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

<span class="kw">let </span><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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <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> implies ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c17">GA</font> =  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> ;<br/>
<span class="kw">assume </span><a NAME="E1:16"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
 <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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E2:16"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E4:16"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a>  <a href="scmpds_2.html#K6" title="SCMPDS_2:func.6">:=</a> 7
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E6:16"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E8:16"/>
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E10:16"/>
4 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E12:16"/>
5 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 5 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> 9
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E14:16"/>
6 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 6 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,6 <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> ,3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E16:16"/>
7 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 7 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K16" title="SCMPDS_2:func.16">Divide</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,2,<a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E18:16"/>
8 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 8 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,7 <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> ,3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E20:16"/>
9 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 9 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<span class="p1">(<span class="default">4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K22" title="SCMPDS_1:func.22">RetSP</a> </span>)</span> <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">:=</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E22:16"/>
10 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E23:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 10 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K12" title="SCMPDS_2:func.12">AddTo</a> <a href="scmp_gcd.html#K2" title="SCMP_GCD:func.2">GBP</a> ,1,4
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>  &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E24:16"/>
11 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 11 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K7" title="SCMPDS_2:func.7">saveIC</a> <a href="scmp_gcd.html#K3" title="SCMP_GCD:func.3">SBP</a> ,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span> &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E26:16"/>
12 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 12 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 7</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 &amp; <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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>  )</span><br/>

<a NAME="E28:16"/>
13 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E29:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 13 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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> </span><br/>

<a NAME="E30:16"/>
14 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T12" target="_self" title="SCMP_GCD:th.12">Th12</a>, <a class="ref" href="afinsq_1.html#T70" title="AFINSQ_1:th.70">AFINSQ_1:70</a></span>;<br/>
<span class="kw">hence </span><a NAME="E31:16"/>
<font color="Maroon" title="c16">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> 14 <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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="ref" href="scmp_gcd.html#T14" target="_self" title="SCMP_GCD:th.14">Th14</a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
