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(* modify it under the terms of the GNU Lesser General Public License *)
(* as published by the Free Software Foundation; either version 2.1   *)
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(*                                                                    *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the      *)
(* GNU General Public License for more details.                       *)
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(* You should have received a copy of the GNU Lesser General Public   *)
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(* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA *)
(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
Require Export Sets.
Require Export Axioms.
Require Export Omega.
Definition ord : forall E E' : Ens, INC E' E -> Prop.
simple induction E.
intros A f HR.
intros E' i.
apply and.
exact (forall a : A, IN (f a) E' -> HR a (f a) (INC_refl (f a))).
exact
(forall (a : A) (e : Ens),
IN (f a) E' -> forall p : INC e (f a), HR a e p -> IN e E').
Defined.

(* Specifications: *)
Lemma ord_ext :
forall (E E' E'' : Ens) (p' : INC E' E) (p'' : INC E'' E),
EQ E' E'' -> ord E E' p' -> ord E E'' p''.