reserve I,X,x,d,i for set;
reserve M for ManySortedSet of I;
reserve EqR1,EqR2 for Equivalence_Relation of X;
reserve I for non empty set;
reserve M for ManySortedSet of I;
reserve EqR,EqR1,EqR2,EqR3,EqR4 for Equivalence_Relation of M;

theorem
  EqCl EqR = EqR
proof
  now
    let i be Element of I;
    reconsider ER = EqR.i as Equivalence_Relation of M.i by MSUALG_4:def 2;
    thus EqR.i = EqCl ER by Th2
      .= EqCl (EqR.i);
  end;
  hence thesis by Def3;
end;
