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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                               *)
(*                                                                          *)
(****************************************************************************)
(*                                  Reg.v                                   *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)
(*                 							*)
(*  AUTOMATES FINIS       						*)
(*    On definit le predicat (automate q qd qa d), ou q represente      *)
(*    l'ensemble des etats, qd ceux de depart, qa ceux d'arrivee,	*)
(*    et d la relation de transition, comme la conjonction de :		*)
(*    qd et qa sont inclus dans q , et d est inclus dans qxalphxq	*)
(*                  							*)
Definition automate (q qd qa d : Ensf) : Prop :=
inclus qa q /\ inclus qd q /\ inclus d (prodcart q (prodcart alph q)).
intros q qd qa d H.
elim H.
intros H1 H0; elim H0; clear H0.
auto.
Qed.
intros q qd qa d H.
elim H.
intros H1 H0; elim H0; clear H0.
auto.
Qed.

Lemma automate_def3 :
forall q qd qa d : Ensf, automate q qd qa d -> inclus qa q.