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

<b>let </b><font color="Maroon" title="c16">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>

<b>set </b><font color="Maroon" title="c17">GA</font> =  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> ;<br/>
<b>set </b><font color="Maroon" title="c18">x</font> = <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c19">y</font> = <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c20">yy</font> = <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>;<br/>
<b>assume </b><a NAME="E1:20"/><i><font color="Green" title="E19">A1</font></i>: 
(  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">s</font> &amp;  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c16">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5 &amp; <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_1"/>
( <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> or <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1"><b>suppose </b></a><a NAME="E1:20_1_1"/>
<font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:20_1_1"/>
 ex <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  st <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<font color="Olive" title="b1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<font color="Olive" title="b1">n</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<font color="Olive" title="b1">n</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span> &amp; ( for <font color="Olive" title="b2">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">j</font> &amp; <font color="Olive" title="b2">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 holds <br/><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b2">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<font color="Olive" title="b1">n</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b2">j</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="scmp_gcd.html#T16" target="_self" title="SCMP_GCD:th.16">Th16</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2"><b>suppose </b></a><a NAME="E1:20_1_2"/>
<font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>
 ;<br/><div class="add"><a NAME="E2:20_1_2"/><b>then </b><i><font color="Green" title="E20">A2</font></i>: 
<font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">y</font> = <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c22">pn</font> = <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="int_1.html#T16" title="INT_1:th.16">INT_1:16</a></i>;<br/><a NAME="E5:20_1_2"/><i><font color="Green" title="E21">A3</font></i>: 
<font color="Maroon" title="c22">pn</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 ;<br/><a NAME="E6:20_1_2"/><b>then </b><i><font color="Green" title="E22">A4</font></i>: 
(  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">5 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 7</span>)</span> &amp;  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4 &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 7</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c21">y</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">y</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">pn</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 11 )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:20_1_2"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E23"><i><font color="Green" title="E15">Lm4</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c23">s8</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8;<br/><i><font color="Green" title="E23">A5</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span>,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 5
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="scmp_gcd.html#T6" target="_self" title="SCMP_GCD:th.6">Th6</a></i>
;<br/><a NAME="E8:20_1_2"/><i><font color="Green" title="E24">A6</font></i>: 
 <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="ami_1.html#T81" title="AMI_1:th.81">AMI_1:81</a></i>;<br/><a NAME="E9:20_1_2"/><i><font color="Green" title="E25">A7</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>;<br/><a NAME="E10:20_1_2"/><i><font color="Green" title="E26">A8</font></i>: 
4 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E11:20_1_2"/><b>then </b><i><font color="Green" title="E27">A9</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E12:20_1_2"/><i><font color="Green" title="E28">A10</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>;<br/><b>set </b><font color="Maroon" title="c24">x1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span>;<br/><b>set </b><font color="Maroon" title="c25">y1</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span>;<br/><i><font color="Green" title="E29">A11</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<font color="Maroon" title="c21">y</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/><i><font color="Green" title="E30">A12</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <font color="Maroon" title="c21">y</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/><a NAME="E15:20_1_2"/><b>then </b><i><font color="Green" title="E31">A13</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c21">y</font>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E2:20_1_2"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="newton.html#T79" title="NEWTON:th.79">NEWTON:79</a></i>;<br/><a NAME="E16:20_1_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:20_1_2"><i><font color="Green" title="E30">A12</font></i></a>, <a class="ref" href="newton.html#T78" title="NEWTON:th.78">NEWTON:78</a></i>;<br/><b>then consider </b><font color="Maroon" title="c26">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E18:20_1_2"/><i><font color="Green" title="E32">A14</font></i>: 
(  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span>,<font color="Maroon" title="c26">m</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span>,<font color="Maroon" title="c26">m</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span>,<font color="Maroon" title="c26">m</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span> &amp; ( for <font color="Olive" title="b1">j</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">j</font> &amp; <font color="Olive" title="b1">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 holds <br/><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span>,<font color="Maroon" title="c26">m</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Olive" title="b1">j</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E7:20_1_2"><i><font color="Green" title="E23">A5</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:20_1_2"><i><font color="Green" title="E24">A6</font></i></a>, <a class="txt" href="scmp_gcd.html#E11:20_1_2"><i><font color="Green" title="E27">A9</font></i></a>, <a class="txt" href="scmp_gcd.html#E12:20_1_2"><i><font color="Green" title="E28">A10</font></i></a>, <a class="txt" href="scmp_gcd.html#E13:20_1_2"><i><font color="Green" title="E29">A11</font></i></a>, <a class="txt" href="scmp_gcd.html#E15:20_1_2"><i><font color="Green" title="E31">A13</font></i></a>, <a class="ref" href="scmp_gcd.html#T16" target="_self" title="SCMP_GCD:th.16">Th16</a></i>;<br/><b>set </b><font color="Maroon" title="c27">s9</font> =  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span>;<br/><a NAME="E19:20_1_2"/><i><font color="Green" title="E33">A15</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E18:20_1_2"><i><font color="Green" title="E32">A14</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>;<br/><i><font color="Green" title="E34">A16</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default">8 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>

