theorem :: WAYBEL_5:23

for L being complete LATTICE holds
( L is continuous iff for J, K being non empty set
for F being Function of [:J,K:], the carrier of L
for X being Subset of L st X = { a where a is Element of L : ex f being non-empty ManySortedSet of J st
( f in Funcs (J,(Fin K)) & ex G being DoubleIndexedSet of f,L st
( ( for j being Element of J
for x being object st x in f . j holds
(G . j) . x = F . (j,x) ) & a = Inf ) ) } holds
Inf = sup X ) by Lm13, Lm14;