
theorem Th22:
  for MS being satisfying_equiv MusicStruct
  for a,b,c,d being Element of MS holds
  a,b equiv c,d iff c,d equiv a,b
  proof
    let MS be satisfying_equiv MusicStruct;
    let a,b,c,d be Element of MS;
    hereby
      assume a,b equiv c,d;
      then (the Ratio of MS).(a,b) = (the Ratio of MS).(c,d) by Def08a;
      hence c,d equiv a,b by Def08a;
    end;
    assume c,d equiv a,b;
    then (the Ratio of MS).(a,b) = (the Ratio of MS).(c,d) by Def08a;
    hence a,b equiv c,d by Def08a;
  end;
