let R be complete LATTICE; :: thesis: lambda R = UniCl (FinMeetCl ((sigma R) \/ (omega R)))
consider S being correct Lawson TopAugmentation of R;
A1: RelStr(# the carrier of S,the InternalRel of S #) = RelStr(# the carrier of R,the InternalRel of R #) by YELLOW_9:def 4;
then A2: ( omega R = omega S & sigma R = sigma S ) by Th3, YELLOW_9:52;
(omega S) \/ (sigma S) is prebasis of S by Def3;
then FinMeetCl ((omega S) \/ (sigma S)) is Basis of S by YELLOW_9:23;
then the topology of S = UniCl (FinMeetCl ((omega S) \/ (sigma S))) by YELLOW_9:22;
hence lambda R = UniCl (FinMeetCl ((sigma R) \/ (omega R))) by A1, A2, Def4; :: thesis: verum