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

theorem Th25:
  the Equidistance of MS is_reflexive_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 be object;
      assume x in C;
      then consider y,z be object such that
A1:   y in the carrier of MS and
A2:   z in the carrier of MS and
A3:   x = [y,z] by ZFMISC_1:def 2;
      reconsider y,z as Element of MS by A1,A2;
      y,z equiv y,z by Th21;
      hence [x,x] in R by A3;
    end;
    hence thesis by RELAT_2:def 1;
  end;
