
theorem lemdeg:
for F being Field
for p being Element of the carrier of Polynom-Ring F
holds deg(NormPolynomial p) = deg p
proof
let F be Field, p be Element of the carrier of Polynom-Ring F;
per cases;
suppose p = 0_.(F);
  hence thesis by RING_4:22;
  end;
suppose p <> 0_.(F); then
  len NormPolynomial(p) = len p by POLYNOM4:5,POLYNOM5:57;
  hence deg NormPolynomial(p) = len p - 1 by HURWITZ:def 2
                             .= deg p by HURWITZ:def 2;
  end;
end;
