unfold Paire in |- *; simpl in |- *; intros; split.
simple induction x.
exists true; auto with zfc.
exists false; auto with zfc.
simple induction y.
exists true; auto with zfc.
exists false; auto with zfc.
Qed.
Hint Resolve Paire_sound_right Paire_sound_left: zfc.
(* The axioms of the pair *)

Theorem IN_Paire_left : forall E E' : Ens, IN E (Paire E E').
unfold Paire in |- *; simpl in |- *; exists true; simpl in |- *;
auto with zfc.