helm/software/matita/contribs/procedural/Coq/Logic/ChoiceFacts.mma

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  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 (*i $Id: ChoiceFacts.v,v 1.7.2.2 2004/08/01 09:29:59 herbelin Exp $ i*)
  34
  35 (*#* We show that the functional formulation of the axiom of Choice
  36    (usual formulation in type theory) is equivalent to its relational
  37    formulation (only formulation of set theory) + the axiom of
  38    (parametric) definite description (aka axiom of unique choice) *)
  39
  40 (*#* This shows that the axiom of choice can be assumed (under its
  41    relational formulation) without known inconsistency with classical logic,
  42    though definite description conflicts with classical logic *)
  43
  44 inline procedural "cic:/Coq/Logic/ChoiceFacts/RelationalChoice.con" as definition.
  45
  46 inline procedural "cic:/Coq/Logic/ChoiceFacts/FunctionalChoice.con" as definition.
  47
  48 inline procedural "cic:/Coq/Logic/ChoiceFacts/ParamDefiniteDescription.con" as definition.
  49
  50 inline procedural "cic:/Coq/Logic/ChoiceFacts/description_rel_choice_imp_funct_choice.con" as lemma.
  51
  52 inline procedural "cic:/Coq/Logic/ChoiceFacts/funct_choice_imp_rel_choice.con" as lemma.
  53
  54 inline procedural "cic:/Coq/Logic/ChoiceFacts/funct_choice_imp_description.con" as lemma.
  55
  56 inline procedural "cic:/Coq/Logic/ChoiceFacts/FunChoice_Equiv_RelChoice_and_ParamDefinDescr.con" as theorem.
  57
  58 (*#* We show that the guarded relational formulation of the axiom of Choice
  59    comes from the non guarded formulation in presence either of the
  60    independance of premises or proof-irrelevance *)
  61
  62 inline procedural "cic:/Coq/Logic/ChoiceFacts/GuardedRelationalChoice.con" as definition.
  63
  64 inline procedural "cic:/Coq/Logic/ChoiceFacts/ProofIrrelevance.con" as definition.
  65
  66 inline procedural "cic:/Coq/Logic/ChoiceFacts/rel_choice_and_proof_irrel_imp_guarded_rel_choice.con" as lemma.
  67
  68 inline procedural "cic:/Coq/Logic/ChoiceFacts/IndependenceOfPremises.con" as definition.
  69
  70 inline procedural "cic:/Coq/Logic/ChoiceFacts/rel_choice_indep_of_premises_imp_guarded_rel_choice.con" as lemma.
  71