proposition: Lemma all_notin_singles : forall xs ys vs, List.Forall (fun x => ¬ List.In x ys) xs -> xs ⊄ (ys ∷ vs).
proof: Proof. intros xs ys vs Hforall. unfold all_notin; intros x Hin. apply notin_singles. apply (List.Forall_forall (fun x => ¬ In x ys) xs); intros; auto. Qed.
imports: Utf8 Equalities