Corollary upd_Znth_eq' : forall {A}{d: Inhabitant A} x (l1 l2 : list A) i (Hi : 0 <= i < Zlength l1)
  (Hlen : Zlength l1 = Zlength l2)
  (Heq : forall j, 0 <= j < Zlength l1 -> j <> i -> Znth j l1 = Znth j l2),
  upd_Znth i l1 x = upd_Znth i l2 x.

Lemma filter_length : forall {A} (f : A -> bool) l, length l = (length (filter f l) + length (filter (fun x => negb (f x)) l))%nat.