theorem :: FCONT_1:2

for x0 being Real
for f being PartFunc of REAL,REAL holds
( f is_continuous_in x0 iff for s1 being Real_Sequence st rng s1 c= dom f & s1 is convergent & lim s1 = x0 & ( for n being Nat holds s1 . n <> x0 ) holds
( f /* s1 is convergent & f . x0 = lim (f /* s1) ) )