(** [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 length_prod : forall (l:list A)(l':list B),
length (list_prod l l') = (length l) * (length l').