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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 *)
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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___,, * 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: Image.v,v 1.6.2.1 2004/07/16 19:31:17 herbelin Exp $ i*)
71 include "Sets/Finite_sets.ma".
73 include "Sets/Constructive_sets.ma".
75 include "Logic/Classical_Type.ma".
77 include "Sets/Classical_sets.ma".
79 include "Sets/Powerset.ma".
81 include "Sets/Powerset_facts.ma".
83 include "Sets/Powerset_Classical_facts.ma".
85 include "Arith/Gt.ma".
87 include "Arith/Lt.ma".
89 include "Arith/Le.ma".
91 include "Sets/Finite_sets_facts.ma".
98 cic:/Coq/Sets/Image/Image/U.var
102 cic:/Coq/Sets/Image/Image/V.var
105 inline procedural "cic:/Coq/Sets/Image/Im.ind".
107 inline procedural "cic:/Coq/Sets/Image/Im_def.con" as lemma.
113 inline procedural "cic:/Coq/Sets/Image/Im_add.con" as lemma.
115 inline procedural "cic:/Coq/Sets/Image/image_empty.con" as lemma.
118 Hint Resolve image_empty.
121 inline procedural "cic:/Coq/Sets/Image/finite_image.con" as lemma.
124 Hint Resolve finite_image.
127 inline procedural "cic:/Coq/Sets/Image/Im_inv.con" as lemma.
129 inline procedural "cic:/Coq/Sets/Image/injective.con" as definition.
131 inline procedural "cic:/Coq/Sets/Image/not_injective_elim.con" as lemma.
133 inline procedural "cic:/Coq/Sets/Image/cardinal_Im_intro.con" as lemma.
135 inline procedural "cic:/Coq/Sets/Image/In_Image_elim.con" as lemma.
137 inline procedural "cic:/Coq/Sets/Image/injective_preserves_cardinal.con" as lemma.
139 inline procedural "cic:/Coq/Sets/Image/cardinal_decreases.con" as lemma.
141 inline procedural "cic:/Coq/Sets/Image/Pigeonhole.con" as theorem.
143 inline procedural "cic:/Coq/Sets/Image/Pigeonhole_principle.con" as lemma.
150 Hint Resolve Im_def image_empty finite_image: sets v62.