theorem :: LIMFUNC1:78

for f being PartFunc of REAL,REAL
for g being Real st f is convergent_in-infty holds
( lim_in-infty f = g iff for g1 being Real st 0 < g1 holds
ex r being Real st
for r1 being Real st r1 < r & r1 in dom f holds
|.((f . r1) - g).| < g1 )