theorem :: LIMFUNC3:27

for x0 being Real
for f, f1 being PartFunc of REAL,REAL st f1 is_divergent_to-infty_in x0 & ex r being Real st
( 0 < r & ].(x0 - r),x0.[ \/ ].x0,(x0 + r).[ c= (dom f) /\ (dom f1) & ( for g being Real st g in ].(x0 - r),x0.[ \/ ].x0,(x0 + r).[ holds
f . g <= f1 . g ) ) holds
f is_divergent_to-infty_in x0