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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                               *)
(*                                                                          *)
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(*                               more_words.v                               *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)
Hint Unfold eqwordset .
Definition l_inclus (l1 l2 : wordset) : Prop := forall w : Word, l1 w -> l2 w.
Hint Unfold l_inclus.
auto.
Qed.
Hint Resolve refl_l_inclus.
auto.
Qed.
Definition l_egal (l1 l2 : wordset) : Prop :=
l_inclus l1 l2 /\ l_inclus l2 l1.
Hint Unfold l_egal.
(*predicat equivalent a eqwordset*)
(*demonstration :                *)
intros a b.
unfold iff in |- *.
split.
intro Hyp; elim Hyp; auto.
intros Hyp.
split; unfold l_inclus in |- *; intro w; elim (Hyp w); auto.
Qed.

Lemma refl_l_egal : forall l1 : wordset, l_egal l1 l1.