theorem :: LIMFUNC4:10

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