theorem :: LIMFUNC2:76

for x0 being Real
for f being PartFunc of REAL,REAL st f is_left_convergent_in x0 & lim_left (f,x0) = 0 & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom f & f . g <> 0 ) ) & ex r being Real st
( 0 < r & ( for g being Real st g in (dom f) /\ ].(x0 - r),x0.[ holds
f . g <= 0 ) ) holds
f ^ is_left_divergent_to-infty_in x0