theorem :: NFCONT_3:20

for S being RealNormSpace
for X, X1 being set
for f1, f2 being PartFunc of REAL, the carrier of S st X c= dom f1 & X1 c= dom f2 & f1 | X is continuous & f2 | X1 is continuous holds
( (f1 + f2) | (X /\ X1) is continuous & (f1 - f2) | (X /\ X1) is continuous )