
theorem
for F being Field,
    p being non zero Element of the carrier of Polynom-Ring F
holds p is monic iff NormPolynomial p = p
proof
let F be Field,
    p be non zero Element of the carrier of Polynom-Ring F;
hereby assume p is monic;
  then LC p = 1.F by RATFUNC1:def 7;
  hence NormPolynomial p = (1.F)" * p by npl .= p by poly2a;
  end;
thus thesis;
end;
