theorem Th58: :: LIMFUNC2:58

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