theorem :: LIMFUNC1:67

for f being PartFunc of REAL,REAL st ex r being Real st
( f | (left_open_halfline r) is decreasing & not f | (left_open_halfline r) is bounded_above ) & ( for r being Real ex g being Real st
( g < r & g in dom f ) ) holds
f is divergent_in-infty_to+infty by Th66;