(* Generate the p element of the base in dimension n *)
Notation "''e_' p" := (gen _ p) (at level 8, format "''e_' p"): g_scope.

(* Specifications: *)
Lemma inj_e n p1 p2 : p1 < n -> p2 < n ->
'e_p1 = 'e_p2 :> vect n -> p1 = p2.