reserve S for non empty non void ManySortedSign,
  A for MSAlgebra over S;
reserve A for non-empty MSAlgebra over S;
reserve S for non empty non void ManySortedSign,
  A for non-empty MSAlgebra over S,
  R for ManySortedRelation of the Sorts of A;

theorem Th44:
  for R being ManySortedRelation of A for E being
  MSEquivalence-like ManySortedRelation of A st R c= E holds EqCl(R,A) c= E
proof
  let R be ManySortedRelation of A;
  let E be MSEquivalence-like ManySortedRelation of A such that
A1: R c= E;
  let i be object;
  assume i in the carrier of S;
  then reconsider s = i as SortSymbol of S;
A2: EqCl(R,A).s = EqCl (R.s) by MSUALG_5:def 3;
  R.s c= E.s by A1;
  hence thesis by A2,MSUALG_5:def 1;
end;
