reserve X for TopSpace;
reserve C for Subset of X;
reserve A, B for Subset of X;
reserve X for non empty TopSpace;
reserve Y for extremally_disconnected non empty TopSpace;

theorem Th44:
  Domains_Lattice Y = Open_Domains_Lattice Y
proof
A1: D-Union Y = OPD-Union Y by Th43;
A2: D-Meet Y = OPD-Meet Y by Th43;
  Domains_of Y = Open_Domains_of Y by Th42;
  hence Domains_Lattice Y =LattStr(#Open_Domains_of Y,OPD-Union Y,OPD-Meet Y#)
  by A1,A2
    .= Open_Domains_Lattice Y;
end;
