theorem :: LIMFUNC2:41

for g, x0 being Real
for f being PartFunc of REAL,REAL st f is_left_convergent_in x0 holds
( lim_left (f,x0) = g iff for g1 being Real st 0 < g1 holds
ex r being Real st
( r < x0 & ( for r1 being Real st r < r1 & r1 < x0 & r1 in dom f holds
|.((f . r1) - g).| < g1 ) ) )