(* Iterated product of a list of vectors *)
Fixpoint joinl n (l: list (vect n)) := match l with
| nil => 0
| a::nil => a
| a::l => a ∨ joinl n l
end.

Lemma joinl_app n l1 l2 :
l1 <> nil -> l2 <> nil -> joinl n (l1 ++ l2)%list = joinl n l1 ∨ joinl n l2.