prolog
[ isGram2 isGram4 inter_union inmon_Der_imp_Der_d inmon_Der_imp_inmon_R1_d ]
15.
(*Intros N_dans_X N_dans_V1 N_dans_V2 u v G_R1 G_R2 inter_V1_V2_empty inmon_X_V1_u Der_Ru_u_v. Apply inmon_Der_imp_inmon_R1_d with u. Apply isGram4 with S1;Assumption.  Apply inmon_Der_imp_Der_d.  Assumption.  Assumption.  Assumption.  Apply isGram4 with S1;Assumption.  Apply isGram4 with S2;Assumption.  Apply inter_union. Apply isGram2 with R2 S2; Assumption. Assumption.  Assumption.  Assumption.  Assumption.*)
Qed.

Lemma Gunion_disj_Derivestar :
~ dans S X ->
~ dans S V1 ->
~ dans S V2 ->
isGram X V1 R1 S1 ->
isGram X V2 R2 S2 ->
inter V1 V2 empty ->
forall u v : Word,
Derivestar Ru u v -> inmonoid (union X V1) u -> Derivestar R1 u v.