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

theorem
f1|X is Lipschitzian & f2|X1 is Lipschitzian
 implies (f1-f2)|(X /\ X1) is Lipschitzian
proof
A1:f1|(X /\ X1) = f1|X|(X /\ X1) & f2|(X /\ X1) = f2|X1|(X /\ X1)
      by RELAT_1:74,XBOOLE_1:17;
A2:(f1-f2)|(X /\ X1) = f1|(X /\ X1)-f2|(X /\ X1) by VFUNCT_1:30;
   assume f1|X is Lipschitzian & f2|X1 is Lipschitzian;
   hence thesis by A1,A2;
end;
