theorem :: LIMFUNC1:56

for f1, f2 being PartFunc of REAL,REAL st f1 is divergent_in-infty_to+infty & ( for r being Real ex g being Real st
( g < r & g in dom (f1 + f2) ) ) & ex r being Real st f2 | (left_open_halfline r) is bounded_below holds
f1 + f2 is divergent_in-infty_to+infty