theorem :: LIMFUNC4:55

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