(* Lift a vector of dimension n into a vector of dimension n+1 whose first component is 0 *)
Notation " x ^'l " := (lift _ x) (at level 9, format "x ^'l"): g_scope.

(* Specifications: *)
(* Lift of generator of the base *)
Lemma gen_lift n i : 'e_i.+1 = 'e_i^'l :> vect n.+1.
Lemma lift_cbl n l (x: vect n) :
cbl _ l x -> cbl _ (map (lift n) l) x^'l.
Lemma lift_inj n (x1 x2: vect n) : x1^'l = x2^'l -> x1 = x2.
Definition dlift (n: nat) (v: vect n) : (vect n.+1) := (v,(0: vect n)).