(* Hodge Duality *)
Fixpoint dual n : vect n -> vect n :=
match n return vect n ->  vect n with
|    0 => fun a => a
| S n1 => fun v => let (x,y) := v in (dual n1 (y ^_'f), dual n1 x)
end.
Notation "'@ x " := (dual _ x) (at level 9).

Lemma dual_add n (v1 v2: vect n) : '@(v1 + v2) = '@v1 + '@v2.