reserve x for set;

theorem Th25: :: 3.6. PROPOSITION (B), p. 169(?)
  for L being complete LATTICE for T being lim-inf TopAugmentation
of L for S being Lawson correct TopAugmentation of L holds T is TopExtension of
  S
proof
  let L be complete LATTICE;
  let T be lim-inf TopAugmentation of L;
  let S be Lawson correct TopAugmentation of L;
  lambda L = the topology of S & xi L = the topology of T by Th10,
WAYBEL19:def 4;
  then
A1: the topology of S c= the topology of T by Th24;
  the RelStr of T = the RelStr of L & the RelStr of S = the RelStr of L by
YELLOW_9:def 4;
  hence thesis by A1,YELLOW_9:def 5;
end;
