(* The left contraction (Dorst inner product) *)
Notation "x ''L[' l ]  y " := (l_contra _ l x y) (at level 40).
Notation hom := (hom p _).

(* Retrieve the Hodge dual from geometric product *)
(* when the quadratic form is nul *)
(* Thanks to Lounesto: Clifford Algebra and Spinors *)
Lemma dualE n x : '@x = 'R[x] [* [1%f]%Kn] E :> vect n.
induction n as [|n IH]; simpl; try Vfold n.