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 Th48:
  for R being invariant ManySortedRelation of A holds EqCl(R,A) is invariant
proof
  let R be invariant ManySortedRelation of A;
  let s1,s2 be SortSymbol of S;
  let t be Function;
  assume
A1: t is_e.translation_of A,s1,s2;
  then reconsider
  t as Function of (the Sorts of A).s1, (the Sorts of A).s2 by Th11;
  let a,b be set;
  assume
A2: [a,b] in EqCl(R,A).s1;
  then reconsider a, b as Element of A,s1 by ZFMISC_1:87;
  a,b are_convertible_wrt R.s1 by A2,Th42;
  then t.a, t.b are_convertible_wrt R.s2 by A1,Th47;
  hence thesis by Th42;
end;
