Definition is_vector n v := cbl _ (base n 1) v.Definition is_vector_space n l := forall x, In x l -> is_vector n x.

(* Specifications: *)
Lemma joinl0_mprod n M : M <> nil -> is_vector_space n M -> joinl n M = 0 -> exists lk, exists i, length lk = length M /\ In i lk /\ i <> 0%f /\ lk *X* M = 0.
Lemma cbl_joinl0_mprod n M x : is_vector_space n M -> cbl _ M x -> joinl n (x::M) = 0.