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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                               *)
(*                                                                          *)
(****************************************************************************)
(*                                 gram_g.v                                 *)
(****************************************************************************)
(*              Formal Language Theory                                      *)
(*                                                                          *)
(*              Judicael Courant - Jean-Christophe Filliatre                *)
(*                                                                          *)
(*              Developped in V5.8  June-July 1993                          *)
(*              Ported     to V5.10 October 1994                            *)
(****************************************************************************)
Inductive Deriveg (X R : Ensf) : Word -> Word -> Prop :=
| Deriveg1 :
forall (u v : Word) (A : Elt),
dans (couple A (word u)) R -> Deriveg X R (cons A v) (Append u v)
| Deriveg2 :
forall (u v : Word) (x : Elt),
dans x X -> Deriveg X R u v -> Deriveg X R (cons x u) (cons x v).
Hint Resolve Deriveg1.
Hint Resolve Deriveg2.
Definition Derivegstar (X R : Ensf) := Rstar Word (Deriveg X R).
intros X R u v Der_g.
elim Der_g.
intros.
apply Derive1; auto.
intros.
apply Derive2; auto.
Qed.

Lemma Derivegstar_Derivestar :
forall (X R : Ensf) (u v : Word), Derivegstar X R u v -> Derivestar R u v.