 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;

theorem Th35:
  for x be Element of F_Real holds
    (Eval(~(^ f_0(m,p)))).x
    = eval(~(^Product((x.(m,p)))),x) * eval(~(^((tau(0))|^(p-'1))),x)
    proof
      let x be Element of F_Real;
      set Pxmp = Product((x.(m,p)));
      set tp1 = (tau(0))|^(p-'1);
      ~^(f_0(m,p)) = ~^(Pxmp*tp1) by GROUP_4:6
      .= ~(^Pxmp * (^tp1)) by E_TRANS1:27
      .= ~(^Pxmp) *' ~(^tp1) by POLYNOM3:def 10; then
      (Eval(~(^ f_0(m,p)))).x
      = eval(~(^Pxmp) *' ~(^tp1), x) by POLYNOM5:def 13;
      hence thesis by POLYNOM4:24;
    end;
