Inductive cbl n (l: list (vect n)): nat -> (vect n) -> Prop :=
| cbl_in: forall v, In v l -> cbl n l 0%nat v
| cbl_add: forall k x y, cbl n l k x -> cbl n l k y -> cbl n l k (x + y)
| cbl_scal: forall k k1 x, cbl n l k x -> cbl n l k (k1 .* x)
| cbl_join: forall k v x, In v l -> cbl n l k x -> cbl n l k.+1 (v ∨ x).

Lemma cbl_joinl0 n (l: list (vect n)) k x :
(forall x, In x l -> hom n 1 x) -> cbl n l k x -> x ∨ joinl n l = 0.