for x0 being Real
for f being PartFunc of REAL,REAL st ex r being Real st
( 0 < r & f | ].(x0 - r),x0.[ is decreasing & not f | ].(x0 - r),x0.[ is bounded_below ) & ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom f ) ) holds
f is_left_divergent_to-infty_in x0 by Th27;