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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************)
(*           The Calculus of Inductive Constructions            *)
(*                       COQ v5.10                              *)
(*                                                              *)
(* Laurent Arditi.  Laboratoire I3S. CNRS ura 1376.             *)
(* Universite de Nice - Sophia Antipolis                        *)
(* arditi@unice.fr, http://wwwi3s.unice.fr/~arditi/lolo.html    *)
(*                                                              *)
(* date: june 1995                                              *)
(* file: Lists_replace                                          *)
(* contents: definition of replace for polymorphic lists        *)
(*                                                              *)
(****************************************************************)
Require Export Lists_field.
Section Lists_replace.
Variable A : Set.
(* Remplace l'element de l a la position par new *)
Fixpoint replace (l : list A) : nat -> A -> list A :=
fun (position : nat) (new : A) =>
match l return (list A) with
| nil =>
(* nil *)  nil | x :: l' => (* (cons x l') *)
match position return (list A) with
| O =>
(* O *)  new :: l' (* (S n') *)
| S n' => x :: replace l' n' new
end
end.

Lemma replace_ok :
forall (l : list A) (i : nat) (x : A),
i < length l -> elemlist A (replace l i x) i = x :: nil.