<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon" title="c1">m</font> =  <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>;<br/>
<a NAME="E1:84"/><i><font color="Green" title="E51">A1</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 0</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a></i>;<br/>
<a NAME="E2:84"/><i><font color="Green" title="E52">A2</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 0</span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c3">i</font> be   <a href="ami_1.html#NM3" title="AMI_1:NM.3">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:84_1"/><i><font color="Green" title="E53">A3</font></i>: 
(  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> &amp; <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c2">n</font></span>)</span> )
 ;<br/><a NAME="E2:84_1"/><b>then </b><i><font color="Green" title="E54">A4</font></i>: 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:84"><i><font color="Green" title="E52">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:84_1"/><b>then </b><i><font color="Green" title="E55">A5</font></i>: 
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:84"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="scmpds_4.html#E1:84_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="ref" href="scmpds_2.html#T21" title="SCMPDS_2:th.21">SCMPDS_2:21</a>, <a class="ref" href="scmpds_2.html#T93" title="SCMPDS_2:th.93">SCMPDS_2:93</a></i>;<br/><b>thus </b><a NAME="E4:84_1"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:84"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="scmpds_4.html#E1:84_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="txt" href="scmpds_4.html#E2:84_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T21" title="SCMPDS_2:th.21">SCMPDS_2:21</a>, <a class="ref" href="scmpds_2.html#T93" title="SCMPDS_2:th.93">SCMPDS_2:93</a></i>;<br/><b>thus </b><a NAME="E5:84_1"/>
 <a href="ami_1.html#K19" title="AMI_1:func.19">InsCode</a> <font color="Maroon" title="c3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:84"><i><font color="Green" title="E51">A1</font></i></a>, <a class="txt" href="scmpds_4.html#E1:84_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="txt" href="scmpds_4.html#E2:84_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T21" title="SCMPDS_2:th.21">SCMPDS_2:21</a>, <a class="ref" href="scmpds_2.html#T93" title="SCMPDS_2:th.93">SCMPDS_2:93</a></i>;<br/><a NAME="E6:84_1"/>
 ex <font color="Olive" title="b1">k1</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> st <br/>( <font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <font color="Olive" title="b1">k1</font> &amp; <font color="Maroon" title="c2">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b1">k1</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_1"><b>proof </b></a><div class="add">

<b>take </b>
0
;<br/>

<b>thus </b><a NAME="E1:84_1_1"/>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:84_1"><i><font color="Green" title="E53">A3</font></i></a>, <a class="txt" href="scmpds_4.html#E2:84_1"><i><font color="Green" title="E54">A4</font></i></a>, <a class="ref" href="cqc_lang.html#T6" title="CQC_LANG:th.6">CQC_LANG:6</a>, <a class="ref" href="scmpds_2.html#T93" title="SCMPDS_2:th.93">SCMPDS_2:93</a></i>;<br/>

<b>thus </b><a NAME="E2:84_1_1"/>
<font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0
 ;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E7:84_1"/>
<font color="Maroon" title="c3">i</font> <a href="scmpds_4.html#R1" title="SCMPDS_4:pred.1">valid_at</a> <font color="Maroon" title="c2">n</font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:84_1"><i><font color="Green" title="E55">A5</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self" title="SCMPDS_4:def.11">Def11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:84"/>
 <a href="scmpds_4.html#K1" title="SCMPDS_4:func.1">Load</a> <span class="p1">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> is <a href="scmpds_4.html#V3" title="SCMPDS_4:attr.3">shiftable</a>
 <b>by </b><i><a class="ref" href="scmpds_4.html#D12" target="_self" title="SCMPDS_4:def.12">Def12</a></i>;<br/>


</div>
