helm/software/matita/contribs/CoRN-Procedural/reals/Bridges_LUB.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 "CoRN.ma".
  18
  19 (* begin hide *)
  20
  21 (* file        : least_upper_bound_principle.v                     *)
  22
  23 (* version     : 1.50 - 03/05/2001                                 *)
  24
  25 (* version     : 1.00 - 27/02/2001                                 *)
  26
  27 (* author      : Milad Niqui                                       *)
  28
  29 (* language    : coq 7.0beta26feb                                  *)
  30
  31 (* dependency  : iso_CReals.v , Expon.v                            *)
  32
  33 (* description : proof of the Bridges' least upper bound principle *)
  34
  35 include "reals/iso_CReals.ma".
  36
  37 include "algebra/Expon.ma".
  38
  39 (* UNEXPORTED
  40 Section LUBP
  41 *)
  42
  43 alias id "R1" = "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var".
  44
  45 (* SUBSECTION ON GENRAL DEFINITIONS *)
  46
  47 (* UNEXPORTED
  48 Section lub_definitions
  49 *)
  50
  51 alias id "OF" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var".
  52
  53 alias id "SS" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var".
  54
  55 inline procedural "cic:/CoRN/reals/Bridges_LUB/member.con".
  56
  57 inline procedural "cic:/CoRN/reals/Bridges_LUB/Pmember.con".
  58
  59 inline procedural "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con".
  60
  61 inline procedural "cic:/CoRN/reals/Bridges_LUB/l_u_b.con".
  62
  63 inline procedural "cic:/CoRN/reals/Bridges_LUB/supremum.con".
  64
  65 inline procedural "cic:/CoRN/reals/Bridges_LUB/Psupremum.con".
  66
  67 (* the following definitions are not used in *)
  68
  69 (* this file but later we will need them     *)
  70
  71 inline procedural "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con".
  72
  73 inline procedural "cic:/CoRN/reals/Bridges_LUB/g_l_b.con".
  74
  75 inline procedural "cic:/CoRN/reals/Bridges_LUB/infimum.con".
  76
  77 inline procedural "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con".
  78
  79 (* UNEXPORTED
  80 End lub_definitions
  81 *)
  82
  83 (* MAIN SECTION *)
  84
  85 (* UNEXPORTED
  86 Section upper_bound_sequence
  87 *)
  88
  89 alias id "A" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var".
  90
  91 alias id "is_inhabitted" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var".
  92
  93 alias id "bounded_above" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var".
  94
  95 alias id "located" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var".
  96
  97 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__".
  98
  99 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__".
 100
 101 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__".
 102
 103 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__".
 104
 105 inline procedural "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con".
 106
 107 inline procedural "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con".
 108
 109 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__".
 110
 111 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__".
 112
 113 inline procedural "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con".
 114
 115 inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink23d.con".
 116
 117 inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink13d.con".
 118
 119 inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink24d.con".
 120
 121 inline procedural "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con".
 122
 123 inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con".
 124
 125 inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con".
 126
 127 (* NOTATION
 128 Notation "( p , q )" := (pairT p q).
 129 *)
 130
 131 inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con".
 132
 133 inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con".
 134
 135 inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con".
 136
 137 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__".
 138
 139 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__".
 140
 141 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__".
 142
 143 inline procedural "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con".
 144
 145 inline procedural "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con".
 146
 147 inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con".
 148
 149 inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con".
 150
 151 inline procedural "cic:/CoRN/reals/Bridges_LUB/V_increase.con".
 152
 153 inline procedural "cic:/CoRN/reals/Bridges_LUB/W_decrease.con".
 154
 155 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con".
 156
 157 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con".
 158
 159 (*  These lemma are *very* similar to those in  *)
 160
 161 (*  Cauchy_rationals_approach_reals.v           *)
 162
 163 inline procedural "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con".
 164
 165 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con".
 166
 167 inline procedural "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con".
 168
 169 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con".
 170
 171 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__".
 172
 173 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con".
 174
 175 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con".
 176
 177 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con".
 178
 179 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con".
 180
 181 inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con".
 182
 183 inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con".
 184
 185 (* Two properties of exponentiation in COrdFields *)
 186
 187 inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con".
 188
 189 inline procedural "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con".
 190
 191 (* A consequence of Archimedean property -         *)
 192
 193 (* the every basis of definition of e=lim(1+1/n)^n *)
 194
 195 inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con".
 196
 197 inline procedural "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con".
 198
 199 inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con".
 200
 201 inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con".
 202
 203 inline procedural "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con".
 204
 205 inline procedural "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con".
 206
 207 inline procedural "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con".
 208
 209 (* UNEXPORTED
 210 End upper_bound_sequence
 211 *)
 212
 213 (* UNEXPORTED
 214 End LUBP
 215 *)
 216
 217 (* end hide *)
 218