Section Elts.
Variable A : Type.
(*****************************)
(** ** Nth element of a list *)
(*****************************)
Fixpoint nth (n:nat) (l:list A) (default:A) {struct l} : A :=
match n, l with
| O, x :: l' => x
| O, other => default
| S m, [] => default
| S m, x :: t => nth m t default
end.
Fixpoint nth_ok (n:nat) (l:list A) (default:A) {struct l} : bool :=
match n, l with
| O, x :: l' => true
| O, other => false
| S m, [] => false
| S m, x :: t => nth_ok m t default
end.

Lemma nth_in_or_default :
forall (n:nat) (l:list A) (d:A), {In (nth n l d) l} + {nth n l d = d}.