theorem :: LIMFUNC2:56

for x0 being Real
for f being PartFunc of REAL,REAL st f is_right_convergent_in x0 & f " {0} = {} & lim_right (f,x0) <> 0 holds
( f ^ is_right_convergent_in x0 & lim_right ((f ^),x0) = (lim_right (f,x0)) " )