theorem Th71: :: LIMFUNC1:71

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