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 uniform_fst {X Y} `{Finite X, Finite Y} (d : dist (X * Y)) :
uniform d ->
uniform (monad_map fst d).