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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 (* This file was automatically generated: do not edit *********************)
16
17 include "Coq.ma".
18
19 (*#***********************************************************************)
20
21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
22
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
24
25 (*   \VV/  **************************************************************)
26
27 (*    //   *      This file is distributed under the terms of the       *)
28
29 (*         *       GNU Lesser General Public License Version 2.1        *)
30
31 (*#***********************************************************************)
32
33 (*#***************************************************************************)
34
35 (*                                                                          *)
36
37 (*                         Naive Set Theory in Coq                          *)
38
39 (*                                                                          *)
40
41 (*                     INRIA                        INRIA                   *)
42
43 (*              Rocquencourt                        Sophia-Antipolis        *)
44
45 (*                                                                          *)
46
47 (*                                 Coq V6.1                                 *)
48
49 (*                                                                          *)
50
51 (*                               Gilles Kahn                                *)
52
53 (*                               Gerard Huet                                *)
54
55 (*                                                                          *)
56
57 (*                                                                          *)
58
59 (*                                                                          *)
60
61 (* Acknowledgments: This work was started in July 1993 by F. Prost. Thanks  *)
62
63 (* to the Newton Institute for providing an exceptional work environment    *)
64
65 (* in Summer 1995. Several developments by E. Ledinot were an inspiration.  *)
66
67 (*#***************************************************************************)
68
69 (*i $Id: Finite_sets_facts.v,v 1.7.2.1 2004/07/16 19:31:17 herbelin Exp $ i*)
70
71 include "Sets/Finite_sets.ma".
72
73 include "Sets/Constructive_sets.ma".
74
75 include "Logic/Classical_Type.ma".
76
77 include "Sets/Classical_sets.ma".
78
79 include "Sets/Powerset.ma".
80
81 include "Sets/Powerset_facts.ma".
82
83 include "Sets/Powerset_Classical_facts.ma".
84
85 include "Arith/Gt.ma".
86
87 include "Arith/Lt.ma".
88
89 (* UNEXPORTED
90 Section Finite_sets_facts
91 *)
92
93 (* UNEXPORTED
94 cic:/Coq/Sets/Finite_sets_facts/Finite_sets_facts/U.var
95 *)
96
97 inline procedural "cic:/Coq/Sets/Finite_sets_facts/finite_cardinal.con" as lemma.
98
99 inline procedural "cic:/Coq/Sets/Finite_sets_facts/cardinal_finite.con" as lemma.
100
101 inline procedural "cic:/Coq/Sets/Finite_sets_facts/Add_preserves_Finite.con" as theorem.
102
103 (* UNEXPORTED
104 Hint Resolve Add_preserves_Finite.
105 *)
106
107 inline procedural "cic:/Coq/Sets/Finite_sets_facts/Singleton_is_finite.con" as theorem.
108
109 (* UNEXPORTED
110 Hint Resolve Singleton_is_finite.
111 *)
112
113 inline procedural "cic:/Coq/Sets/Finite_sets_facts/Union_preserves_Finite.con" as theorem.
114
115 inline procedural "cic:/Coq/Sets/Finite_sets_facts/Finite_downward_closed.con" as lemma.
116
117 inline procedural "cic:/Coq/Sets/Finite_sets_facts/Intersection_preserves_finite.con" as lemma.
118
119 inline procedural "cic:/Coq/Sets/Finite_sets_facts/cardinalO_empty.con" as lemma.
120
121 (* UNEXPORTED
122 Hint Resolve cardinalO_empty.
123 *)
124
125 inline procedural "cic:/Coq/Sets/Finite_sets_facts/inh_card_gt_O.con" as lemma.
126
127 inline procedural "cic:/Coq/Sets/Finite_sets_facts/card_soustr_1.con" as lemma.
128
129 inline procedural "cic:/Coq/Sets/Finite_sets_facts/cardinal_is_functional.con" as lemma.
130
131 inline procedural "cic:/Coq/Sets/Finite_sets_facts/cardinal_Empty.con" as lemma.
132
133 inline procedural "cic:/Coq/Sets/Finite_sets_facts/cardinal_unicity.con" as lemma.
134
135 inline procedural "cic:/Coq/Sets/Finite_sets_facts/card_Add_gen.con" as lemma.
136
137 inline procedural "cic:/Coq/Sets/Finite_sets_facts/incl_st_card_lt.con" as lemma.
138
139 inline procedural "cic:/Coq/Sets/Finite_sets_facts/incl_card_le.con" as lemma.
140
141 inline procedural "cic:/Coq/Sets/Finite_sets_facts/G_aux.con" as lemma.
142
143 (* UNEXPORTED
144 Hint Unfold not.
145 *)
146
147 inline procedural "cic:/Coq/Sets/Finite_sets_facts/Generalized_induction_on_finite_sets.con" as lemma.
148
149 (* UNEXPORTED
150 End Finite_sets_facts
151 *)
152