theorem Th49: :: LIMFUNC2:49

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 ) ) holds
( f ^ is_left_convergent_in x0 & lim_left ((f ^),x0) = (lim_left (f,x0)) " )