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