theorem
  f|X is Lipschitzian & X1 c= X implies f|X1 is Lipschitzian
proof
  assume that
A1: f|X is Lipschitzian and
A2: X1 c= X;
  f|X1 = f|X|X1 by A2,RELAT_1:74;
  hence thesis by A1;
end;
