Monomorphic Universe hlist_large.Polymorphic Universe Ui Uv.Inductive hlist : list iT -> Type :=
  | Hnil  : hlist nil
  | Hcons : forall l ls, F l -> hlist ls -> hlist (l :: ls).Inductive hlist : list iT -> Type :=
  | Hnil  : hlist nil
  | Hcons : forall l ls, F l -> hlist ls -> hlist (l :: ls).Inductive hlist : list iT -> Type :=
  | Hnil  : hlist nil
  | Hcons : forall l ls, F l -> hlist ls -> hlist (l :: ls).Definition hlist_hd {a b} (hl : hlist (a :: b)) : F a :=
    match hl in hlist x return match x return Type@{Uv} with
                               | nil => unit
                               | l :: _ => F l
                               end with
    | Hnil => tt
    | Hcons _ _ x _ => x
    end.Definition hlist_tl {a b} (hl : hlist (a :: b)) : hlist b :=
    match hl in hlist x return match x return Type@{hlist_large} with
                                 | nil => unit
                                 | _ :: ls => hlist ls
                               end with
      | Hnil => tt
      | Hcons _ _ _ x => x
    end.

(* Specifications: *)
Lemma hlist_eta : forall ls (h : hlist ls), h = match ls as ls return hlist ls -> hlist ls with | nil => fun _ => Hnil | a :: b => fun h => Hcons (hlist_hd h) (hlist_tl h) end h.