matita/contribs/CoRN-Decl/model/structures/Qpossec.ma

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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qpossec".
  18
  19 include "CoRN.ma".
  20
  21 (* $Id: Qpossec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
  22
  23 (*#* printing Qpos $\mathbb{Q}^{+}$ #Q<SUP>+</SUP># *)
  24
  25 include "model/structures/Qsec.ma".
  26
  27 include "algebra/CLogic.ma".
  28
  29 (*#* **About [Qpos]
  30 We will prove some lemmas concerning rationals bigger than 0.
  31
  32 ***Constants
  33 One, two and four are all bigger than zero.
  34 *)
  35
  36 inline "cic:/CoRN/model/structures/Qpossec/pos_QONE.con".
  37
  38 inline "cic:/CoRN/model/structures/Qpossec/pos_QTWO.con".
  39
  40 inline "cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con".
  41
  42 (*#* A positive rational is not zero.
  43 *)
  44
  45 inline "cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con".
  46
  47 (*#* ***Multiplication
  48 The product of two positive rationals is again positive.
  49 *)
  50
  51 inline "cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con".
  52
  53 (*#* ***Inverse
  54 The inverse of a positive rational is again positive.
  55 *)
  56
  57 inline "cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con".
  58
  59 (*#* ***Special multiplication
  60 Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y)
  61 &#x21A6; xy/2#. We will see that its unit is 2. Its inverse map is $x
  62 \mapsto 4/x$ #x &#x21A6; 4/x#.
  63 *)
  64
  65 inline "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con".
  66
  67 inline "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con".
  68
  69 inline "cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con".
  70