theorem :: LIMFUNC4:24

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_right_convergent_in x0 & f2 is_right_divergent_to-infty_in lim_right (f1,x0) & ( for r being Real st x0 < r holds
ex g being Real st
( g < r & x0 < g & g in dom (f2 * f1) ) ) & ex g being Real st
( 0 < g & ( for r being Real st r in (dom f1) /\ ].x0,(x0 + g).[ holds
lim_right (f1,x0) < f1 . r ) ) holds
f2 * f1 is_right_divergent_to-infty_in x0