reserve n,m for Element of NAT;
reserve r,s for Real;
reserve z for Complex;
reserve CNS,CNS1,CNS2 for ComplexNormSpace;
reserve RNS for RealNormSpace;
reserve X,X1 for set;

theorem
  for f1,f2 be PartFunc of CNS,RNS 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 f1,f2 be PartFunc of CNS,RNS;
  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 Th57,
XBOOLE_1:17;
  hence thesis by Th63;
end;
