:: deftheorem defines is_continuous_in FCONT_1:def 1 :
for f being PartFunc of REAL,REAL
for x0 being 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 holds
( f /* s1 is convergent & f . x0 = lim (f /* s1) ) );