theorem Th17: :: WAYBEL24:17

for R, S, T being LATTICE
for f being monotone Function of [:R,S:],T
for a being Element of R
for b being Element of S
for X being directed Subset of [:R,S:] st ex_sup_of f .: X,T & a in proj1 X & b in proj2 X holds
f . [a,b] <= sup (f .: X)