theorem Th35: :: LIMFUNC2:35

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