theorem :: LIMFUNC2:20

for x0 being Real
for f1, f2 being PartFunc of REAL,REAL st f1 is_right_divergent_to+infty_in x0 & ( for r being Real st x0 < r holds
ex g being Real st
( g < r & x0 < g & g in dom (f1 (#) f2) ) ) & ex r, r1 being Real st
( 0 < r & 0 < r1 & ( for g being Real st g in (dom f2) /\ ].x0,(x0 + r).[ holds
r1 <= f2 . g ) ) holds
f1 (#) f2 is_right_divergent_to+infty_in x0