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

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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 set "baseuri" "cic:/matita/CoRN-Decl/reals/R_morphism".
  18
  19 (* begin hide *)
  20
  21 (* In this file a notion of morphism between two arbitrary real number
  22    structures, is introduced together with te proofs that this notion of
  23    morphism preserves the basic algebraic structure. *)
  24
  25 (* INCLUDE
  26 CReals
  27 *)
  28
  29 (* This comes from CReals1.v *)
  30
  31 inline cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con.
  32
  33 (* UNEXPORTED
  34 Section morphism.
  35 *)
  36
  37 inline cic:/CoRN/reals/R_morphism/R1.var.
  38
  39 inline cic:/CoRN/reals/R_morphism/R2.var.
  40
  41 (* UNEXPORTED
  42 Section morphism_details.
  43 *)
  44
  45 inline cic:/CoRN/reals/R_morphism/phi.var.
  46
  47 inline cic:/CoRN/reals/R_morphism/p1.var.
  48
  49 inline cic:/CoRN/reals/R_morphism/p2.var.
  50
  51 inline cic:/CoRN/reals/R_morphism/f1.var.
  52
  53 inline cic:/CoRN/reals/R_morphism/f2.var.
  54
  55 inline cic:/CoRN/reals/R_morphism/g1.var.
  56
  57 inline cic:/CoRN/reals/R_morphism/g2.var.
  58
  59 inline cic:/CoRN/reals/R_morphism/fun_pres_relation.con.
  60
  61 inline cic:/CoRN/reals/R_morphism/fun_pres_un_fun.con.
  62
  63 inline cic:/CoRN/reals/R_morphism/fun_pres_bin_fun.con.
  64
  65 (*
  66 Definition fun_pres_partial_fun:=(x:R1;H1:x[#]Zero;H2:(phi x)[#]Zero)
  67 (phi (nzinj R1 (i1 (nzpro R1 x H1))))[=](nzinj R2 (i2 (nzpro R2 (phi x) H2))).
  68 *)
  69
  70 inline cic:/CoRN/reals/R_morphism/fun_pres_Lim.con.
  71
  72 (* UNEXPORTED
  73 End morphism_details.
  74 *)
  75
  76 inline cic:/CoRN/reals/R_morphism/Homomorphism.ind.
  77
  78 (* This might be useful later...
  79 Definition Homo_as_CSetoid_fun:=
  80     [f:Homomorphism]
  81          (Build_CSetoid_fun R1 R2 f
  82            (fun_strext_imp_wd R1 R2 f (!map_strext f))
  83            (!map_strext f)
  84           ).
  85 *****************)
  86
  87 inline cic:/CoRN/reals/R_morphism/map_strext_unfolded.con.
  88
  89 inline cic:/CoRN/reals/R_morphism/map_wd_unfolded.con.
  90
  91 inline cic:/CoRN/reals/R_morphism/map_pres_less_unfolded.con.
  92
  93 inline cic:/CoRN/reals/R_morphism/map_pres_plus_unfolded.con.
  94
  95 inline cic:/CoRN/reals/R_morphism/map_pres_mult_unfolded.con.
  96
  97 (* Now we start to derive some useful properties of a Homomorphism *)
  98
  99 inline cic:/CoRN/reals/R_morphism/map_pres_zero.con.
 100
 101 inline cic:/CoRN/reals/R_morphism/map_pres_zero_unfolded.con.
 102
 103 inline cic:/CoRN/reals/R_morphism/map_pres_minus.con.
 104
 105 inline cic:/CoRN/reals/R_morphism/map_pres_minus_unfolded.con.
 106
 107 inline cic:/CoRN/reals/R_morphism/map_pres_apartness.con.
 108
 109 (* Merely a useful special case *)
 110
 111 inline cic:/CoRN/reals/R_morphism/map_pres_ap_zero.con.
 112
 113 inline cic:/CoRN/reals/R_morphism/map_pres_one.con.
 114
 115 inline cic:/CoRN/reals/R_morphism/map_pres_one_unfolded.con.
 116
 117 (* I will not use the following lemma *)
 118
 119 inline cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con.
 120
 121 (* UNEXPORTED
 122 End morphism.
 123 *)
 124
 125 (* UNEXPORTED
 126 Section composition.
 127 *)
 128
 129 inline cic:/CoRN/reals/R_morphism/R1.var.
 130
 131 inline cic:/CoRN/reals/R_morphism/R2.var.
 132
 133 inline cic:/CoRN/reals/R_morphism/R3.var.
 134
 135 inline cic:/CoRN/reals/R_morphism/f.var.
 136
 137 inline cic:/CoRN/reals/R_morphism/g.var.
 138
 139 inline cic:/CoRN/reals/R_morphism/compose.con.
 140
 141 inline cic:/CoRN/reals/R_morphism/compose_strext.con.
