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[helm.git] / matita / contribs / CoRN-Decl / model / structures / Qpossec.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Qpossec".
+
+include "CoRN.ma".
+
+(* $Id: Qpossec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
+
+(*#* printing Qpos $\mathbb{Q}^{+}$ #Q<SUP>+</SUP># *)
+
+include "model/structures/Qsec.ma".
+
+include "algebra/CLogic.ma".
+
+(*#* **About [Qpos]
+We will prove some lemmas concerning rationals bigger than 0.
+
+***Constants
+One, two and four are all bigger than zero.
+*)
+
+inline "cic:/CoRN/model/structures/Qpossec/pos_QONE.con".
+
+inline "cic:/CoRN/model/structures/Qpossec/pos_QTWO.con".
+
+inline "cic:/CoRN/model/structures/Qpossec/pos_QFOUR.con".
+
+(*#* A positive rational is not zero.
+*)
+
+inline "cic:/CoRN/model/structures/Qpossec/pos_imp_nonzero.con".
+
+(*#* ***Multiplication
+The product of two positive rationals is again positive.
+*)
+
+inline "cic:/CoRN/model/structures/Qpossec/Qmult_pres_pos0.con".
+
+(*#* ***Inverse
+The inverse of a positive rational is again positive.
+*)
+
+inline "cic:/CoRN/model/structures/Qpossec/inv_pres_pos0.con".
+
+(*#* ***Special multiplication
+Now we will investigate the function $(x,y) \mapsto xy/2$#(x,y)
+&#x21A6; xy/2#. We will see that its unit is 2. Its inverse map is $x
+\mapsto 4/x$ #x &#x21A6; 4/x#.
+*)
+
+inline "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_rht_unit0.con".
+
+inline "cic:/CoRN/model/structures/Qpossec/QTWOpos_is_left_unit0.con".
+
+inline "cic:/CoRN/model/structures/Qpossec/multdiv2_is_inv.con".
+