(* Skip the first elements of a list *)
Fixpoint skip_n (l : list A) (n : nat) {struct n} : 
 list A :=
  match n with
  | O => l
  | S n1 => match l with
            | nil => nil
            | a :: l1 => skip_n l1 n1
            end
  end.

Theorem skip_n_id : forall l : list A, skip_n l (length l) = nil.