helm/software/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