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)).