Definition bijection {X Y} (f : X -> Y) : Prop :=
  exists g : Y -> X,
    (forall x, g (f x) = x) /\
    (forall y, f (g y) = y).

Lemma uniform_snd {X Y} `{Finite X, Finite Y} (d : dist (X * Y)) : uniform d -> uniform (monad_map snd d).