theorem Th86: :: LIMFUNC1:86

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