
theorem
  for frequency being Element of RAT_Music
  ex r being positive Real st frequency = r &
  (for n being non zero Nat holds n * r is Element of RAT_Music)
  proof
    let frequency be Element of RAT_Music;
    reconsider r = frequency as positive Rational by Th2;
    take r;
    now
      let n be non zero Nat;
      n * r in RATPLUS;
      hence n * r is Element of RAT_Music;
    end;
    hence thesis;
  end;
