theorem :: FDIFF_12:30

for x0 being Real
for f being PartFunc of REAL,REAL st f is_Lcontinuous_in x0 & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom f ) ) holds
( f is_left_convergent_in x0 & lim_left (f,x0) = f . x0 )