helm/software/matita/contribs/procedural/CoRN/model/structures/Qpossec.mma

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