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

theorem Th42:
  REAL_Music is satisfying_octave_constructible
  proof
    let frequency be Element of REAL_Music;
    consider fr,qr be positive Real such that
A1: fr = frequency and qr = 2 * fr and
A2: [fr,qr] in octave(REAL_Music) by Th41;
    fr is Element of REAL_Music & qr is Element of REAL_Music by Th1;
    hence thesis by A1,A2;
  end;
