
theorem Th3:
  for M being multMagma, r being Relators of M,
      R being compatible Equivalence_Relation of M
  st (for i being set, v,w being Element of M st i in dom r & r.i = [v,w]
       holds v in Class(R,w))
  holds equ_rel r c= R
proof
  let M be multMagma;
  let r be Relators of M;
  let R be compatible Equivalence_Relation of M;
  assume A1: for i being set, v,w being Element of M
                 st i in dom r & r.i = [v,w] holds v in Class(R,w);
      let X be object;
      R in {R9 where R9 is compatible Equivalence_Relation of M:
        for i being set, v,w being Element of M st i in dom r & r.i = [v,w]
          holds v in Class(R9,w)} by A1;
      hence thesis by SETFAM_1:def 1;
end;
