(** A curryfied function with multiple parameters **)
Definition arrows_left: list Type -> Type -> Type :=
  fold_left (fun A B => B -> A).(** A curryfied function with multiple parameters **)
Definition arrows_right: Type -> list Type -> Type :=
  fold_right (fun A B => A -> B).(** A tuple is a heterogeneous list. For convenience, we use pairs. **)
Fixpoint tuple (types : list Type) : Type :=
  match types with
  | nil => unit
  | t::q => prod t (tuple q)
  end.

Lemma JMeq_eqrect: forall (U:Type) (a b:U) (P:U -> Type) (x:P a) (e:a=b), eq_rect a P x b e ~= x.