]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/procedural/Coq/Logic/ChoiceFacts.mma
made executable again
[helm.git] / matita / matita / contribs / procedural / Coq / Logic / ChoiceFacts.mma
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 include "Init/Prelude.ma".
20
21 (*#***********************************************************************)
22
23 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
24
25 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
26
27 (*   \VV/  **************************************************************)
28
29 (*    //   *      This file is distributed under the terms of the       *)
30
31 (*         *       GNU Lesser General Public License Version 2.1        *)
32
33 (*#***********************************************************************)
34
35 (*i $Id: ChoiceFacts.v,v 1.7.2.2 2004/08/01 09:29:59 herbelin Exp $ i*)
36
37 (*#* We show that the functional formulation of the axiom of Choice
38    (usual formulation in type theory) is equivalent to its relational
39    formulation (only formulation of set theory) + the axiom of
40    (parametric) definite description (aka axiom of unique choice) *)
41
42 (*#* This shows that the axiom of choice can be assumed (under its
43    relational formulation) without known inconsistency with classical logic,
44    though definite description conflicts with classical logic *)
45
46 inline procedural "cic:/Coq/Logic/ChoiceFacts/RelationalChoice.con" as definition.
47
48 inline procedural "cic:/Coq/Logic/ChoiceFacts/FunctionalChoice.con" as definition.
49
50 inline procedural "cic:/Coq/Logic/ChoiceFacts/ParamDefiniteDescription.con" as definition.
51
52 inline procedural "cic:/Coq/Logic/ChoiceFacts/description_rel_choice_imp_funct_choice.con" as lemma.
53
54 inline procedural "cic:/Coq/Logic/ChoiceFacts/funct_choice_imp_rel_choice.con" as lemma.
55
56 inline procedural "cic:/Coq/Logic/ChoiceFacts/funct_choice_imp_description.con" as lemma.
57
58 inline procedural "cic:/Coq/Logic/ChoiceFacts/FunChoice_Equiv_RelChoice_and_ParamDefinDescr.con" as theorem.
59
60 (*#* We show that the guarded relational formulation of the axiom of Choice
61    comes from the non guarded formulation in presence either of the
62    independance of premises or proof-irrelevance *)
63
64 inline procedural "cic:/Coq/Logic/ChoiceFacts/GuardedRelationalChoice.con" as definition.
65
66 inline procedural "cic:/Coq/Logic/ChoiceFacts/ProofIrrelevance.con" as definition.
67
68 inline procedural "cic:/Coq/Logic/ChoiceFacts/rel_choice_and_proof_irrel_imp_guarded_rel_choice.con" as lemma.
69
70 inline procedural "cic:/Coq/Logic/ChoiceFacts/IndependenceOfPremises.con" as definition.
71
72 inline procedural "cic:/Coq/Logic/ChoiceFacts/rel_choice_indep_of_premises_imp_guarded_rel_choice.con" as lemma.
73