
theorem Th24:
  for S being satisfying_interval satisfying_equiv MusicStruct
  for a,b,c being Element of S holds
  (a,b equiv a,c iff b = c)
  proof
    let S be satisfying_interval satisfying_equiv MusicStruct;
    let a,b,c be Element of S;
    now
      assume a,b equiv a,c;
      then (the Ratio of S).(a,b) = (the Ratio of S).(a,c) by Def08a;
      hence b = c by Def09a;
    end;
    hence thesis by Th21;
  end;
