Definition Class_succ (E : Ens) := Union (Paire E (Sing E)).(*
Inductive Ord : Ens -> Prop :=
  Oo : (Ord Vide)
| So : (E:Ens)(Ord E)->(Ord (Class_succ E))
| Lo : (E:Ens)((e:Ens)(IN e E)->(Ord e))->(Ord (Union E))
| Eo : (E,E':Ens)(Ord E)->(EQ E E')->(Ord E').

Hints Resolve Oo So Lo : zfc.
*)


Definition Nat : nat -> Ens.(*
Theorem Nat_Ord : (n:nat)(Ord (Nat n)).
Induction n; Simpl; Auto with zfc.
Save.
*)

Definition Omega : Ens := sup nat Nat.

Theorem Nat_IN_Omega : forall n : nat, IN (Nat n) Omega.