Definition respectful {X} (P : dist X -> Prop) : Prop :=
  forall d1 d2, d1 ==d d2 -> P d1 <-> P d2.

Lemma uniform_count {X} `{Finite X} (d : dist X) (E : X -> bool) : uniform d -> eval_dist d E == Q_of_nat (count E) / Q_of_nat (card X).