<?xml version="1.0"?>
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<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> , <font color="Maroon">p0</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="trees_4.html#M1">FinSequence</a> of  <a href="mesfunc1.html#K2">INT</a> ;<br/>





<b>assume </b><a NAME="E1:10"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">p0</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 &amp; <font color="Maroon">f</font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Maroon">s</font>,<font color="Maroon">p0</font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 ;<br/>

<b>set </b><font color="Maroon">a</font> =  <a href="scmp_gcd.html#K2">GBP</a> ;<br/>
<b>set </b><font color="Maroon">i1</font> = <a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0;<br/>
<b>set </b><font color="Maroon">i2</font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0;<br/>
<b>set </b><font color="Maroon">i3</font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">i4</font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon">t0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">I4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">t1</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">t2</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">t3</font> =  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span>,<font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">t4</font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">s</font></span>)</span>;<br/>
<a NAME="E2:10"/><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</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>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>;<br/>
<a NAME="E3:10"/><i><font color="Green">E47</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 1
 
<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">E48</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="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</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></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#T47">SCMPDS_5:47</a></i>
<br/>.= 
0
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<i><font color="Green">E63</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="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</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> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</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></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E6:10"/><i><font color="Green">E64</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <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="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">E65</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"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</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_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E8:10"/><i><font color="Green">E66</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 1 <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="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E68</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"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</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> 1</span>)</span>
<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_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<i><font color="Green">E70</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"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</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/>.= 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E11:10"/><i><font color="Green">E71</font></i>: 
 <a href="scmp_gcd.html#K2">GBP</a>  <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>, <a class="ref" href="scmp_gcd.html#D2">SCMP_GCD:def 2</a></i>;<br/>
<i><font color="Green">E72</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></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_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E13:10"/><i><font color="Green">E73</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 1 <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/>
<i><font color="Green">E74</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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> 1</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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> 1</span>)</span>
<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_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E15:10"/><i><font color="Green">E75</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> 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/>
<i><font color="Green">E76</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font>
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<i><font color="Green">E78</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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_5.html#T46">SCMPDS_5:46</a></i>
<br/>.= 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_10"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:10_10"/><i><font color="Green">E79</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> )
 ;<br/><a NAME="E2:10_10"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E3:10_10"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E4:10_10"/><b>then </b><i><font color="Green">E96</font></i>: 
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:10_10"/><b>then </b>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 3
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E6:10_10"/><b>then </b><i><font color="Green">E97</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span> <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="E7:10_10"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:10_10"/><b>then </b><i><font color="Green">E100</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span> <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="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E9:10_10"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E10:10_10"/><b>then </b><i><font color="Green">E101</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> 1
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E11:10_10"/>
<font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E12:10_10"/><b>then </b><i><font color="Green">E102</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span> <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><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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></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="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</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> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</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> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</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></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</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="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</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> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<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> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
<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> <span class="p2">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="wsierp_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E19:10"/><b>then </b>
<font color="Maroon">f</font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font>,<font color="Maroon">p0</font>
 
<b>by </b><i><a class="ref" href="scpisort.html#D1">SCPISORT:def 1</a></i>;<br/>
<a NAME="E20:10"/><b>then </b><i><font color="Green">E103</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_8.html#K2">while&lt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p5">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1</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> ,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"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p5">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</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> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K6">Sum</a> <font color="Maroon">f</font> &amp;  <a href="scmpds_8.html#K2">while&lt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1</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> ,3,1</span>)</span></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font> &amp;  <a href="scmpds_8.html#K2">while&lt;0</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,1,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <a href="scmp_gcd.html#K2">GBP</a> ,2,1</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> ,3,1</span>)</span></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a>  <a href="scmpds_4.html#K9">IExec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K2">GBP</a>  <a href="scmpds_2.html#K6">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 1</span>)</span> <a href="scmpds_2.html#K6">:=</a> 0</span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 2</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">n</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_4.html#K5">';'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> 3</span>)</span> <a href="scmpds_2.html#K6">:=</a> <span class="p3">(<span class="default"><font color="Maroon">p0</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>,<font color="Maroon">s</font> )
 
<b>by </b><i>, , , , , </i>;<br/>
<b>thus </b><a NAME="E21:10"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><a href="scpinvar.html#K1" target="_self">sum</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font></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> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="wsierp_1.html#K6">Sum</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="scpisort.html#T8">SCPISORT:8</a></i>;<br/>

<b>thus </b><a NAME="E22:10"/>
 <a href="scpinvar.html#K1" target="_self">sum</a> <font color="Maroon">n</font>,<font color="Maroon">p0</font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">s</font>
 <b>by </b><i>, <a class="ref" href="scpisort.html#T10">SCPISORT:10</a></i>;<br/>


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