theorem :: LIMFUNC1:46

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
( r < g & g in dom f ) ) & ( for g being Real ex r being Real st
for r1 being Real st r < r1 & r1 in dom f holds
g < f . r1 ) ) )