for x0 being Real
for f being PartFunc of REAL,REAL st ( f is_right_divergent_to+infty_in x0 or f is_right_divergent_to-infty_in x0 ) & ( for r being Real st x0 < r holds
ex g being Real st
( g < r & x0 < g & g in dom f & f . g <> 0 ) ) holds
( f ^ is_right_convergent_in x0 & lim_right ((f ^),x0) = 0 )