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_flat_map {X Y} (f : X -> list (Y * Q)) (xs : list X) : sum_dist (flat_map f xs) == Qsum (map (fun x => sum_dist (f x)) xs).