+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+include "Coq.ma".
+
+(*#**********************************************************************)
+
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+
+(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
+
+(* \VV/ *************************************************************)
+
+(* // * This file is distributed under the terms of the *)
+
+(* * GNU Lesser General Public License Version 2.1 *)
+
+(*#**********************************************************************)
+
+(*#***************************************************************************)
+
+(* *)
+
+(* Naive Set Theory in Coq *)
+
+(* *)
+
+(* INRIA INRIA *)
+
+(* Rocquencourt Sophia-Antipolis *)
+
+(* *)
+
+(* Coq V6.1 *)
+
+(* *)
+
+(* Gilles Kahn *)
+
+(* Gerard Huet *)
+
+(* *)
+
+(* *)
+
+(* *)
+
+(* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks *)
+
+(* to the Newton Institute for providing an exceptional work environment *)
+
+(* in Summer 1995. Several developments by E. Ledinot were an inspiration. *)
+
+(*#***************************************************************************)
+
+(*i $Id: Powerset.v,v 1.5 2003/11/29 17:28:43 herbelin Exp $ i*)
+
+include "Sets/Ensembles.ma".
+
+include "Sets/Relations_1.ma".
+
+include "Sets/Relations_1_facts.ma".
+
+include "Sets/Partial_Order.ma".
+
+include "Sets/Cpo.ma".
+
+(* UNEXPORTED
+Section The_power_set_partial_order
+*)
+
+(* UNEXPORTED
+cic:/Coq/Sets/Powerset/The_power_set_partial_order/U.var
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Power_set.ind".
+
+(* UNEXPORTED
+Hint Resolve Definition_of_Power_set.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Empty_set_minimal.con" as theorem.
+
+(* UNEXPORTED
+Hint Resolve Empty_set_minimal.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Power_set_Inhabited.con" as theorem.
+
+(* UNEXPORTED
+Hint Resolve Power_set_Inhabited.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Inclusion_is_an_order.con" as theorem.
+
+(* UNEXPORTED
+Hint Resolve Inclusion_is_an_order.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Inclusion_is_transitive.con" as theorem.
+
+(* UNEXPORTED
+Hint Resolve Inclusion_is_transitive.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Power_set_PO.con" as definition.
+
+(* UNEXPORTED
+Hint Unfold Power_set_PO.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Strict_Rel_is_Strict_Included.con" as theorem.
+
+(* UNEXPORTED
+Hint Resolve Strict_Rel_Transitive Strict_Rel_is_Strict_Included.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Strict_inclusion_is_transitive_with_inclusion.con" as lemma.
+
+inline procedural "cic:/Coq/Sets/Powerset/Strict_inclusion_is_transitive_with_inclusion_left.con" as lemma.
+
+inline procedural "cic:/Coq/Sets/Powerset/Strict_inclusion_is_transitive.con" as lemma.
+
+inline procedural "cic:/Coq/Sets/Powerset/Empty_set_is_Bottom.con" as theorem.
+
+(* UNEXPORTED
+Hint Resolve Empty_set_is_Bottom.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Union_minimal.con" as theorem.
+
+(* UNEXPORTED
+Hint Resolve Union_minimal.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Intersection_maximal.con" as theorem.
+
+inline procedural "cic:/Coq/Sets/Powerset/Union_increases_l.con" as theorem.
+
+inline procedural "cic:/Coq/Sets/Powerset/Union_increases_r.con" as theorem.
+
+inline procedural "cic:/Coq/Sets/Powerset/Intersection_decreases_l.con" as theorem.
+
+inline procedural "cic:/Coq/Sets/Powerset/Intersection_decreases_r.con" as theorem.
+
+(* UNEXPORTED
+Hint Resolve Union_increases_l Union_increases_r Intersection_decreases_l
+ Intersection_decreases_r.
+*)
+
+inline procedural "cic:/Coq/Sets/Powerset/Union_is_Lub.con" as theorem.
+
+inline procedural "cic:/Coq/Sets/Powerset/Intersection_is_Glb.con" as theorem.
+
+(* UNEXPORTED
+End The_power_set_partial_order
+*)
+
+(* UNEXPORTED
+Hint Resolve Empty_set_minimal: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Power_set_Inhabited: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Inclusion_is_an_order: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Inclusion_is_transitive: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Union_minimal: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Union_increases_l: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Union_increases_r: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Intersection_decreases_l: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Intersection_decreases_r: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Empty_set_is_Bottom: sets v62.
+*)
+
+(* UNEXPORTED
+Hint Resolve Strict_inclusion_is_transitive: sets v62.
+*)
+