theorem :: LIMFUNC4:14

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_left_divergent_to-infty_in x0 & f2 is divergent_in-infty_to-infty & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom (f2 * f1) ) ) holds
f2 * f1 is_left_divergent_to-infty_in x0