(* 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.

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)).