for f1, f2 being PartFunc of REAL,REAL st f1 is convergent_in+infty & f2 is_convergent_in lim_in+infty f1 & ( for r being Real ex g being Real st
( r < g & g in dom (f2 * f1) ) ) & ex r being Real st
for g being Real st g in (dom f1) /\ (right_open_halfline r) holds
f1 . g <> lim_in+infty f1 holds
( f2 * f1 is convergent_in+infty & lim_in+infty (f2 * f1) = lim (f2,(lim_in+infty f1)) )