On (too) short lists

Consider the following definition:
Require Import List.
Require Import Arith.

Fixpoint nth_option (A:Set)(n:nat)(l:list A) {struct l}
  : option A :=
  match n, l with
  | O, cons a tl =>  Some a
  | S p, cons a tl => nth_option A p tl
  | n, nil => None
Prove the following theorem:
Lemma nth_length : 
  forall (A:Set)(n:nat)(l:list A), nth_option _ n l = None <->
                                   length l <= n.


Look at this file

Going home
Pierre Castéran