(* Proof [R:Ensf][x,y:Word][D : (Derive R x y)] (Derive_inv2 R x y (Derive_inv1 R x y D)). *)
prolog [ Derive_inv1 Derive Derive_inv2 ] 7.
Qed.

(* Specifications: *)
Lemma in_mon_X_Der_imp_inmon_X :
forall (X V R : Ensf) (u v : Word),
Regles X V R ->
Derive R u v -> inmonoid (union X V) u -> inmonoid (union X V) v.