#[deprecated(use = snd_list_prod)]
Notation map_snd_list_prod := snd_list_prod (only parsing).(** Sum of elements of a list of [nat]: [list_sum] *)

Definition list_sum l := fold_right plus 0 l.

Lemma length_flat_map A B (f: A -> list B) l: length (flat_map f l) = list_sum (map (fun x => length (f x)) l).