proposition: Lemma distinct_pairs_and_app : forall A R l1 l2, distinct_pairs_and (A := A) R l1 -> distinct_pairs_and R l2 -> (forall x y, In x l1 -> In y l2 -> R x y) -> distinct_pairs_and R (l1 ++ l2).
proof: Proof. Proof using. induction l1; intros; simpl in *; intuition. find_apply_lem_hyp in_app_or. intuition eauto. Qed.
imports: Verdi(Verdi)