Definition sumF {X} `{Finite X} (f : X -> nat) : nat :=
  list_sum (map f enum).Definition sumFQ {X} `{Finite X} (f : X -> Q) : Q :=
  Qsum(map f enum).

Lemma count_sumF {X} `{Finite X} (p : X -> bool) : count p = sumF (fun x => indicate_nat (p x)).