
theorem
  PrimeDivisors 1 = {}
  proof
    assume PrimeDivisors 1 <> {}; then
    consider p being object such that
A1: p in { k where k is Prime : k divides 1 } by XBOOLE_0:def 1;
    consider pp being Prime such that
A2: pp = p & pp divides 1 by A1;
    pp = 1 or pp = -1 by A2,INT_2:13;
    hence thesis by INT_2:def 4;
  end;
