theorem :: LIMFUNC4:15

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