theorem Th15: :: WAYBEL17:15

for S, T being non empty RelStr
for D being Subset of S
for f being Function of S,T st ( ( ex_sup_of D,S & ex_sup_of f .: D,T ) or ( S is complete & S is antisymmetric & T is complete & T is antisymmetric ) ) & f is monotone holds
sup (f .: D) <= f . (sup D)