theorem
  f|X is Lipschitzian implies -f|X is Lipschitzian & (abs f)|X is Lipschitzian
proof
  assume
A1: f|X is Lipschitzian;
  hence -f|X is Lipschitzian;
  (abs f)|X = abs(f|X) by RFUNCT_1:46;
  hence thesis by A1;
end;
