
theorem thirr2:
for F being Field,
    p being Element of the carrier of Polynom-Ring F
holds NormPolynomial(p) is irreducible iff p is irreducible
proof
let F be Field, p be Element of the carrier of Polynom-Ring F;
now assume B: NormPolynomial p is irreducible;
   NormPolynomial p is_associated_to p by np3;
   hence p is irreducible by B, RING_2:23;
   end;
hence thesis by np3,RING_2:23;
end;
