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;

theorem
  for S being OrderSortedSign, X being OrderSortedSet of S holds OSCl X = X
proof
  let S be OrderSortedSign, X be OrderSortedSet of S;
  X c= OSCl X & OSCl X c= X by Th7,Th8;
  hence thesis by PBOOLE:146;
end;
