(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)
(*i 	$Id$	 i*)
Section LSort.
Variable A : Type.
Fixpoint alist_sorted (l:alist A) : bool :=
match l with
| nil => true
| (a, _) :: l' =>
match l' with
| nil => true
| (a', y') :: l'' => andb (Nless a a') (alist_sorted l')
end
end.
Fixpoint alist_nth_ad (n:nat) (l:alist A) {struct l} : ad :=
match l with
| nil => N0 (* dummy *)
| (a, y) :: l' => match n with
| O => a
| S n' => alist_nth_ad n' l'
end
end.
Definition alist_sorted_1 (l:alist A) :=
forall n:nat,
S (S n) <= length l ->
Nless (alist_nth_ad n l) (alist_nth_ad (S n) l) = true.

Lemma alist_sorted_imp_1 :
forall l:alist A, alist_sorted l = true -> alist_sorted_1 l.