reserve x for set,
  R for non empty Poset;
reserve S1 for OrderSortedSign,
  OU0 for OSAlgebra of S1;
reserve s,s1,s2,s3,s4 for SortSymbol of S1;
reserve U0 for non-empty OSAlgebra of S1;

theorem
  for U0 be strict non-empty OSAlgebra of S1 holds Top (OSSubAlLattice(
  U0)) = U0
proof
  let U0 be strict non-empty OSAlgebra of S1;
  reconsider B = the Sorts of U0 as MSSubset of U0 by PBOOLE:def 18;
  B is OrderSortedSet of S1 by OSALG_1:17;
  then reconsider B = the Sorts of U0 as OSSubset of U0 by Def2;
  thus Top (OSSubAlLattice(U0)) = GenOSAlg(B) by Th50
    .= U0 by Th34;
end;
