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 sum_dist_app {X} (l l' : list (X * Q)) :
sum_dist (l ++ l') == sum_dist l + sum_dist l'.