for f being PartFunc of REAL,REAL st ( f is divergent_in-infty_to+infty or f is divergent_in-infty_to-infty ) & ( for r being Real ex g being Real st
( g < r & g in dom f & f . g <> 0 ) ) holds
( f ^ is convergent_in-infty & lim_in-infty (f ^) = 0 )