theorem :: LIMFUNC1:108

for f being PartFunc of REAL,REAL st f is convergent_in+infty & lim_in+infty f = 0 & ( for r being Real ex g being Real st
( r < g & g in dom f & f . g <> 0 ) ) & ex r being Real st
for g being Real st g in (dom f) /\ (right_open_halfline r) holds
0 <= f . g holds
f ^ is divergent_in+infty_to+infty