theorem :: LIMFUNC4:54

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
( r < g & g in dom (f2 * f1) ) ) holds
( f2 * f1 is convergent_in+infty & lim_in+infty (f2 * f1) = lim_in-infty f2 )