let Y be non empty extremally_disconnected TopSpace; :: thesis: Domains_Lattice Y = Closed_Domains_Lattice Y
( Domains_of Y = Closed_Domains_of Y & D-Union Y = CLD-Union Y & D-Meet Y = CLD-Meet Y ) by Th41, Th42;
hence Domains_Lattice Y = LattStr(# (Closed_Domains_of Y),(CLD-Union Y),(CLD-Meet Y) #) by TDLAT_1:def 4
.= Closed_Domains_Lattice Y by TDLAT_1:def 8 ;
:: thesis: verum