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

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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB".
  18
  19 include "CoRN.ma".
  20
  21 (* begin hide *)
  22
  23 (* file        : least_upper_bound_principle.v                     *)
  24
  25 (* version     : 1.50 - 03/05/2001                                 *)
  26
  27 (* version     : 1.00 - 27/02/2001                                 *)
  28
  29 (* author      : Milad Niqui                                       *)
  30
  31 (* language    : coq 7.0beta26feb                                  *)
  32
  33 (* dependency  : iso_CReals.v , Expon.v                            *)
  34
  35 (* description : proof of the Bridges' least upper bound principle *)
  36
  37 include "reals/iso_CReals.ma".
  38
  39 include "algebra/Expon.ma".
  40
  41 (* UNEXPORTED
  42 Section LUBP
  43 *)
  44
  45 alias id "R1" = "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var".
  46
  47 (* SUBSECTION ON GENRAL DEFINITIONS *)
  48
  49 (* UNEXPORTED
  50 Section lub_definitions
  51 *)
  52
  53 alias id "OF" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var".
  54
  55 alias id "SS" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var".
  56
  57 inline "cic:/CoRN/reals/Bridges_LUB/member.con".
  58
  59 inline "cic:/CoRN/reals/Bridges_LUB/Pmember.con".
  60
  61 inline "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con".
  62
  63 inline "cic:/CoRN/reals/Bridges_LUB/l_u_b.con".
  64
  65 inline "cic:/CoRN/reals/Bridges_LUB/supremum.con".
  66
  67 inline "cic:/CoRN/reals/Bridges_LUB/Psupremum.con".
  68
  69 (* the following definitions are not used in *)
  70
  71 (* this file but later we will need them     *)
  72
  73 inline "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con".
  74
  75 inline "cic:/CoRN/reals/Bridges_LUB/g_l_b.con".
  76
  77 inline "cic:/CoRN/reals/Bridges_LUB/infimum.con".
  78
  79 inline "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con".
  80
  81 (* UNEXPORTED
  82 End lub_definitions
  83 *)
  84
  85 (* MAIN SECTION *)
  86
  87 (* UNEXPORTED
  88 Section upper_bound_sequence
  89 *)
  90
  91 alias id "A" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var".
  92
  93 alias id "is_inhabitted" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var".
  94
  95 alias id "bounded_above" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var".
  96
  97 alias id "located" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var".
  98
  99 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__".
 100
 101 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__".
 102
 103 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__".
 104
 105 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__".
 106
 107 inline "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con".
 108
 109 inline "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con".
 110
 111 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__".
 112
 113 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__".
 114
 115 inline "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con".
 116
 117 inline "cic:/CoRN/reals/Bridges_LUB/shrink23d.con".
 118
 119 inline "cic:/CoRN/reals/Bridges_LUB/shrink13d.con".
 120
 121 inline "cic:/CoRN/reals/Bridges_LUB/shrink24d.con".
 122
 123 inline "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con".
 124
 125 inline "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con".
 126
 127 inline "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con".
 128
 129 (* NOTATION
 130 Notation "( p , q )" := (pairT p q).
 131 *)
 132
 133 inline "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con".
 134
 135 inline "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con".
 136
 137 inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con".
 138
 139 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__".
 140
 141 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__".
 142
 143 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__".
 144
 145 inline "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con".
 146
 147 inline "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con".
 148
 149 inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con".
 150
 151 inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con".
 152
 153 inline "cic:/CoRN/reals/Bridges_LUB/V_increase.con".
 154
 155 inline "cic:/CoRN/reals/Bridges_LUB/W_decrease.con".
 156
 157 inline "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con".
 158
 159 inline "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con".
 160
 161 (*  These lemma are *very* similar to those in  *)
 162
 163 (*  Cauchy_rationals_approach_reals.v           *)
 164
 165 inline "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con".
 166
 167 inline "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con".
 168
 169 inline "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con".
 170
 171 inline "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con".
 172
 173 inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__".
 174
 175 inline "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con".
 176
 177 inline "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con".
 178
 179 inline "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con".
 180
 181 inline "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con".
 182
 183 inline "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con".
 184
 185 inline "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con".
 186
 187 (* Two properties of exponentiation in COrdFields *)
 188
 189 inline "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con".
 190
 191 inline "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con".
 192
 193 (* A consequence of Archimedean property -         *)
 194
 195 (* the every basis of definition of e=lim(1+1/n)^n *)
 196
 197 inline "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con".
 198
 199 inline "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con".
 200
 201 inline "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con".
 202
 203 inline "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con".
 204
 205 inline "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con".
 206
 207 inline "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con".
 208
 209 inline "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con".
 210
 211 (* UNEXPORTED
 212 End upper_bound_sequence
 213 *)
 214
 215 (* UNEXPORTED
 216 End LUBP
 217 *)
 218
 219 (* end hide *)
 220