
theorem Th46:
  for n being non zero Element of NAT holds unital_poly(F_Complex
  , n) = poly_with_roots((n-roots_of_1, 1)-bag)
proof
  let n be non zero Element of NAT;
  set p = unital_poly(F_Complex, n);
  len p = n+1 by Th40;
  then p.(len p-'1) = p.n by NAT_D:34
    .= 1_F_Complex by Th38;
  hence unital_poly(F_Complex, n) = poly_with_roots BRoots unital_poly(
  F_Complex, n) by UPROOTS:65
    .= poly_with_roots((n-roots_of_1, 1)-bag) by Th45;
end;
