helm/software/matita/contribs/procedural/CoRN/reals/iso_CReals.mma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  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 "CoRN.ma".
  18
  19 (* begin hide *)
  20
  21 (* in this file the  concrete canonical isomorphism -in te sense of
  22    R_morphisms.v - between two arbitrary model of real numbers is built *)
  23
  24 include "reals/Q_dense.ma".
  25
  26 include "reals/R_morphism.ma".
  27
  28 inline procedural "cic:/CoRN/reals/iso_CReals/less_pres_Lim.con" as lemma.
  29
  30 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_less.con" as lemma.
  31
  32 inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_less.con" as lemma.
  33
  34 inline procedural "cic:/CoRN/reals/iso_CReals/less_inj_seq.con" as lemma.
  35
  36 inline procedural "cic:/CoRN/reals/iso_CReals/SeqLimit_unique.con" as theorem.
  37
  38 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_well_def.con" as lemma.
  39
  40 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_one_one.con" as lemma.
  41
  42 inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_well_def.con" as lemma.
  43
  44 inline procedural "cic:/CoRN/reals/iso_CReals/inj_Q_one_one.con" as lemma.
  45
  46 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_plus.con" as lemma.
  47
  48 inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_plus.con" as lemma.
  49
  50 (* This theorem can be avoided but it is interesting *)
  51
  52 inline procedural "cic:/CoRN/reals/iso_CReals/nonarchemaedian_bound_for_Lim.con" as theorem.
  53
  54 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con" as lemma.
  55
  56 inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_mult.con" as lemma.
  57
  58 (* UNEXPORTED
  59 Section Concrete_iso_between_Creals
  60 *)
  61
  62 (* UNEXPORTED
  63 cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R1.var
  64 *)
  65
  66 (* UNEXPORTED
  67 cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var
  68 *)
  69
  70 inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con" as lemma.
  71
  72 inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy21.con" as lemma.
  73
  74 inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq12.con" as definition.
  75
  76 inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq21.con" as definition.
  77
  78 inline procedural "cic:/CoRN/reals/iso_CReals/f12.con" as definition.
  79
  80 inline procedural "cic:/CoRN/reals/iso_CReals/g21.con" as definition.
  81
  82 (*#****** ISO FROM R1 TO R2 ********)
  83
  84 inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_inverse_g21.con" as theorem.
  85
  86 inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_surjective.con" as theorem.
  87
  88 inline procedural "cic:/CoRN/reals/iso_CReals/f12_strong_ext.con" as theorem.
  89
  90 inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_less.con" as theorem.
  91
  92 inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_plus.con" as theorem.
  93
  94 inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_mult.con" as theorem.
  95
  96 (*#********* ISO FROM R2 TO R1 **********)
  97
  98 inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_inverse_f12.con" as theorem.
  99
 100 inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_surjective.con" as theorem.
 101
 102 inline procedural "cic:/CoRN/reals/iso_CReals/g21_strong_ext.con" as theorem.
 103
 104 inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_less.con" as theorem.
 105
 106 inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_plus.con" as theorem.
 107
 108 inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_mult.con" as theorem.
 109
 110 (*#** Building Homomorphisms out of f12 and g21 ***)
 111
 112 inline procedural "cic:/CoRN/reals/iso_CReals/f12_as_Homomorphism.con" as definition.
 113
 114 inline procedural "cic:/CoRN/reals/iso_CReals/g21_as_Homomorphism.con" as definition.
 115
 116 inline procedural "cic:/CoRN/reals/iso_CReals/f12_inverse_lft.con" as lemma.
 117
 118 inline procedural "cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con" as lemma.
 119
 120 inline procedural "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con" as definition.
 121
 122 (* UNEXPORTED
 123 End Concrete_iso_between_Creals
 124 *)
 125
 126 (* end hide *)
 127