theorem Th10: :: WAYBEL31:10

for L1 being lower-bounded continuous sup-Semilattice
for T1 being Scott TopAugmentation of L1
for T2 being correct Lawson TopAugmentation of L1
for B2 being Basis of T2 holds { (uparrow V) where V is Subset of T2 : V in B2 } is Basis of T1