Section suml.
Fixpoint suml (l : list nat) : nat :=
match l with
| nil => 0
| n :: l' => n + suml l'
end.

Lemma length_suml_filter b n l:
(forall x, In x l -> b <= x < b + n) ->
suml (map (fun r => length(filter (beq_nat r) l )) (seq b n)) = length l.