1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
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15 (* This file was automatically generated: do not edit *********************)
19 (*#**********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
25 (* \VV/ *************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#**********************************************************************)
33 (*#***************************************************************************)
37 (* Naive Set Theory in Coq *)
43 (* Rocquencourt Sophia-Antipolis *)
61 (* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks *)
63 (* to the Newton Institute for providing an exceptional work environment *)
65 (* in Summer 1995. Several developments by E. Ledinot were an inspiration. *)
67 (*#***************************************************************************)
69 (*i $Id: Powerset_facts.v,v 1.8 2003/12/15 19:48:23 barras Exp $ i*)
71 include "Sets/Ensembles.ma".
73 include "Sets/Constructive_sets.ma".
75 include "Sets/Relations_1.ma".
77 include "Sets/Relations_1_facts.ma".
79 include "Sets/Partial_Order.ma".
81 include "Sets/Cpo.ma".
83 include "Sets/Powerset.ma".
86 Section Sets_as_an_algebra
90 cic:/Coq/Sets/Powerset_facts/Sets_as_an_algebra/U.var
97 inline procedural "cic:/Coq/Sets/Powerset_facts/Empty_set_zero.con" as theorem.
100 Hint Resolve Empty_set_zero.
103 inline procedural "cic:/Coq/Sets/Powerset_facts/Empty_set_zero'.con" as theorem.
106 Hint Resolve Empty_set_zero'.
109 inline procedural "cic:/Coq/Sets/Powerset_facts/less_than_empty.con" as lemma.
112 Hint Resolve less_than_empty.
115 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_commutative.con" as theorem.
117 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_associative.con" as theorem.
120 Hint Resolve Union_associative.
123 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_idempotent.con" as theorem.
125 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_absorbs.con" as lemma.
127 inline procedural "cic:/Coq/Sets/Powerset_facts/Couple_as_union.con" as theorem.
129 inline procedural "cic:/Coq/Sets/Powerset_facts/Triple_as_union.con" as theorem.
131 inline procedural "cic:/Coq/Sets/Powerset_facts/Triple_as_Couple.con" as theorem.
133 inline procedural "cic:/Coq/Sets/Powerset_facts/Triple_as_Couple_Singleton.con" as theorem.
135 inline procedural "cic:/Coq/Sets/Powerset_facts/Intersection_commutative.con" as theorem.
137 inline procedural "cic:/Coq/Sets/Powerset_facts/Distributivity.con" as theorem.
139 inline procedural "cic:/Coq/Sets/Powerset_facts/Distributivity'.con" as theorem.
141 inline procedural "cic:/Coq/Sets/Powerset_facts/Union_add.con" as theorem.
144 Hint Resolve Union_add.
147 inline procedural "cic:/Coq/Sets/Powerset_facts/Non_disjoint_union.con" as theorem.
149 inline procedural "cic:/Coq/Sets/Powerset_facts/Non_disjoint_union'.con" as theorem.
151 inline procedural "cic:/Coq/Sets/Powerset_facts/singlx.con" as lemma.
157 inline procedural "cic:/Coq/Sets/Powerset_facts/incl_add.con" as lemma.
160 Hint Resolve incl_add.
163 inline procedural "cic:/Coq/Sets/Powerset_facts/incl_add_x.con" as lemma.
165 inline procedural "cic:/Coq/Sets/Powerset_facts/Add_commutative.con" as lemma.
167 inline procedural "cic:/Coq/Sets/Powerset_facts/Add_commutative'.con" as lemma.
169 inline procedural "cic:/Coq/Sets/Powerset_facts/Add_distributes.con" as lemma.
171 inline procedural "cic:/Coq/Sets/Powerset_facts/setcover_intro.con" as lemma.
174 Hint Resolve setcover_intro.
178 End Sets_as_an_algebra
182 Hint Resolve Empty_set_zero Empty_set_zero' Union_associative Union_add
183 singlx incl_add: sets v62.