matita/contribs/CoRN-Decl/model/structures/Qpossec.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/model/structures/Qpossec".
  18
  19 (* $Id: Qpossec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
  20
  21 (*#* printing Qpos $\mathbb{Q}^{+}$ #Q<SUP>+</SUP># *)
  22
  23 (* INCLUDE
  24 Qsec
  25 *)
  26
  27 (* INCLUDE
  28 CLogic
  29 *)
  30
  31 (*#* **About [Qpos]
  32 We will prove some lemmas concerning rationals bigger than 0.
  33
  34 ***Constants
  35 One, two and four are all bigger than zero.
  36 *)
  37
  38 inline cic:/CoRN/model/structures/Qpossec/pos_QONE.con.
  39
  40 inline cic:/CoRN/model/structures/Qpossec/pos_QTWO.con.
  41
  42 inline cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con.
  43
  44 (*#* A positive rational is not zero.
  45 *)
  46
  47 inline cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con.
  48
  49 (*#* ***Multiplication
  50 The product of two positive rationals is again positive.
  51 *)
  52
  53 inline cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con.
  54
  55 (*#* ***Inverse
  56 The inverse of a positive rational is again positive.
  57 *)
  58
  59 inline cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con.
  60
  61 (*#* ***Special multiplication
  62 Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y)
  63 &#x21A6; xy/2#. We will see that its unit is 2. Its inverse map is $x
  64 \mapsto 4/x$ #x &#x21A6; 4/x#.
  65 *)
  66
  67 inline cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con.
  68
  69 inline cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con.
  70
  71 inline cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con.
  72