theorem :: LIMFUNC1:48

for f being PartFunc of REAL,REAL holds
( f is divergent_in-infty_to+infty iff ( ( for r being Real ex g being Real st
( g < r & g in dom f ) ) & ( for g being Real ex r being Real st
for r1 being Real st r1 < r & r1 in dom f holds
g < f . r1 ) ) )