(* The base as the list of all the generators *)
Fixpoint base (n : nat) : list (kn n) :=
  match n return list (kn n) with
  | 0 => nil
  | S n1 => ('e_0: kn (S n1)) :: map (lift n1) (base n1)
  end.

Lemma e_in_base n i : i < n -> In ('e_i) (base n).