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

theorem Th48:
  REAL_Music is satisfying_octave_descendent_constructible
  proof
    let frequency be Element of REAL_Music;
    consider fr,qr be positive Real such that
A2: fr = frequency and
    qr = (1 qua Real) / 2 * fr and
A4: [qr,fr] in octave(REAL_Music) by Th47;
    fr is Element of REAL_Music & qr is Element of REAL_Music by Th1;
    hence thesis by A2,A4;
  end;
