(* 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.

(* Lift of generator of the base *)
Lemma gen_lift n i : 'e_i.+1 = 'e_i^'l :> vect n.+1.