(* Dual lift*)
Notation "x ^'dl" := (dlift _ x) (at level 9, format "x ^'dl" ): g_scope.

Lemma dlift_add n x y : (x + y)^'dl = x^'dl + y^'dl :> vect n.+1.
Fixpoint proj (n: nat) k: (vect n) -> (list K) :=
match n return vect n -> list  K with
| O => fun a  =>
match k with | O => a::nil | _ => nil end
| S n1 => fun l => let (l1,l2) := l in
match k with | O => proj n1 k l2 | S k1 =>
(proj n1 k1 l1 ++ proj n1 k l2)%list
end
end.