<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:20_1_2"><i><font color="Green" title="E32">A14</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
;<br/><a NAME="E21:20_1_2"/><i><font color="Green" title="E35">A17</font></i>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E10:20_1_2"><i><font color="Green" title="E26">A8</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E22:20_1_2"/>
<font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><b>then </b><i><font color="Green" title="E36">A18</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span>,<font color="Maroon" title="c26">m</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:20_1_2"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E21:20_1_2"><i><font color="Green" title="E35">A17</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
;<br/><a NAME="E24:20_1_2"/>
5 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E25:20_1_2"/><b>then </b><i><font color="Green" title="E37">A19</font></i>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5
 <b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><i><font color="Green" title="E38">A20</font></i>:  <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 11 = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span>,<font color="Maroon" title="c26">m</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E18:20_1_2"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E25:20_1_2"><i><font color="Green" title="E37">A19</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E19:20_1_2"><i><font color="Green" title="E33">A15</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a>, <a class="ref" href="scmpds_1.html#D23" title="SCMPDS_1:def.23">SCMPDS_1:def 23</a></i>
;<br/><i><font color="Green" title="E39">A21</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> </span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:20_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">11 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E26:20_1_2"><i><font color="Green" title="E38">A20</font></i></a>, <a class="ref" href="scmp_gcd.html#T3" target="_self" title="SCMP_GCD:th.3">Th3</a></i>
;<br/><b>then </b><i><font color="Green" title="E40">A22</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> = 
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 13</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/><i><font color="Green" title="E41">A23</font></i>:  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default">9 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
 <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>

