theorem :: LIMFUNC4:58

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_left_divergent_to-infty_in x0 & f2 is convergent_in-infty & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom (f2 * f1) ) ) holds
( f2 * f1 is_left_convergent_in x0 & lim_left ((f2 * f1),x0) = lim_in-infty f2 )