1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
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 *)
24 include "reals/Q_dense.ma".
26 include "reals/R_morphism.ma".
28 inline procedural "cic:/CoRN/reals/iso_CReals/less_pres_Lim.con" as lemma.
30 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_less.con" as lemma.
32 inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_less.con" as lemma.
34 inline procedural "cic:/CoRN/reals/iso_CReals/less_inj_seq.con" as lemma.
36 inline procedural "cic:/CoRN/reals/iso_CReals/SeqLimit_unique.con" as theorem.
38 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_well_def.con" as lemma.
40 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_one_one.con" as lemma.
42 inline procedural "cic:/CoRN/reals/iso_CReals/inj_seq_well_def.con" as lemma.
44 inline procedural "cic:/CoRN/reals/iso_CReals/inj_Q_one_one.con" as lemma.
46 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_plus.con" as lemma.
48 inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_plus.con" as lemma.
50 (* This theorem can be avoided but it is interesting *)
52 inline procedural "cic:/CoRN/reals/iso_CReals/nonarchemaedian_bound_for_Lim.con" as theorem.
54 inline procedural "cic:/CoRN/reals/iso_CReals/Lim_pres_mult.con" as lemma.
56 inline procedural "cic:/CoRN/reals/iso_CReals/G_pres_mult.con" as lemma.
59 Section Concrete_iso_between_Creals
63 cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R1.var
67 cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var
70 inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con" as lemma.
72 inline procedural "cic:/CoRN/reals/iso_CReals/image_Cauchy21.con" as lemma.
74 inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq12.con" as definition.
76 inline procedural "cic:/CoRN/reals/iso_CReals/image_G_as_CauchySeq21.con" as definition.
78 inline procedural "cic:/CoRN/reals/iso_CReals/f12.con" as definition.
80 inline procedural "cic:/CoRN/reals/iso_CReals/g21.con" as definition.
82 (*#****** ISO FROM R1 TO R2 ********)
84 inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_inverse_g21.con" as theorem.
86 inline procedural "cic:/CoRN/reals/iso_CReals/f12_is_surjective.con" as theorem.
88 inline procedural "cic:/CoRN/reals/iso_CReals/f12_strong_ext.con" as theorem.
90 inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_less.con" as theorem.
92 inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_plus.con" as theorem.
94 inline procedural "cic:/CoRN/reals/iso_CReals/f12_pres_mult.con" as theorem.
96 (*#********* ISO FROM R2 TO R1 **********)
98 inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_inverse_f12.con" as theorem.
100 inline procedural "cic:/CoRN/reals/iso_CReals/g21_is_surjective.con" as theorem.
102 inline procedural "cic:/CoRN/reals/iso_CReals/g21_strong_ext.con" as theorem.
104 inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_less.con" as theorem.
106 inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_plus.con" as theorem.
108 inline procedural "cic:/CoRN/reals/iso_CReals/g21_pres_mult.con" as theorem.
110 (*#** Building Homomorphisms out of f12 and g21 ***)
112 inline procedural "cic:/CoRN/reals/iso_CReals/f12_as_Homomorphism.con" as definition.
114 inline procedural "cic:/CoRN/reals/iso_CReals/g21_as_Homomorphism.con" as definition.
116 inline procedural "cic:/CoRN/reals/iso_CReals/f12_inverse_lft.con" as lemma.
118 inline procedural "cic:/CoRN/reals/iso_CReals/g21_inverse_rht.con" as lemma.
120 inline procedural "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con" as definition.
123 End Concrete_iso_between_Creals