reserve n,m,k for Element of NAT;
reserve x, X,X1,Z,Z1 for set;
reserve s,g,r,p,x0,x1,x2 for Real;
reserve s1,s2,q1 for Real_Sequence;
reserve Y for Subset of REAL;
reserve f,f1,f2 for PartFunc of REAL,REAL;

theorem
  f|X is Lipschitzian & X c= dom f implies (p(#)f)|X is Lipschitzian
proof
  (p(#)f)|X = p(#)(f|X) by RFUNCT_1:49;
  hence thesis;
end;
