reserve MS for satisfying_equiv MusicStruct;
reserve a,b,c,d,e,f for Element of MS;

theorem Th54:
  for MS being classical_fifth satisfying_fifth_constructible
  satisfying_harmonic_closed satisfying_Nat satisfying_interval
  satisfying_equiv MusicStruct
  for frequency being Element of MS holds
  ex r,s being positive Real st r = frequency &
  s = (3 qua Real) / 2 * r & Fifth(MS,frequency) = s
  proof
    let MS be classical_fifth satisfying_fifth_constructible
    satisfying_harmonic_closed satisfying_Nat satisfying_interval
    satisfying_equiv MusicStruct;
    let frequency be Element of MS;
    consider fr be positive Real such that
A1: frequency = fr & Fifth(MS,frequency) = (3 qua Real) / 2 * fr
      by Def12;
    reconsider s = (3 qua Real) / 2 * fr as positive Real;
    take fr,s;
    thus thesis by A1;
  end;
