theorem :: LIMFUNC4:60

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_right_divergent_to-infty_in x0 & f2 is convergent_in-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_convergent_in x0 & lim_right ((f2 * f1),x0) = lim_in-infty f2 )