theorem Th13: :: FCONT_1:13

for X being set
for f being PartFunc of REAL,REAL st X c= dom f holds
( f | X is continuous iff for s1 being Real_Sequence st rng s1 c= X & s1 is convergent & lim s1 in X holds
( f /* s1 is convergent & f . (lim s1) = lim (f /* s1) ) )