Proof fun X P Q x p q E f => f x p q.
(** ** Existential quantification over all small types **)
Definition exT (P : Typ1 -> Prop) : Prop :=
forall E : Prop, (forall X : Typ1, P X -> E) -> E.

(* Specifications: *)
Lemma exT_intro : forall (P : Typ1 -> Prop) (X : Typ1), P X -> exT P.
Proof fun P X p E f => f X p.