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

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   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 (* UNEXPORTED
  44 cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var
  45 *)
  46
  47 (* SUBSECTION ON GENRAL DEFINITIONS *)
  48
  49 (* UNEXPORTED
  50 Section lub_definitions
  51 *)
  52
  53 (* UNEXPORTED
  54 cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var
  55 *)
  56
  57 (* UNEXPORTED
  58 cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var
  59 *)
  60
  61 inline procedural "cic:/CoRN/reals/Bridges_LUB/member.con" as definition.
  62
  63 inline procedural "cic:/CoRN/reals/Bridges_LUB/Pmember.con" as definition.
  64
  65 inline procedural "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con" as definition.
  66
  67 inline procedural "cic:/CoRN/reals/Bridges_LUB/l_u_b.con" as definition.
  68
  69 inline procedural "cic:/CoRN/reals/Bridges_LUB/supremum.con" as definition.
  70
  71 inline procedural "cic:/CoRN/reals/Bridges_LUB/Psupremum.con" as definition.
  72
  73 (* the following definitions are not used in *)
  74
  75 (* this file but later we will need them     *)
  76
  77 inline procedural "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con" as definition.
  78
  79 inline procedural "cic:/CoRN/reals/Bridges_LUB/g_l_b.con" as definition.
  80
  81 inline procedural "cic:/CoRN/reals/Bridges_LUB/infimum.con" as definition.
  82
  83 inline procedural "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con" as definition.
  84
  85 (* UNEXPORTED
  86 End lub_definitions
  87 *)
  88
  89 (* MAIN SECTION *)
  90
  91 (* UNEXPORTED
  92 Section upper_bound_sequence
  93 *)
  94
  95 (* UNEXPORTED
  96 cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var
  97 *)
  98
  99 (* UNEXPORTED
 100 cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var
 101 *)
 102
 103 (* UNEXPORTED
 104 cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var
 105 *)
 106
 107 (* UNEXPORTED
 108 cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var
 109 *)
 110
 111 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__" as definition.
 112
 113 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__" as definition.
 114
 115 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__" as definition.
 116
 117 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__" as definition.
 118
 119 inline procedural "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con" as lemma.
 120
 121 inline procedural "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con" as lemma.
 122
 123 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__" as definition.
 124
 125 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__" as definition.
 126
 127 inline procedural "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con" as lemma.
 128
 129 inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink23d.con" as lemma.
 130
 131 inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink13d.con" as lemma.
 132
 133 inline procedural "cic:/CoRN/reals/Bridges_LUB/shrink24d.con" as lemma.
 134
 135 inline procedural "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con" as definition.
 136
 137 inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con" as definition.
 138
 139 inline procedural "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con" as lemma.
 140
 141 (* NOTATION
 142 Notation "( p , q )" := (pairT p q).
 143 *)
 144
 145 inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con" as definition.
 146
 147 inline procedural "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con" as lemma.
 148
 149 inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con" as definition.
 150
 151 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__" as definition.
 152
 153 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__" as definition.
 154
 155 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__" as definition.
 156
 157 inline procedural "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con" as lemma.
 158
 159 inline procedural "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con" as lemma.
 160
 161 inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con" as lemma.
 162
 163 inline procedural "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con" as lemma.
 164
 165 inline procedural "cic:/CoRN/reals/Bridges_LUB/V_increase.con" as lemma.
 166
 167 inline procedural "cic:/CoRN/reals/Bridges_LUB/W_decrease.con" as lemma.
 168
 169 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con" as lemma.
 170
 171 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con" as lemma.
 172
 173 (*  These lemma are *very* similar to those in  *)
 174
 175 (*  Cauchy_rationals_approach_reals.v           *)
 176
 177 inline procedural "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con" as lemma.
 178
 179 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con" as lemma.
 180
 181 inline procedural "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con" as lemma.
 182
 183 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con" as definition.
 184
 185 inline procedural "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__" as definition.
 186
 187 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con" as lemma.
 188
 189 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con" as lemma.
 190
 191 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con" as lemma.
 192
 193 inline procedural "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con" as lemma.
 194
 195 inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con" as lemma.
 196
 197 inline procedural "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con" as lemma.
 198
 199 (* Two properties of exponentiation in COrdFields *)
 200
 201 inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con" as lemma.
 202
 203 inline procedural "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con" as lemma.
 204
 205 (* A consequence of Archimedean property -         *)
 206
 207 (* the every basis of definition of e=lim(1+1/n)^n *)
 208
 209 inline procedural "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con" as lemma.
 210
 211 inline procedural "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con" as lemma.
 212
 213 inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con" as lemma.
 214
 215 inline procedural "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con" as lemma.
 216
 217 inline procedural "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con" as lemma.
 218
 219 inline procedural "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con" as lemma.
 220
 221 inline procedural "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con" as theorem.
 222
 223 (* UNEXPORTED
 224 End upper_bound_sequence
 225 *)
 226
 227 (* UNEXPORTED
 228 End LUBP
 229 *)
 230
 231 (* end hide *)
 232