reserve MS for satisfying_equiv MusicStruct;
reserve a,b,c,d,e,f for Element of MS;
reserve MS for satisfying_octave_descendent_constructible
  classical_octave satisfying_octave_constructible classical_fifth
  satisfying_fifth_constructible satisfying_harmonic_closed satisfying_Nat
  satisfying_commutativity satisfying_interval satisfying_equiv satisfying_Real
  non empty MusicStruct,
  fondamentale,frequency for Element of MS;
reserve                              MS for MusicSpace,
        fondamentale, frequency, f1, f2 for Element of MS;
reserve       HPS for Heptatonic_Pythagorean_Score,
        frequency for Element of HPS;
reserve       HPS for Heptatonic_Pythagorean_Score,
        frequency for Element of HPS;

theorem Th93:
  for HPS being satisfying_euclidean Heptatonic_Pythagorean_Score
  for f1,f2 being Element of HPS
  holds intrval(f1,f2) = (the Ratio of HPS).(f1,f2)
  proof
    let HPS be satisfying_euclidean Heptatonic_Pythagorean_Score;
    let f1,f2 be Element of HPS;
    (the Ratio of HPS).(f1,f2) = @f2 / @f1 by Def25;
    hence thesis by Def21;
  end;
