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 Th40:
  D-Union Y = CLD-Union Y & D-Meet Y = CLD-Meet Y
proof
A1: Domains_of Y = Closed_Domains_of Y by Th39;
  hence D-Union Y = (D-Union Y)||Closed_Domains_of Y by RELSET_1:19
    .= CLD-Union Y by TDLAT_1:39;
  thus D-Meet Y = (D-Meet Y)||Closed_Domains_of Y by A1,RELSET_1:19
    .= CLD-Meet Y by TDLAT_1:40;
end;
