theorem :: LIMFUNC3:28

for g, x0 being Real
for f being PartFunc of REAL,REAL st f is_convergent_in x0 holds
( lim (f,x0) = g iff for g1 being Real st 0 < g1 holds
ex g2 being Real st
( 0 < g2 & ( for r1 being Real st 0 < |.(x0 - r1).| & |.(x0 - r1).| < g2 & r1 in dom f holds
|.((f . r1) - g).| < g1 ) ) )