unfold Vide in |- *; simple induction E; simpl in |- *; intros A e H H0;
split.
intros; elim (H0 (e x)); auto with zfc.
exists x; auto with zfc.
simple induction y.
Qed.
(* Pair *)
Definition Paire : forall E E' : Ens, Ens.
intros.
apply (sup bool).
simple induction 1.
exact E.
exact E'.
Defined.
(* The pair construction is extentional *)

(* Specifications: *)
Theorem Paire_sound_left :
forall A A' B : Ens, EQ A A' -> EQ (Paire A B) (Paire A' B).
Theorem Paire_sound_left :
forall A A' B : Ens, EQ A A' -> EQ (Paire A B) (Paire A' B).