theorem :: LIMFUNC1:52

for f1, f2 being PartFunc of REAL,REAL st f1 is divergent_in-infty_to+infty & f2 is divergent_in-infty_to+infty & ( for r being Real ex g being Real st
( g < r & g in (dom f1) /\ (dom f2) ) ) holds
( f1 + f2 is divergent_in-infty_to+infty & f1 (#) f2 is divergent_in-infty_to+infty )