reserve L for complete Scott TopLattice,
  x for Element of L,
  X, Y for Subset of L,
  V, W for Element of InclPoset sigma L,
  VV for Subset of InclPoset sigma L;

theorem Th24:
  X in sigma L iff X is open
proof
  sigma L =the topology of L by Th23;
  hence thesis by PRE_TOPC:def 2;
end;
