Fixpoint sum (n : nat) (f: (nat -> vect n)) (m : nat) {struct m} :
    vect n :=
  match m with
  | 0%nat => f 0%nat
  | S m1 => f m + sum n f m1
  end.

Lemma first_deg0i n v : first_deg n v = 0%nat -> hom n 0 v.