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

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>set </b><font color="Maroon">i</font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1;<br/>
<b>set </b><font color="Maroon">I</font> =  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span>;<br/>
<b>set </b><font color="Maroon">FD</font> =  <a href="scmpds_7.html#K2" target="_self">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">a</font> =  <a href="scmp_gcd.html#K1">intpos</a> 3;<br/>
<b>assume </b><a NAME="E1:81"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">s</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a>   st <font color="Olive">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K2" target="_self">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span></span>)</span>,<font color="Olive">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span></span>)</span>;<br/>
<a NAME="E2:81"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/>

<b>assume </b><a NAME="E1:81_1"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<a NAME="E2:81_1"/><b>then </b>
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/>
<b>hence </b><a NAME="E3:81_1"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K2" target="_self">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 0 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, </i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E54</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="81_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:81_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font>]
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:81_2_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E2:81_2_1"/><b>then </b><i><font color="Green">E57</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/><a NAME="E3:81_2_1"/><b>then </b><i><font color="Green">E83</font></i>: 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i/>;<br/><a NAME="E4:81_2_1"/><i><font color="Green">E84</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K2">GBP</a> 
 <b>by </b><i><a class="ref" href="scmpds_7.html#T10" target="_self">Th10</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/><a NAME="E5:81_2_1"/><b>then </b><i><font color="Green">E85</font></i>: 
not  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="scmp_gcd.html#K2">GBP</a> </span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E6:81_2_1"/><i><font color="Green">E86</font></i>: 
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="scmpds_5.html#T6">SCMPDS_5:6</a></i>;<br/><div><i><font color="Green">E87</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="81_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:81_2_1_1"/><i><font color="Green">E88</font></i>: 
( ( for <font color="Olive">x</font> being   <a href="scmpds_2.html#M1">Int_position</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="scmp_gcd.html#K2">GBP</a> </span><a href="tarski.html#K1">}</a></span> holds <br/><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">x</font> ) &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  )
 ;<br/><b>set </b><font color="Maroon">t0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font>;<br/><a NAME="E2:81_2_1_1"/>
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, , <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/><a NAME="E3:81_2_1_1"/><b>then </b><i><font color="Green">E89</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/><a NAME="E4:81_2_1_1"/><b>then </b><i><font color="Green">E98</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K2">GBP</a> 
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/><b>thus </b><i><font color="Green">E99</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T45">SCMPDS_5:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_7.html#T18" target="_self">Th18</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><b>set </b><font color="Maroon">cv</font> =  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2;<br/><a NAME="E6:81_2_1_1"/>
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/><a NAME="E7:81_2_1_1"/><b>then </b><i><font color="Green">E107</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2
 <b>by </b><i><a class="ref" href="scmpds_7.html#T17" target="_self">Th17</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T45">SCMPDS_5:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><b>thus </b><a NAME="E9:81_2_1_1"/>
(  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">t</font> &amp;  <a href="scmpds_4.html#K1">Load</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="scmpds_6.html#T34">SCMPDS_6:34</a>, <a class="ref" href="scmpds_6.html#T35">SCMPDS_6:35</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:81_2_1_1_3"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="scmp_gcd.html#K2">GBP</a> </span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:81_2_1_1_3"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K2">GBP</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:81_2_1_1_3"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T19" target="_self">Th19</a></i>;<br/></div>
<b>end;</b></div></div><b>end;</b></div><b>set </b><font color="Maroon">j</font> =  <a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon">s0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font>;<br/><b>set </b><font color="Maroon">s1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/><b>set </b><font color="Maroon">s2</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/><b>set </b><font color="Maroon">l2</font> =  <a href="scmp_gcd.html#K1">intpos</a> 2;<br/><a NAME="E8:81_2_1"/><i><font color="Green">E108</font></i>: 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>;<br/><a NAME="E9:81_2_1"/><b>then </b><i><font color="Green">E109</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/><a NAME="E10:81_2_1"/><b>then </b><i><font color="Green">E110</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K2">GBP</a> 
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/><i><font color="Green">E111</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T45">SCMPDS_5:45</a></i>
<br/>.= 
0
<b>by </b><i>, <a class="ref" href="scmpds_7.html#T18" target="_self">Th18</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/><a NAME="E12:81_2_1"/><b>then </b><i><font color="Green">E112</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default">0 <a href="nat_1.html#K1">+</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/><a NAME="E13:81_2_1"/><b>then </b><i><font color="Green">E113</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 3
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E14:81_2_1"/><i><font color="Green">E114</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 2
 <b>by </b><i><a class="ref" href="scmpds_7.html#T17" target="_self">Th17</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><i><font color="Green">E115</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T23" target="_self">Th23</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T45">SCMPDS_5:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="scmpds_7.html#T17" target="_self">Th17</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><i><font color="Green">E116</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T45">SCMPDS_5:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T24" target="_self">Th24</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
<br/>.= 
<font color="Maroon">k</font>

;<br/><a NAME="E17:81_2_1"/><i><font color="Green">E117</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> </span>)</span>,2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K2">GBP</a> 
 <b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/><i><font color="Green">E118</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <a href="scmp_gcd.html#K2">GBP</a> 
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="scmpds_7.html#T19" target="_self">Th19</a>, , <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K2" target="_self">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K2" target="_self">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_7.html#T12" target="_self">Th12</a>, <a class="ref" href="scmpds_7.html#T14" target="_self">Th14</a>, <a class="ref" href="scmpds_7.html#T15" target="_self">Th15</a>, <a class="ref" href="scmpds_7.html#T16" target="_self">Th16</a>, </i>
<br/>.= 
<font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T8" target="_self">Th8</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span></span>)</span>
<b>by </b><i/>
;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:81_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1]
 ;<br/></div><b>end;</b></div>
<a NAME="E4:81"/>
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>);<br/></i>
<b>hence </b><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scmpds_7.html#K2" target="_self">for-down</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1,<span class="p3">(<span class="default"><a href="scmpds_4.html#K1">Load</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,3,1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> = 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> 0
<b>by </b><i/>
<br/>.= 
<font color="Maroon">n</font>

;<br/><br/>


</div>
