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 contra_join n lf k1 k2 M1 M2 : hom n k1 M1 -> hom n k2 M2 ->
#<lf, M1 ∨ M2># = #<lf, M1># ∨ M2 + ((- (1))^k1).* M1 ∨ #<lf, M2>#.