theorem :: LIMFUNC2:9

for x0 being Real
for f being PartFunc of REAL,REAL holds
( f is_left_divergent_to-infty_in x0 iff ( ( for r being Real st r < x0 holds
ex g being Real st
( r < g & g < x0 & g in dom f ) ) & ( for g1 being Real ex r being Real st
( r < x0 & ( for r1 being Real st r < r1 & r1 < x0 & r1 in dom f holds
f . r1 < g1 ) ) ) ) )