
theorem np3:
for F being Field,
    p being Element of the carrier of Polynom-Ring F
holds NormPolynomial(p) is_associated_to p
proof
let F be Field, p be Element of the carrier of Polynom-Ring F;
reconsider a = p, b = NormPolynomial(p) as Element of Polynom-Ring F;
A: p *' 1_.(F) = p by POLYNOM3:35;
then B: p divides NormPolynomial(p) by T2,np2;
NormPolynomial(p) divides p by A,np1,T2;
hence thesis by B;
end;
