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

theorem Th29:
  for S being satisfying_tonic satisfying_equiv MusicStruct
  for a,b,c being Element of S st
  a,a equiv b,c holds b = c
  proof
    let S be satisfying_tonic satisfying_equiv MusicStruct;
    let a,b,c be Element of S;
    assume a,a equiv b,c;
    then (the Ratio of S).(a,a) = (the Ratio of S).(b,c) by Def08a;
    hence thesis by Def10a;
  end;
