theorem
for X,X1,f1,f2 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
proof
   let X,X1,f1,f2;
   assume X c= dom f1 & X1 c= dom f2; then
A1:X /\ X1 c= dom f1 /\ dom f2 by XBOOLE_1:27;
   assume f1|X is continuous & f2|X1 is continuous; then
   f1|(X /\ X1) is continuous & f2|(X /\ X1) is continuous by Th18,XBOOLE_1:17;
   hence thesis by A1,Th19;
end;
