proposition: Lemma Regles_V : forall X V R V' : Ensf, inclus V V' -> Regles X V R -> Regles X V' R.
proof: Proof. unfold Regles in |- *. intros X V R V' inclus_V_V' Regles_X_V_R x dans_x_R. elim (Regles_X_V_R x dans_x_R). intros A dans_A_V temp; elim temp; clear temp. intros B egal_B inmonoid_B. exists A. auto. exists B. assumption. apply inmonoid_inclus with (union X V); auto. Qed.
imports: Ensf Words more_words need fonctions Relations