
theorem
  for n being Nat holds
    PrimeDivisors n c= NatDivisors n
  proof
    let n be Nat;
    PrimeDivisors n c= NatDivisors n
    proof
      let x be object;
      assume x in PrimeDivisors n; then
      consider k being Prime such that
A1:   x = k & k divides n;
      k in {l where l is Nat : l <> 0 & l divides n} by A1;
      hence thesis by A1,MOEBIUS1:def 4;
    end;
    hence thesis;
  end;
