helm/software/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma

   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 set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB".
  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
  36 iso_CReals
  37 *)
  38
  39 (* INCLUDE
  40 Expon
  41 *)
  42
  43 (* UNEXPORTED
  44 Section LUBP.
  45 *)
  46
  47 inline cic:/CoRN/reals/Bridges_LUB/R1.var.
  48
  49 (* SUBSECTION ON GENRAL DEFINITIONS *)
  50
  51 (* UNEXPORTED
  52 Section lub_definitions.
  53 *)
  54
  55 inline cic:/CoRN/reals/Bridges_LUB/OF.var.
  56
  57 inline cic:/CoRN/reals/Bridges_LUB/SS.var.
  58
  59 inline cic:/CoRN/reals/Bridges_LUB/member.con.
  60
  61 inline cic:/CoRN/reals/Bridges_LUB/Pmember.con.
  62
  63 inline cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con.
  64
  65 inline cic:/CoRN/reals/Bridges_LUB/l_u_b.con.
  66
  67 inline cic:/CoRN/reals/Bridges_LUB/supremum.con.
  68
  69 inline cic:/CoRN/reals/Bridges_LUB/Psupremum.con.
  70
  71 (* the following definitions are not used in *)
  72
  73 (* this file but later we will need them     *)
  74
  75 inline cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con.
  76
  77 inline cic:/CoRN/reals/Bridges_LUB/g_l_b.con.
  78
  79 inline cic:/CoRN/reals/Bridges_LUB/infimum.con.
  80
  81 inline cic:/CoRN/reals/Bridges_LUB/Pinfimum.con.
  82
  83 (* UNEXPORTED
  84 End lub_definitions.
  85 *)
  86
  87 (* MAIN SECTION *)
  88
  89 (* UNEXPORTED
  90 Section upper_bound_sequence.
  91 *)
  92
  93 inline cic:/CoRN/reals/Bridges_LUB/A.var.
  94
  95 inline cic:/CoRN/reals/Bridges_LUB/is_inhabitted.var.
  96
  97 inline cic:/CoRN/reals/Bridges_LUB/bounded_above.var.
  98
  99 inline cic:/CoRN/reals/Bridges_LUB/located.var.
 100
 101 inline cic:/CoRN/reals/Bridges_LUB/s.con.
 102
 103 inline cic:/CoRN/reals/Bridges_LUB/Ps.con.
 104
 105 inline cic:/CoRN/reals/Bridges_LUB/b0.con.
 106
 107 inline cic:/CoRN/reals/Bridges_LUB/Pb0.con.
 108
 109 inline cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con.
 110
 111 inline cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con.
 112
 113 inline cic:/CoRN/reals/Bridges_LUB/dstart_l.con.
 114
 115 inline cic:/CoRN/reals/Bridges_LUB/dstart_r.con.
 116
 117 inline cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con.
 118
 119 inline cic:/CoRN/reals/Bridges_LUB/shrink23d.con.
 120
 121 inline cic:/CoRN/reals/Bridges_LUB/shrink13d.con.
 122
 123 inline cic:/CoRN/reals/Bridges_LUB/shrink24d.con.
 124
 125 inline cic:/CoRN/reals/Bridges_LUB/Real_Interval.con.
 126
 127 inline cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con.
 128
 129 inline cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con.
 130
 131 inline cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con.
 132
 133 inline cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con.
 134
 135 inline cic:/CoRN/reals/Bridges_LUB/dIntrvl.con.
 136
 137 inline cic:/CoRN/reals/Bridges_LUB/U.con.
 138
 139 inline cic:/CoRN/reals/Bridges_LUB/V.con.
 140
 141 inline cic:/CoRN/reals/Bridges_LUB/W.con.
 142
 143 inline cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con.
 144
 145 inline cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con.
 146
 147 inline cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con.
 148
 149 inline cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con.
 150
 151 inline cic:/CoRN/reals/Bridges_LUB/V_increase.con.
 152
 153 inline cic:/CoRN/reals/Bridges_LUB/W_decrease.con.
 154
 155 inline cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con.
 156
 157 inline 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 cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con.
 164
 165 inline cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con.
 166
 167 inline cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con.
 168
 169 inline cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con.
 170
 171 inline cic:/CoRN/reals/Bridges_LUB/B.con.
 172
 173 inline cic:/CoRN/reals/Bridges_LUB/U_minus_V.con.
 174
 175 inline cic:/CoRN/reals/Bridges_LUB/U_minus_W.con.
 176
 177 inline cic:/CoRN/reals/Bridges_LUB/U_V_upper.con.
 178
 179 inline cic:/CoRN/reals/Bridges_LUB/U_W_lower.con.
 180
 181 inline cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con.
 182
 183 inline cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con.
 184
 185 (* Two properties of exponentiation in COrdFields *)
 186
 187 inline cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con.
 188
 189 inline 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 cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con.
 196
 197 inline cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con.
 198
 199 inline cic:/CoRN/reals/Bridges_LUB/B_limit_V.con.
 200
 201 inline cic:/CoRN/reals/Bridges_LUB/B_limit_W.con.
 202
 203 inline cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con.
 204
 205 inline cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con.
 206
 207 inline 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