theorem Th33: :: LIMFUNC2:33

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