unfold Paire in |- *; simpl in |- *.
simple induction 1; intros b; elim b; simpl in |- *; auto with zfc.
Qed.
Hint Resolve IN_Paire_left IN_Paire_right Vide_est_vide: zfc.
(* The singleton set  *)
(* Note that we could define it directly using the base type Un *)
Definition Sing (E : Ens) := Paire E E.
(* The axioms  *)

Theorem IN_Sing : forall E : Ens, IN E (Sing E).
unfold Sing in |- *; auto with zfc.