intros.
unfold Ru in |- *; unfold C in |- *; unfold Gunion in |- *; simpl in |- *.
apply Regles_union; unfold Vu in |- *; unfold C in |- *;
unfold Gunion in |- *; simpl in |- *.
apply Regles_V with V1;
[ auto | apply isGram4 with S1; auto ].
apply Regles_V with V2;
[ auto | apply isGram4 with S2; auto ].
Qed.

(* Specifications: *)
Lemma inmon_Der_imp_Der :
Regles X V1 R1 ->
Regles X V2 R2 ->
inter (union X V1) V2 empty ->
forall u v : Word, Derive Ru u v -> inmonoid (union X V1) u -> Derive R1 u v.