proposition: Lemma inmon_Der_imp_inmon : forall u v : Word, isGram X V1 R1 S1 -> isGram X V2 R2 S2 -> inter V1 V2 empty -> inmonoid (union X V1) u -> Derive Ru u v -> inmonoid (union X V1) v.
proof: Proof. intros u v G_R1 G_R2 inter_V1_V2_empty inmon_X_V1_u Der_Ru_u_v. apply inmon_Der_imp_inmon_R1 with u. apply isGram4 with S1; assumption. apply inmon_Der_imp_Der. apply isGram4 with S1; assumption. apply isGram4 with S2; assumption. apply inter_union. apply isGram2 with R2 S2; assumption. assumption. assumption. assumption. assumption. Qed.
imports: Ensf Words more_words need fonctions Relations gram