
theorem npl:
for F being Field,
    p being non zero Element of the carrier of Polynom-Ring F
holds NormPolynomial p = (LC p)" * p
proof
let F be Field,
    p be non zero Element of the carrier of Polynom-Ring F;
now let x be object;
  assume x in NAT;
  then reconsider i = x as Element of NAT;
  thus ((LC p)" * p).x = (LC p)" * (p.i) by POLYNOM5:def 4
          .= p.i / p.(len p-'1)
          .= (NormPolynomial p).x by POLYNOM5:def 11;
  end;
hence thesis by FUNCT_2:12;
end;
