reserve T for 1-sorted;
reserve T for TopSpace;

theorem
  Closed_Domains_Lattice T is SubLattice of Domains_Lattice T
proof
  set L = Domains_Lattice T, CL = Closed_Domains_Lattice T;
  thus the carrier of CL c= the carrier of L by Th31;
  thus the L_join of CL = (the L_join of L)||the carrier of CL by Th39;
  thus thesis by Th40;
end;
