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 NoDup_list_prod {X Y} (xs : list X) : forall (ys : list Y),
NoDup xs -> NoDup ys -> NoDup (list_prod xs ys).