
theorem Th60:
  for L be Field for p be Polynomial of L st len p <> 0 holds p is
  with_roots iff NormPolynomial(p) is with_roots
proof
  let L be Field;
  let p be Polynomial of L;
  assume
A1: len p <> 0;
  thus p is with_roots implies NormPolynomial(p) is with_roots
  proof
    assume p is with_roots;
    then consider x be Element of L such that
A2: x is_a_root_of p;
    x is_a_root_of NormPolynomial(p) by A1,A2,Th59;
    hence thesis;
  end;
  assume NormPolynomial(p) is with_roots;
  then consider x be Element of L such that
A3: x is_a_root_of NormPolynomial(p);
  x is_a_root_of p by A1,A3,Th59;
  hence thesis;
end;
