theorem Th27: :: WAYBEL24:27

for S being non empty RelStr
for T being complete LATTICE
for F being non empty Subset of (T |^ the carrier of S)
for D being non empty Subset of S holds (sup F) .: D = { ("\/" ( { (f . i) where f is Element of (T |^ the carrier of S) : f in F } ,T)) where i is Element of S : i in D }