
theorem
  for n being non zero Element of NAT holds ex x being Element of
  MultGroup F_Complex st ord x = n
proof
  let n be non zero Element of NAT;
  set x = [** cos((2*PI*1)/n), sin((2*PI*1)/n) **];
  n-roots_of_1 c= the carrier of MultGroup F_Complex & x in n-roots_of_1
  by Th24,Th32;
  then reconsider y=x as Element of MultGroup F_Complex;
  ord y = n div (1 gcd n) & 1 gcd n = 1 by Th31,WSIERP_1:8;
  hence thesis by NAT_2:4;
end;
