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

theorem
  Open_Domains_Lattice T is SubLattice of Domains_Lattice T
proof
  set L = Domains_Lattice T, OL = Open_Domains_Lattice T;
  thus the carrier of OL c= the carrier of L by Th35;
  thus the L_join of OL = (the L_join of L)||the carrier of OL by Th42;
  thus thesis by Th43;
end;
