theorem :: LIMFUNC2:13

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_left_divergent_to+infty_in x0 & f2 is_left_divergent_to+infty_in x0 & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in (dom f1) /\ (dom f2) ) ) holds
( f1 + f2 is_left_divergent_to+infty_in x0 & f1 (#) f2 is_left_divergent_to+infty_in x0 )