(** [list_prod] has the same signature as [combine], but unlike [combine], it adds every possible pairs, not only those at the same position. *)
Fixpoint list_prod (l:list A) (l':list B) :
list (A * B) :=
match l with
| [] => []
| x :: t => (map (fun y:B => (x, y)) l')++(list_prod t l')
end.

Lemma list_prod_as_flat_map : forall l l',
list_prod l l' = flat_map (fun a => map (pair a) l') l.