Global Instance Finite_prod {X Y} `{Finite X, Finite Y} : Finite (X * Y).
Definition indicate (b : bool) : Q :=
if b then 1 else 0.
Definition indicate_nat (b : bool) : nat :=
if b then 1 else O.

Lemma eval_dist_sigma_dist {X} (d : dist X) (E : X -> bool) :
eval_dist d E ==
sigma_dist d (fun x q => q * indicate (E x)).