
theorem Th36:
  for n being non zero Element of NAT, x being set holds x in n
  -roots_of_1 iff ex y being Element of MultGroup F_Complex st x = y & ord y
  divides n
proof
  set MGFC = MultGroup F_Complex;
  set cMGFC = the carrier of MultGroup F_Complex;
  let n be non zero Element of NAT, x be set;
A1: n-roots_of_1 c= cMGFC by Th32;
  hereby
    assume
A2: x in n-roots_of_1;
    then reconsider a = x as Element of MGFC by A1;
    ord a divides n by A2,Th34;
    hence ex y being Element of MultGroup F_Complex st x = y & ord y divides n;
  end;
  thus thesis by Th34;
end;
