for x0 being Complex
for f being PartFunc of COMPLEX,COMPLEX holds
( f is_continuous_in x0 iff ( x0 in dom f & ( for s1 being Complex_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) ) ) ) )