for S, T being complete Scott TopLattice
for F being non empty Subset of (ContMaps (S,T))
for D being non empty directed Subset of S holds "\/" ( { ("\/" ( { (g . i) where i is Element of S : i in D } ,T)) where g is Element of (T |^ the carrier of S) : g in F } ,T) = "\/" ( { ("\/" ( { (g9 . i9) where g9 is Element of (T |^ the carrier of S) : g9 in F } ,T)) where i9 is Element of S : i9 in D } ,T)