theorem :: LIMFUNC3:16

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_divergent_to+infty_in x0 & ( for r1, r2 being Real st r1 < x0 & x0 < r2 holds
ex g1, g2 being Real st
( r1 < g1 & g1 < x0 & g1 in dom (f1 + f2) & g2 < r2 & x0 < g2 & g2 in dom (f1 + f2) ) ) & ex r being Real st
( 0 < r & f2 | (].(x0 - r),x0.[ \/ ].x0,(x0 + r).[) is bounded_below ) holds
f1 + f2 is_divergent_to+infty_in x0