theorem :: LIMFUNC2:18

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_left_divergent_to+infty_in x0 & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom (f1 (#) f2) ) ) & ex r, r1 being Real st
( 0 < r & 0 < r1 & ( for g being Real st g in (dom f2) /\ ].(x0 - r),x0.[ holds
r1 <= f2 . g ) ) holds
f1 (#) f2 is_left_divergent_to+infty_in x0