 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 Th31:
  for u be Element of the carrier of Polynom-Ring INT.Ring,
  a,b be Element of INT.Ring holds eval(a*(~u),b) in {a}-Ideal
  proof
    let u be Element of the carrier of Polynom-Ring INT.Ring,
        a,b be Element of INT.Ring;
    eval(a*(~u),b) = a*eval(~u,b) by RING_5:7;
    hence thesis by RING_2:18,GCD_1:def 1;
  end;
