proposition: Lemma ball_map_true : forall A, forall f : A -> bool, forall l : list A, ball (map f l) = true <=> forall x, LIn x l -> f x = true.
proof: Proof. induction l; simpl; sp. trw andb_eq_true. trw IHl; split; sp; subst; sp. Qed.
imports: UsefulTypes bin_rels Omega