theorem :: FDIFF_12:31

for x0 being Real
for f being PartFunc of REAL,REAL st f is_Rcontinuous_in x0 & ( for r being Real st x0 < r holds
ex g being Real st
( g < r & x0 < g & g in dom f ) ) holds
( f is_right_convergent_in x0 & lim_right (f,x0) = f . x0 )