<br/>.= 
 <a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T14" title="AMI_1:th.14">AMI_1:14</a></i>
<br/>.= 
 <a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6</span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E28:20_1_2"><i><font color="Green" title="E40">A22</font></i></a></i>
;<br/><i><font color="Green" title="E42">A24</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span>,<a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="txt" href="scmp_gcd.html#E19:20_1_2"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="scmp_gcd.html#E20:20_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a>, <a class="ref" href="scmpds_1.html#D22" title="SCMPDS_1:def.22">SCMPDS_1:def 22</a></i>
<br/>.= 
<font color="Maroon" title="c22">pn</font>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="txt" href="scmp_gcd.html#E23:20_1_2"><i><font color="Green" title="E36">A18</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
;<br/><a NAME="E31:20_1_2"/>
 <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E22"><i><font color="Green" title="E14">Lm3</font></i></a></i>;<br/><b>then </b><i><font color="Green" title="E43">A25</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 6</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:20_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:20_1_2"><i><font color="Green" title="E32">A14</font></i></a>, <a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
;<br/> <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 10</span>)</span></span>)</span> = 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:20_1_2"><i><font color="Green" title="E41">A23</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> <span class="p1">(<span class="default">13 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E27:20_1_2"><i><font color="Green" title="E39">A21</font></i></a></i>
;<br/><b>then </b><i><font color="Green" title="E44">A26</font></i>:  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 10</span>)</span></span>)</span> = 
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="scmpds_3.html#K2" title="SCMPDS_3:func.2">inspos</a> 14</span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
 <a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E19"><i><font color="Green" title="E11">Lm1</font></i></a></i>
;<br/><div><b>hereby </b>
<div class="add"><b>take </b><font color="Maroon" title="c28">n</font> = <font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 10;<br/><b>thus </b><a NAME="E1:20_1_2_14"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<font color="Maroon" title="c28">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K5" title="SCMPDS_2:func.5">return</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E34:20_1_2"><i><font color="Green" title="E44">A26</font></i></a></i>;<br/><a NAME="E2:20_1_2_14"/><i><font color="Green" title="E45">A27</font></i>: 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <span class="p1">(<span class="default"><font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E30:20_1_2"><i><font color="Green" title="E42">A24</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>;<br/><a NAME="E3:20_1_2_14"/><b>then </b>
 <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E22"><i><font color="Green" title="E14">Lm3</font></i></a></i>;<br/><b>hence </b><a NAME="E4:20_1_2_14"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<font color="Maroon" title="c28">n</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E29:20_1_2"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:20_1_2"><i><font color="Green" title="E42">A24</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<font color="Maroon" title="c28">n</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <font color="Maroon" title="c22">pn</font>,6</span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:20_1_2"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scmp_gcd.html#E30:20_1_2"><i><font color="Green" title="E42">A24</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_1.html#K6" title="INT_1:func.6">mod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E13:20_1_2"><i><font color="Green" title="E29">A11</font></i></a>, <a class="txt" href="scmp_gcd.html#E14:20_1_2"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="scmp_gcd.html#E32:20_1_2"><i><font color="Green" title="E43">A25</font></i></a>, <a class="ref" href="scmp_gcd.html#T5" target="_self" title="SCMP_GCD:th.5">Th5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:20_1_2"><i><font color="Green" title="E20">A2</font></i></a>, <a class="ref" href="nat_d.html#T30" title="NAT_D:th.30">NAT_D:30</a></i>
;<br/><div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c29">j</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:20_1_2_14_2"/><i><font color="Green" title="E46">A28</font></i>: 
( 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c29">j</font> &amp; <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 )
 ;<br/><a NAME="E2:20_1_2_14_2"/>
<font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E9:20_1_2"><i><font color="Green" title="E25">A7</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E3:20_1_2_14_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E4:20_1_2_14_2"/><b>then </b><i><font color="Green" title="E47">A29</font></i>: 
<font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_1_2_14_2"><i><font color="Green" title="E46">A28</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:20_1_2_14_2"/>
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> 
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20_1_2_14_2"><i><font color="Green" title="E46">A28</font></i></a>, <a class="ref" href="ami_3.html#T52" title="AMI_3:th.52">AMI_3:52</a></i>;<br/><b>then </b><i><font color="Green" title="E48">A30</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 8</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E20:20_1_2"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="scmpds_2.html#T70" title="SCMPDS_2:th.70">SCMPDS_2:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span>,<font color="Maroon" title="c26">m</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T51" title="AMI_1:th.51">AMI_1:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E18:20_1_2"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:20_1_2_14_2"><i><font color="Green" title="E46">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E4:20_1_2_14_2"><i><font color="Green" title="E47">A29</font></i></a></i>
;<br/><a NAME="E7:20_1_2_14_2"/>
<font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c22">pn</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E8:20_1_2_14_2"/><b>then </b><i><font color="Green" title="E49">A31</font></i>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c26">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 9</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> </span>)</span>,2
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E2:20_1_2_14"><i><font color="Green" title="E45">A27</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:20_1_2_14_2"><i><font color="Green" title="E46">A28</font></i></a>, <a class="ref" href="ami_3.html#T52" title="AMI_3:th.52">AMI_3:52</a></i>;<br/><a NAME="E9:20_1_2_14_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,7</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span>
 <b>by </b><i><a class="txt" href="scmp_gcd.html#E1:20"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="scmp_gcd.html#E2:20_1_2"><i><font color="Green" title="E20">A2</font></i></a>, <a class="txt" href="scmp_gcd.html#E5:20_1_2"><i><font color="Green" title="E21">A3</font></i></a>, <a class="txt" href="scmp_gcd.html#E1:20_1_2_14_2"><i><font color="Green" title="E46">A28</font></i></a>, <a class="txt" href="scmp_gcd.html#E24"><i><font color="Green" title="E16">Lm5</font></i></a></i>;<br/><b>hence </b><font color="Maroon" title="c16">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,8</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E6:20_1_2"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="scmpds_2.html#T66" title="SCMPDS_2:th.66">SCMPDS_2:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c16">s</font>,<font color="Maroon" title="c28">n</font></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> <font color="Maroon" title="c29">j</font></span>)</span>
<b>by </b><i><a class="txt" href="scmp_gcd.html#E29:20_1_2"><i><font color="Green" title="E41">A23</font></i></a>, <a class="txt" href="scmp_gcd.html#E6:20_1_2_14_2"><i><font color="Green" title="E48">A30</font></i></a>, <a class="txt" href="scmp_gcd.html#E8:20_1_2_14_2"><i><font color="Green" title="E49">A31</font></i></a>, <a class="ref" href="scmpds_2.html#T59" title="SCMPDS_2:th.59">SCMPDS_2:59</a></i>
;<br/><br/></div>
<b>end;</b></div></div>
<b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

</div>
