proposition: Lemma Exists_eq_count_pos : forall P l, Exists P l = (count P l > 0).
proof: Proof. Proof using. intros. induction l; rew_listx. { extens. iff M; false; math. } { rewrite IHl. extens. iff [M|M] M; case_if; try math. { left~. } { right. math. } } Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)