
theorem Th45:
  for n being non zero Element of NAT holds BRoots unital_poly(
  F_Complex, n) = (n-roots_of_1, 1)-bag
proof
  let n being non zero Element of NAT;
  set p = unital_poly(F_Complex, n);
A1: degree BRoots p = len p -' 1 by UPROOTS:59
    .= n+1 -'1 by Th40
    .= n by NAT_D:34;
A2: card (n-roots_of_1) = n by Th27;
  Roots p = n-roots_of_1 & support BRoots p = Roots p by Th42,UPROOTS:def 9;
  hence thesis by A1,A2,UPROOTS:13;
end;
