valued Polynomial of F_Rat holds
  f is Polynomial of INT.Ring
  proof
    let f be INT -valued Polynomial of F_Rat;
    rng f c= INT; then
    reconsider f1 = f as sequence of INT.Ring by FUNCT_2:6;
    0.F_Rat = 0 by GAUSSINT:def 14; then
    f1 is finite-Support by ALGSEQ_1:def 1;
    hence thesis;
  end;
