reserve x for set,
  R for non empty Poset;

theorem Th4:
  for S being OrderSortedSign, U0 being OSAlgebra of S holds
  MSAlgebra (#the Sorts of U0,the Charact of U0#) is order-sorted
proof
  let S be OrderSortedSign, U0 be OSAlgebra of S;
  the Sorts of U0 is OrderSortedSet of S by OSALG_1:17;
  hence thesis by OSALG_1:17;
end;
