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 join_hom_odd n k x : (1+1 <> (0: K))%f -> hom n k x -> odd k -> x ∨ x = 0.