Fixpoint v2k (n : nat) : vect n -> kn n :=
match n return vect n -> kn n  with
| O => fun v : vect 0 => tt
| S n1  => fun v => let (v1,v2) := v in
('C[v1], v2k n1 v2)
end.

Lemma is_vector_space_swap n x l :
is_vector_space n l -> In x l ->
exists l1, is_vector_space n (x::l1) /\ joinl n l = joinl n (x::l1).