theorem :: LIMFUNC4:21

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