(* Turn a vector in a list of scalar to be used for multiple product *)
Fixpoint v2l (n: nat) : vect n -> list K :=
match n return vect n -> list K with
O => fun k => k :: nil
| S n1 => fun x => let (x1, x2) := x in
(v2l n1 x1 ++ v2l n1 x2)%list
end.

(* The length is 2^n *)
Lemma v2l_length n v : length (v2l n v) = exp 2 n.