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
f|X is Lipschitzian & X c= dom f implies (p(#)f) | X is Lipschitzian
proof
   (p(#)f)|X = p(#)(f|X) by VFUNCT_1:31;
   hence thesis;
end;
