helm/software/matita/contribs/procedural/Coq/Logic/Eqdep_dec.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 (*#**********************************************************************)
  20
  21 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
  22
  23 (* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
  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: Eqdep_dec.v,v 1.14 2003/11/29 17:28:33 herbelin Exp $ i*)
  34
  35 (*#* We prove that there is only one proof of [x=x], i.e [(refl_equal ? x)].
  36    This holds if the equality upon the set of [x] is decidable.
  37    A corollary of this theorem is the equality of the right projections
  38    of two equal dependent pairs.
  39
  40    Author:   Thomas Kleymann |<tms@dcs.ed.ac.uk>| in Lego
  41              adapted to Coq by B. Barras
  42
  43    Credit:   Proofs up to [K_dec] follows an outline by Michael Hedberg
  44 *)
  45
  46 (*#* We need some dependent elimination schemes *)
  47
  48 (* UNEXPORTED
  49 Set Implicit Arguments.
  50 *)
  51
  52 (*#* Bijection between [eq] and [eqT] *)
  53
  54 inline procedural "cic:/Coq/Logic/Eqdep_dec/eq2eqT.con" as definition.
  55
  56 inline procedural "cic:/Coq/Logic/Eqdep_dec/eqT2eq.con" as definition.
  57
  58 inline procedural "cic:/Coq/Logic/Eqdep_dec/eq_eqT_bij.con" as lemma.
  59
  60 inline procedural "cic:/Coq/Logic/Eqdep_dec/eqT_eq_bij.con" as lemma.
  61
  62 (* UNEXPORTED
  63 Section DecidableEqDep
  64 *)
  65
  66 (* UNEXPORTED
  67 cic:/Coq/Logic/Eqdep_dec/DecidableEqDep/A.var
  68 *)
  69
  70 inline procedural "cic:/Coq/Logic/Eqdep_dec/DecidableEqDep/comp.con" "DecidableEqDep__" as definition.
  71
  72 inline procedural "cic:/Coq/Logic/Eqdep_dec/trans_sym_eqT.con" as remark.
  73
  74 (* UNEXPORTED
  75 cic:/Coq/Logic/Eqdep_dec/DecidableEqDep/eq_dec.var
  76 *)
  77
  78 (* UNEXPORTED
  79 cic:/Coq/Logic/Eqdep_dec/DecidableEqDep/x.var
  80 *)
  81
  82 inline procedural "cic:/Coq/Logic/Eqdep_dec/DecidableEqDep/nu.con" "DecidableEqDep__" as definition.
  83
  84 inline procedural "cic:/Coq/Logic/Eqdep_dec/DecidableEqDep/nu_constant.con" "DecidableEqDep__" as definition.
  85
  86 inline procedural "cic:/Coq/Logic/Eqdep_dec/DecidableEqDep/nu_inv.con" "DecidableEqDep__" as definition.
  87
  88 inline procedural "cic:/Coq/Logic/Eqdep_dec/nu_left_inv.con" as remark.
  89
  90 inline procedural "cic:/Coq/Logic/Eqdep_dec/eq_proofs_unicity.con" as theorem.
  91
  92 inline procedural "cic:/Coq/Logic/Eqdep_dec/K_dec.con" as theorem.
  93
  94 (*#* The corollary *)
  95
  96 inline procedural "cic:/Coq/Logic/Eqdep_dec/DecidableEqDep/proj.con" "DecidableEqDep__" as definition.
  97
  98 inline procedural "cic:/Coq/Logic/Eqdep_dec/inj_right_pair.con" as theorem.
  99
 100 (* UNEXPORTED
 101 End DecidableEqDep
 102 *)
 103
 104 (*#* We deduce the [K] axiom for (decidable) Set *)
 105
 106 inline procedural "cic:/Coq/Logic/Eqdep_dec/K_dec_set.con" as theorem.
 107