theorem :: LIMFUNC2:69

for x0 being Real
for f being PartFunc of REAL,REAL st ( f is_left_divergent_to+infty_in x0 or f 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 f & f . g <> 0 ) ) holds
( f ^ is_left_convergent_in x0 & lim_left ((f ^),x0) = 0 )