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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(****************************************************************************)
(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA                        ENS-CNRS                *)
(*              Rocquencourt                        Lyon                    *)
(*                                                                          *)
(*                                Coq V5.10                                 *)
(*                              Nov 25th 1994                               *)
(*                                                                          *)
(****************************************************************************)
(*                               fonctions.v                                *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)
Hint Resolve dans_map_inv.
Hint Resolve dans_map.
Hint Resolve dans_add1.
Definition comp (f g : Elt -> Elt) (x : Elt) := f (g x).
intros f g.
simple induction E; simpl in |- *; auto.
Qed.
Definition comp_word (f g : Word -> Word) (x : Word) := f (g x).
Definition eg_f_W_W (f g : Word -> Word) := forall x : Word, f x = g x :>Word.

Lemma comp_Word_ext :
forall f g : Elt -> Elt,
eg_f_W_W (Word_ext (comp f g)) (comp_word (Word_ext f) (Word_ext g)).