<?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>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="E1:84"/><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; <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">pp</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">pD</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> )
 ;<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">I</font> = <span class="p1">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p2">(<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="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:84_1"/>
( <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> <a href="xxreal_0.html#R1">&lt;=</a> 0 or <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> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_1"><b>suppose </b></a><a NAME="E1:84_1_1"/>
<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> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:84_1_1"/>
(  <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> <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> <font color="Maroon">s</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_2"><b>suppose </b></a><a NAME="E1:84_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:84_1_2"/>
<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#T6" target="_self">Th6</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="E4:84_1_2"/><i><font color="Green">E51</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">n</font>,<font color="Maroon">cv</font> <a href="hidden.html#R1">=</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="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/><a NAME="E5:84_1_2"/>
<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">cv</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E6:84_1_2"/><b>then </b><i><font color="Green">E54</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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">cv</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#T6" target="_self">Th6</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/><a NAME="E7:84_1_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">fr</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">n</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">cv</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E8:84_1_2"/><b>then </b><i><font color="Green">E56</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">pp</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E9:84_1_2"/>
 <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">cv</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#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_7.html#T8" target="_self">Th8</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/><a NAME="E10:84_1_2"/><b>then </b><i><font color="Green">E57</font></i>: 
not  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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">cv</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E11:84_1_2"/><i><font color="Green">E83</font></i>: 
 <a href="card_1.html#K4">card</a> <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="hidden.html#R1">=</a> 2
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T9">SCMP_GCD:9</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">t</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:84_1_2_1"/><i><font color="Green">E84</font></i>: 
( ( for <font color="Olive">x</font> being   <a href="scmpds_2.html#M1">Int_position</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span></span><a href="tarski.html#K2">}</a></span> holds <br/><font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <font color="Olive">x</font> ) &amp; <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></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="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span> )
 ;<br/><b>set </b><font color="Maroon">t0</font> =  <a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font>;<br/><b>set </b><font color="Maroon">t1</font> =  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span>,<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span>;<br/><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">t</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_7.html#T15" target="_self">Th15</a>, <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="E3:84_1_2_1"/>
<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#T29">NAT_1:29</a></i>;<br/><a NAME="E4:84_1_2_1"/><b>then </b>
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <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#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_7.html#T16" target="_self">Th16</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>then </b><i><font color="Green">E86</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#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>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
<br/>.= 
<font color="Maroon">t</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>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><a NAME="E6:84_1_2_1"/><i><font color="Green">E87</font></i>: 
 <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><a NAME="E7:84_1_2_1"/>
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <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">pp</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_7.html#T16" target="_self">Th16</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>then </b><i><font color="Green">E88</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#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>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
<br/>.= 
<font color="Maroon">t</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">pp</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><a NAME="E9:84_1_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#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>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">pD</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_7.html#T15" target="_self">Th15</a>, <a class="ref" href="scmpds_7.html#T17" target="_self">Th17</a></i>;<br/><a NAME="E10:84_1_2_1"/><b>then </b><i><font color="Green">E89</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span></span>)</span>,0 <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon">pD</font> <a href="nat_1.html#K1">+</a> 0</span>)</span>
 <b>by </b><i><a class="ref" href="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/><a NAME="E11:84_1_2_1"/>
<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#T29">NAT_1:29</a></i>;<br/><a NAME="E12:84_1_2_1"/><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#T6" target="_self">Th6</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E13:84_1_2_1"/><b>then </b>
<font color="Maroon">sp</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">pp</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a>, <a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E14:84_1_2_1"/><b>then </b><i><font color="Green">E98</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span></span>)</span>,0 <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#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_7.html#T19" target="_self">Th19</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><b>thus </b><i><font color="Green">E99</font></i>: <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<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="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="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"><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 class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</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/>.= 
<font color="Maroon">t</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>
<b>by </b><i>, , <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</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"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<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="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="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"><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 class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</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">t</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">pp</font></span>)</span>
<b>by </b><i><a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a>, <a class="ref" href="scmpds_7.html#T18" target="_self">Th18</a>, <a class="ref" href="scmpds_7.html#T19" target="_self">Th19</a>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
;<br/><b>set </b><font color="Maroon">Dv</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">cv</font>;<br/><a NAME="E17:84_1_2_1"/><i><font color="Green">E108</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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">cv</font> <a href="hidden.html#R1">=</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="scmp_gcd.html#T5">SCMP_GCD:5</a></i>;<br/><a NAME="E18:84_1_2_1"/><b>then </b><i><font color="Green">E109</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</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="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">cv</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T10" target="_self">Th10</a>, <a class="ref" href="scmpds_7.html#T16" target="_self">Th16</a>, <a class="ref" href="scmp_gcd.html#T4">SCMP_GCD:4</a></i>;<br/><a NAME="E19:84_1_2_1"/><i><font color="Green">E110</font></i>: 
 <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span></span>)</span>,0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="scmpds_2.html#K3">DataLoc</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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">cv</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T6" target="_self">Th6</a>, , <a class="ref" href="scmpds_7.html#T19" target="_self">Th19</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"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<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="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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="ami_1.html#K4">Exec</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 class="p2">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pD</font></span>)</span>,0</span>)</span>,<span class="p3">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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>
<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="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>,<span class="p2">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T60">SCMPDS_2:60</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_5.html#K1">Initialized</a> <font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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>
<b>by </b><i>, <a class="ref" href="scmpds_2.html#T61">SCMPDS_2:61</a></i>
<br/>.= 
<font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="scmpds_2.html#K2">.</a> <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>
<b>by </b><i><a class="ref" href="scmpds_5.html#T40">SCMPDS_5:40</a></i>
;<br/><b>thus </b><a NAME="E21:84_1_2_1"/>
( <span class="p1">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p2">(<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="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">t</font> &amp; <span class="p1">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p2">(<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="p1">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="scmpds_6.html#T34">SCMPDS_6:34</a>, <a class="ref" href="scmpds_6.html#T35">SCMPDS_6:35</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon">y</font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>assume </b><a NAME="E1:84_1_2_1_7"/><i><font color="Green">E111</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font></span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span></span><a href="tarski.html#K2">}</a></span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_2_1_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:84_1_2_1_7_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font> )
 </span><b>by </b><i>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_2_1_7_1_1"><b>suppose </b></a><a NAME="E1:84_1_2_1_7_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">sp</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:84_1_2_1_7_1_1"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<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="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T23" target="_self">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="84_1_2_1_7_1_2"><b>suppose </b></a><a NAME="E1:84_1_2_1_7_1_2"/>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:84_1_2_1_7_1_2"/>
<span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K13">AddTo</a> <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>,<span class="p4">(<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="p3">(<span class="default"><a href="scmpds_2.html#K12">AddTo</a> <span class="p4">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">pp</font></span>)</span>,0,1</span>)</span></span>)</span>,<font color="Maroon">t</font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="scmpds_7.html#T24" target="_self">Th24</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E13:84_1_2"/>
(  <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> <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> <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="txt" href="scmpds_7.html#E10:84_1_2"><i><font color="Green">E57</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
