theorem :: LIMFUNC1:75

for f, f1 being PartFunc of REAL,REAL st f1 is divergent_in+infty_to-infty & ex r being Real st
( right_open_halfline r c= (dom f) /\ (dom f1) & ( for g being Real st g in right_open_halfline r holds
f . g <= f1 . g ) ) holds
f is divergent_in+infty_to-infty