 142
 143 inline cic:/CoRN/reals/R_morphism/compose_pres_less.con.
 144
 145 inline cic:/CoRN/reals/R_morphism/compose_pres_plus.con.
 146
 147 inline cic:/CoRN/reals/R_morphism/compose_pres_mult.con.
 148
 149 inline cic:/CoRN/reals/R_morphism/compose_pres_Lim.con.
 150
 151 inline cic:/CoRN/reals/R_morphism/Compose.con.
 152
 153 (* UNEXPORTED
 154 End composition.
 155 *)
 156
 157 (* UNEXPORTED
 158 Section isomorphism.
 159 *)
 160
 161 inline cic:/CoRN/reals/R_morphism/R1.var.
 162
 163 inline cic:/CoRN/reals/R_morphism/R2.var.
 164
 165 (* UNEXPORTED
 166 Section identity_map.
 167 *)
 168
 169 inline cic:/CoRN/reals/R_morphism/R3.var.
 170
 171 inline cic:/CoRN/reals/R_morphism/f.var.
 172
 173 inline cic:/CoRN/reals/R_morphism/map_is_id.con.
 174
 175 (* UNEXPORTED
 176 End identity_map.
 177 *)
 178
 179 inline cic:/CoRN/reals/R_morphism/Isomorphism.ind.
 180
 181 (* UNEXPORTED
 182 End isomorphism.
 183 *)
 184
 185 (* UNEXPORTED
 186 Section surjective_map.
 187 *)
 188
 189 inline cic:/CoRN/reals/R_morphism/R1.var.
 190
 191 inline cic:/CoRN/reals/R_morphism/R2.var.
 192
 193 inline cic:/CoRN/reals/R_morphism/f.var.
 194
 195 inline cic:/CoRN/reals/R_morphism/map_is_surjective.con.
 196
 197 (* UNEXPORTED
 198 End surjective_map.
 199 *)
 200
 201 (* UNEXPORTED
 202 Section simplification.
 203 *)
 204
 205 inline cic:/CoRN/reals/R_morphism/R1.var.
 206
 207 inline cic:/CoRN/reals/R_morphism/R2.var.
 208
 209 inline cic:/CoRN/reals/R_morphism/f.var.
 210
 211 inline cic:/CoRN/reals/R_morphism/H1.var.
 212
 213 inline cic:/CoRN/reals/R_morphism/f_well_def.con.
 214
 215 (* UNEXPORTED
 216 Section with_less.
 217 *)
 218
 219 inline cic:/CoRN/reals/R_morphism/H2.var.
 220
 221 inline cic:/CoRN/reals/R_morphism/less_pres_f.con.
 222
 223 inline cic:/CoRN/reals/R_morphism/leEq_pres_f.con.
 224
 225 inline cic:/CoRN/reals/R_morphism/f_pres_leEq.con.
 226
 227 inline cic:/CoRN/reals/R_morphism/f_pres_apartness.con.
 228
 229 (* UNEXPORTED
 230 End with_less.
 231 *)
 232
 233 (* UNEXPORTED
 234 Section with_plus.
 235 *)
 236
 237 inline cic:/CoRN/reals/R_morphism/H3.var.
 238
 239 inline cic:/CoRN/reals/R_morphism/f_pres_Zero.con.
 240
 241 inline cic:/CoRN/reals/R_morphism/f_pres_minus.con.
 242
 243 inline cic:/CoRN/reals/R_morphism/f_pres_min.con.
 244
 245 (* UNEXPORTED
 246 End with_plus.
 247 *)
 248
 249 (* UNEXPORTED
 250 Section with_plus_less.
 251 *)
 252
 253 inline cic:/CoRN/reals/R_morphism/H2.var.
 254
 255 inline cic:/CoRN/reals/R_morphism/H3.var.
 256
 257 inline cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con.
 258
 259 (* UNEXPORTED
 260 Section surjectivity_helps.
 261 *)
 262
 263 inline cic:/CoRN/reals/R_morphism/f_surj.var.
 264
 265 inline cic:/CoRN/reals/R_morphism/f_pres_Lim.con.
 266
 267 (* UNEXPORTED
 268 End surjectivity_helps.
 269 *)
 270
 271 (* UNEXPORTED
 272 Section with_mult_plus_less.
 273 *)
 274
 275 inline cic:/CoRN/reals/R_morphism/H4.var.
 276
 277 inline cic:/CoRN/reals/R_morphism/f_pres_one.con.
 278
 279 inline cic:/CoRN/reals/R_morphism/f_pres_inv.con.
 280
 281 inline cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con.
 282
 283 (* UNEXPORTED
 284 End with_mult_plus_less.
 285 *)
 286
 287 (* UNEXPORTED
 288 End with_plus_less.
 289 *)
 290
 291 (* UNEXPORTED
 292 End simplification.
 293 *)
 294
 295 (* end hide *)
 296