<?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">sp</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">cv</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">fr</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">pp</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">pD</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="numbers.html#K5">NAT</a> ;<br/>





<b>set </b><font color="Maroon">BP</font> =  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font>;<br/>
<b>set </b><font color="Maroon">PD</font> =  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font>;<br/>
<b>set </b><font color="Maroon">PP</font> =  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font>;<br/>
<b>assume </b><a NAME="E1:86"/><i><font color="Green">E49</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> <font color="Maroon">sp</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">sp</font> &amp; <font color="Maroon">cv</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">fr</font> &amp; <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> <font color="Maroon">sp</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">fr</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">pp</font> &amp; <font color="Maroon">pp</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">pD</font> &amp; <font color="Maroon">pD</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <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> <font color="Maroon">pD</font></span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <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> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">cv</font></span>)</span> &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f</font> <a href="wsierp_1.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <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> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Olive">k</font></span>)</span> ) )
 ;<br/>

<b>set </b><font color="Maroon">i0</font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</a> 0;<br/>
<b>set </b><font color="Maroon">i1</font> = <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font>;<br/>
<b>set </b><font color="Maroon">Hi</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">i2</font> =  <a href="scmpds_2.html#K13">AddTo</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font>,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0;<br/>
<b>set </b><font color="Maroon">i3</font> =  <a href="scmpds_2.html#K12">AddTo</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1;<br/>
<b>set </b><font color="Maroon">FD</font> =  <a href="scmpds_7.html#K2" target="_self">for-down</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">cv</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span></span>)</span>;<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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">s</font>;<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="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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/>
<b>set </b><font color="Maroon">a</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> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font>;<br/>
<b>set </b><font color="Maroon">a1</font> =  <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font>;<br/>
<a NAME="E2:86"/>
<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> <font color="Maroon">sp</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">n</font> = <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> <font color="Maroon">sp</font></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/>
<a NAME="E4:86"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a></i>;<br/>
<a NAME="E5:86"/><b>then </b>
<font color="Maroon">sp</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E6:86"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E54</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> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font> = 
 <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">n</font>,<font color="Maroon">fr</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
<br/>.= 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
;<br/>
<a NAME="E8:86"/><b>then </b><i><font color="Green">E55</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> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_7.html#T8" target="_self">Th8</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E56</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#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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> <font color="Maroon">sp</font></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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">sp</font></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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">sp</font></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> <font color="Maroon">sp</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
<br/>.= 
<font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<i><font color="Green">E57</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#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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> <font color="Maroon">pp</font></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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T47">SCMPDS_5:47</a></i>
<br/>.= 
<font color="Maroon">pD</font>
<b>by </b><i><a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
;<br/>
<a NAME="E11:86"/><i><font color="Green">E83</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<a NAME="E12:86"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">pD</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E13:86"/><i><font color="Green">E85</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> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_7.html#T10" target="_self">Th10</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E86</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#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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> <font color="Maroon">pD</font></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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pD</font></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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pD</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T15" target="_self">Th15</a>, <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> <font color="Maroon">pD</font></span>)</span>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</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> <font color="Maroon">pD</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/>
<a NAME="E15:86"/><i><font color="Green">E87</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<i><font color="Green">E88</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#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font></span>)</span> = 
<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#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T12" target="_self">Th12</a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T18" target="_self">Th18</a>, <a class="ref" href="scmpds_2.html#T57">SCMPDS_2:57</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="scmpds_7.html#T10" target="_self">Th10</a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</a></i>
;<br/>
<a NAME="E17:86"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E18:86"/><b>then </b><i><font color="Green">E98</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font>
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/>
<a NAME="E19:86"/><i><font color="Green">E99</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> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</font></span>)</span>
 
<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></i>;<br/>
<i><font color="Green">E107</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#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">cv</font></span>)</span> = 
<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#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T12" target="_self">Th12</a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</font></span>)</span></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#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">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</font></span>)</span></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#T58">SCMPDS_2:58</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">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
;<br/>
<div><i><font color="Green">E108</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="86_7"><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="E1:86_7"/><i><font color="Green">E109</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font>
 ;<br/><a NAME="E2:86_7"/>
<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> <font color="Maroon">pD</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a></i>;<br/><b>then reconsider </b><font color="Maroon">m</font> = <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> <font color="Maroon">pD</font></span>)</span> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="int_1.html#T16">INT_1:16</a></i>;<br/><a NAME="E4:86_7"/><i><font color="Green">E110</font></i>: 
<font color="Maroon">pp</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E5:86_7"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:86_7"/><b>then </b><i><font color="Green">E112</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font>
 <b>by </b><i>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E7:86_7"/>
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <a class="ref" href="scmpds_7.html#T16" target="_self">Th16</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E8:86_7"/><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_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> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T10" target="_self">Th10</a>, <a class="txt" href="scmpds_7.html#E11:86"><i><font color="Green">E83</font></i></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"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span> = 
<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#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T17" target="_self">Th17</a>, <a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span>,<span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</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"><span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_7.html#E12:86"><i><font color="Green">E84</font></i></a>, <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">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_7.html#E13:86"><i><font color="Green">E85</font></i></a>, <a class="ref" href="scmpds_2.html#T58">SCMPDS_2:58</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">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">k</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">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> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">k</font></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="wsierp_1.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="nat_1.html#K1">+</a> 1</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>
<a NAME="E22:86"/><i><font color="Green">E114</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">s</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</a> 0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">s</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/>
<a NAME="E23:86"/><i><font color="Green">E115</font></i>: 
(  <a href="scmpds_7.html#K2" target="_self">for-down</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">cv</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</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"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">s</font> &amp;  <a href="scmpds_7.html#K2" target="_self">for-down</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">cv</font>,1,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font>,<span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</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"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">s</font> )
 
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <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#T17" target="_self">Th17</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#K4" target="_self">sum</a> <font color="Maroon">sp</font>,<font color="Maroon">cv</font>,<font color="Maroon">fr</font>,<font color="Maroon">pp</font>,<font color="Maroon">pD</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="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font></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> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">cv</font>,1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font>,<span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span> <a href="scmpds_4.html#K6">';'</a> <span class="p4">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p5">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</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"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></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="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<font color="Maroon">fr</font> <a href="scmpds_2.html#K11">:=</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> <font color="Maroon">pp</font></span>)</span> <a href="scmpds_2.html#K6">:=</a> <font color="Maroon">pD</font></span>)</span></span>)</span>,<font color="Maroon">s</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p3">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span></span>)</span>,<font color="Maroon">fr</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T12" target="_self">Th12</a>, , , </i>
<br/>.= 
 <a href="wsierp_1.html#K7">Sum</a> <font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="scmpds_7.html#T7" target="_self">Th7</a>, <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#T17" target="_self">Th17</a>, <a class="ref" href="scmpds_7.html#T19" target="_self">Th19</a>, , , <a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a></i>
;<br/>


</div>
