reserve n,m,i,k for Element of NAT;
reserve x,X,X1 for set;
reserve r,p for Real;
reserve s,x0,x1,x2 for Real;
reserve f,f1,f2 for PartFunc of REAL,REAL n;
reserve h for PartFunc of REAL,REAL-NS n;
reserve W for non empty set;

theorem
  f|X is Lipschitzian & X c= dom f implies (p(#)f) | X is Lipschitzian
proof
   assume A1: f|X is Lipschitzian & X c= dom f;
   reconsider g= f as PartFunc of REAL,REAL-NS n
     by REAL_NS1:def 4;
A2: (p(#)g) | X is Lipschitzian by A1,NFCONT_3:30;
   p(#)g = p(#)f by Th6;
   hence thesis by A2;
end;
