theorem :: LIMFUNC4:37

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_divergent_to-infty_in x0 & f2 is divergent_in-infty_to+infty & ( for r1, r2 being Real st r1 < x0 & x0 < r2 holds
ex g1, g2 being Real st
( r1 < g1 & g1 < x0 & g1 in dom (f2 * f1) & g2 < r2 & x0 < g2 & g2 in dom (f2 * f1) ) ) holds
f2 * f1 is_divergent_to+infty_in x0