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

theorem Th26:
  the Equidistance of MS is_symmetric_in
   [:the carrier of MS,the carrier of MS:]
  proof
    set R = the Equidistance of MS,
    C = [:the carrier of MS,the carrier of MS:];
    now
      let x,y be object;
      assume that
A1: x in C and
A2: y in C and
A3: [x,y] in R;
      consider x1,x2 be object such that
A4:   x1 in the carrier of MS and
A5:   x2 in the carrier of MS and
A6:   x = [x1,x2] by A1,ZFMISC_1:def 2;
      consider y1,y2 be object such that
A7:   y1 in the carrier of MS and
A8:   y2 in the carrier of MS and
A9:   y = [y1,y2] by A2,ZFMISC_1:def 2;
      reconsider x1,x2,y1,y2 as Element of MS by A4,A5,A7,A8;
      x1,x2 equiv y1,y2 by A3,A6,A9;
      then y1,y2 equiv x1,x2 by Th22;
      hence [y,x] in R by A6,A9;
    end;
    hence thesis by RELAT_2:def 3;
  end;
