X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fstructures%2FZsec.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Fmodel%2Fstructures%2FZsec.ma;h=b7aa226b1e3cf59977007a73a1d124a0fb99f70a;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/model/structures/Zsec.ma b/matita/contribs/CoRN-Decl/model/structures/Zsec.ma new file mode 100644 index 000000000..b7aa226b1 --- /dev/null +++ b/matita/contribs/CoRN-Decl/model/structures/Zsec.ma @@ -0,0 +1,100 @@ +(**************************************************************************) +(* ___ *) +(* ||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/Zsec". + +include "CoRN.ma". + +(* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *) + +(*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *) + +include "algebra/CLogic.ma". + +(*#* *[Z] +** About [Z] +We consider the implementation of integers as signed binary sequences (the +datatype [Z] as defined in [ZArith], in the standard library). + +***Apartness +We define the apartness as the negation of the Leibniz equality: +*) + +inline "cic:/CoRN/model/structures/Zsec/ap_Z.con". + +(* NOTATION +Infix "{#Z}" := ap_Z (no associativity, at level 90). +*) + +(*#* Some properties of apartness: +*) + +inline "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con". + +inline "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con". + +inline "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con". + +inline "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con". + +inline "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con". + +(*#* ***Addition +Some properties of the addition. [Zplus] is also defined in the standard +library. +*) + +inline "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con". + +inline "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con". + +(*#* ***Multiplication +The multiplication is extensional: +*) + +inline "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con". + +(*#* ***Miscellaneous +*) + +inline "cic:/CoRN/model/structures/Zsec/Zpos.con". + +(* begin hide *) + +coercion cic:/Coq/ZArith/BinInt/Z.ind#xpointer(1/1/2) 0 (* compounds *). + +(* end hide *) + +inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con". + +inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con". + +inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con". + +inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con". + +inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con". + +inline "cic:/CoRN/model/structures/Zsec/Zpos_pos.con". + +inline "cic:/CoRN/model/structures/Zsec/Zpos_neg.con". + +inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con". + +inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con". + +inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con". +