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 Th42:
  for S being non empty set, A being non-empty ManySortedSet of S
  for R being ManySortedRelation of A for s being Element of S for a,b being
  Element of A.s holds [a,b] in (EqCl R).s iff a,b are_convertible_wrt R.s
proof
  let S be non empty set, A be non-empty ManySortedSet of S;
  let R be ManySortedRelation of A;
  let s be Element of S;
  (EqCl R).s = EqCl (R.s) by MSUALG_5:def 3;
  hence thesis by Th41;
end;
