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 *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
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_Classical_facts.v,v 1.5.2.1 2004/07/16 19:31:18 herbelin 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".
85 include "Sets/Powerset_facts.ma".
87 include "Logic/Classical_Type.ma".
89 include "Sets/Classical_sets.ma".
92 Section Sets_as_an_algebra
96 cic:/Coq/Sets/Powerset_Classical_facts/Sets_as_an_algebra/U.var
99 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/sincl_add_x.con" as lemma.
101 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/incl_soustr_in.con" as lemma.
104 Hint Resolve incl_soustr_in: sets v62.
107 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/incl_soustr.con" as lemma.
110 Hint Resolve incl_soustr: sets v62.
113 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/incl_soustr_add_l.con" as lemma.
116 Hint Resolve incl_soustr_add_l: sets v62.
119 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/incl_soustr_add_r.con" as lemma.
122 Hint Resolve incl_soustr_add_r: sets v62.
125 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/add_soustr_2.con" as lemma.
127 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/add_soustr_1.con" as lemma.
130 Hint Resolve add_soustr_1 add_soustr_2: sets v62.
133 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/add_soustr_xy.con" as lemma.
136 Hint Resolve add_soustr_xy: sets v62.
139 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/incl_st_add_soustr.con" as lemma.
141 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/Sub_Add_new.con" as lemma.
143 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/Simplify_add.con" as lemma.
145 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/Included_Add.con" as lemma.
147 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/setcover_inv.con" as lemma.
149 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/Add_covers.con" as theorem.
151 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/covers_Add.con" as theorem.
153 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/covers_is_Add.con" as theorem.
155 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/Singleton_atomic.con" as theorem.
157 inline procedural "cic:/Coq/Sets/Powerset_Classical_facts/less_than_singleton.con" as lemma.
160 End Sets_as_an_algebra
164 Hint Resolve incl_soustr_in: sets v62.
168 Hint Resolve incl_soustr: sets v62.
172 Hint Resolve incl_soustr_add_l: sets v62.
176 Hint Resolve incl_soustr_add_r: sets v62.
180 Hint Resolve add_soustr_1 add_soustr_2: sets v62.
184 Hint Resolve add_soustr_xy: sets v62.