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

theorem Th40:
  for MS being satisfying_harmonic_closed satisfying_Nat
  satisfying_tonic satisfying_interval satisfying_equiv MusicStruct
  for frequency being Element of MS holds
  1-harmonique(MS,frequency) = frequency
  proof
    let MS be satisfying_harmonic_closed satisfying_Nat
    satisfying_tonic satisfying_interval satisfying_equiv MusicStruct;
    let frequency be Element of MS;
A1: NATPLUS c= the carrier of MS by Def12a;
    1 in NATPLUS by NAT_LAT:def 6;
    then reconsider x = 1 as Element of MS by A1;
    [frequency,1-harmonique(MS,frequency)] in
      Class(the Equidistance of MS,[1,1]) by Def08b;
    then x,x equiv frequency,1-harmonique(MS,frequency) by EQREL_1:18;
    hence thesis by Th29;
  end;
