reserve n,m for Nat;
reserve x,X,X1 for set;
reserve s,g,r,p for Real;
reserve S,T for RealNormSpace;
reserve f,f1,f2 for PartFunc of S,T;
reserve s1,s2 for sequence of S;
reserve x0,x1,x2 for Point of S;
reserve Y for Subset of S;

theorem
  for X,X1,f1,f2 st f1 is_continuous_on X & f2 is_continuous_on X1 holds
  f1+f2 is_continuous_on X /\ X1 & f1-f2 is_continuous_on X /\ X1
proof
  let X,X1,f1,f2;
  assume f1 is_continuous_on X & f2 is_continuous_on X1;
  then f1 is_continuous_on X /\ X1 & f2 is_continuous_on X /\ X1 by Th23,
XBOOLE_1:17;
  hence thesis by Th25;
end;
