Definition normalize {X} `{Finite X} (d : dist X) : dist X.
refine {|
dist_pmf := map (fun x => (x, eval_dist d (Classes.eqb x))) enum;
dist_law := _;
|}.

Lemma list_sum_map_plus {X} (f g : X -> nat) (xs : list X) :
list_sum (map (fun x => f x + g x)%nat xs) =
(list_sum (map f xs) + list_sum (map g xs))%nat.