intros R1 R2 u v inclus_R1_R2 Der_R1.
unfold Derivestar, Rstar in Der_R1.
pattern u, v in |- *.
apply Der_R1.
auto.
intros; prolog [ Derive_inclus Derivestar_R ] 3.
(*Intros a b c Der_a_b Der_b_c. Apply Derivestar_R with b. Apply Derive_inclus with R1;Assumption. Assumption.*)
Qed.
(* LG X V R S est l'ensemble de mots engendre par la grammaire (X V R S) *)
Definition LG (X V R : Ensf) (S : Elt) : wordset :=
fun w : Word => Derivestar R (cons S nil) w /\ inmonoid X w.

Lemma LG_inv :
forall (X V R : Ensf) (S : Elt) (w : Word), LG X V R S w -> inmonoid X w.