X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fstructures%2FQpossec.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fstructures%2FQpossec.ma;h=38f43ac3876a55c0703cbc053989ecfdcf0717db;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/model/structures/Qpossec.ma b/matita/contribs/CoRN-Decl/model/structures/Qpossec.ma new file mode 100644 index 000000000..38f43ac38 --- /dev/null +++ b/matita/contribs/CoRN-Decl/model/structures/Qpossec.ma @@ -0,0 +1,70 @@ +(**************************************************************************) +(* ___ *) +(* ||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+# *) + +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) +↦ xy/2#. We will see that its unit is 2. Its inverse map is $x +\mapsto 4/x$ #x ↦ 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". +