Fixpoint lnzhead l :=
  match l with
  | nil => nil
  | cons d l' =>
    match d with
    | d0 => lnzhead l'
    | _ => l
    end
  end.

(* Specifications: *)
Lemma nzhead_spec u : to_list (nzhead u) = lnzhead (to_list u).
Lemma nzhead_spec u : to_list (nzhead u) = lnzhead (to_list u).