proposition: Lemma all_notin_concat_inv : forall xs F G, xs ⊄ (F & G) -> xs ⊄ F ∧ xs ⊄ G.
proof: Proof. intros xs F G Hnotincl. unfold all_notin in *. split; intros x Hin; apply Hnotincl in Hin; apply notin_concat_inv in Hin; destruct Hin; auto. Qed.
imports: Utf8 Equalities