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

<span class="kw">let </span><font color="Maroon" title="c16">p</font> be   <a href="memstr_0.html#NM4" title="MEMSTR_0:NM.4">FinPartState</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b2">y</font> <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="Olive" title="b1">x</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Olive" title="b2">y</font> &amp; <font color="Maroon" title="c16">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) holds <br/> <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> is  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c17">x</font>, <font color="Maroon" title="c18">y</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c18">y</font> <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="c17">x</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c18">y</font> &amp; <font color="Maroon" title="c16">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>) implies  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> is  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a>  )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c19">GA</font> =  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c20">a</font> =  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9;<br/>
<span class="kw">set </span><font color="Maroon" title="c21">b</font> =  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:25"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
<font color="Maroon" title="c18">y</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E2:25"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c17">x</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c18">y</font>
 <span class="kw">and </span><br/><a NAME="E3:25"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
<font color="Maroon" title="c16">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span>) <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> (<font color="Maroon" title="c17">x</font>,<font color="Maroon" title="c18">y</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> is  <a href="scmp_gcd.html#K4" title="SCMP_GCD:func.4">GCD-Algorithm</a>  <a href="extpro_1.html#V4" title="EXTPRO_1:attr.4">-autonomic</a> </span><br/>

<a NAME="E4:25"/><span class="lab"><font color="Green" title="E24">A4</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c16">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="funct_4.html#T62" title="FUNCT_4:th.62">FUNCT_4:62</a></span>;<br/>
<a NAME="E5:25"/>
(  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  &amp;  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#D2" title="SCMPDS_2:def.2">SCMPDS_2:def 2</a></span>;<br/>
<a NAME="E6:25"/><span class="kw">then </span>
(  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>  &amp;  <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T84" title="SCMPDS_2:th.84">SCMPDS_2:84</a></span>;<br/>
<a NAME="E7:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A5</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:25"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T32" title="ZFMISC_1:th.32">ZFMISC_1:32</a></span>;<br/>
<a NAME="E8:25"/>
 not  <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#T3" title="STRUCT_0:th.3">STRUCT_0:3</a></span>;<br/>
<a NAME="E9:25"/><span class="kw">then </span>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T50" title="ZFMISC_1:th.50">ZFMISC_1:50</a></span>;<br/>
<a NAME="E10:25"/><span class="kw">then </span>
 <a href="memstr_0.html#NK3" title="MEMSTR_0:NK.3">Data-Locations</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
;<br/>
<a NAME="E11:25"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c16">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:25"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="ref" href="xboole_1.html#T63" title="XBOOLE_1:th.63">XBOOLE_1:63</a></span>;<br/>
<a NAME="E12:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A7</font></span>: 
<font color="Maroon" title="c16">p</font> is  <a href="memstr_0.html#V3" title="MEMSTR_0:attr.3">data-only</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#D6" title="MEMSTR_0:def.6">MEMSTR_0:def 6</a></span>;<br/>
<a NAME="E13:25"/>
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 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> <font color="Maroon" title="c16">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:25"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E14:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">B12</font></span>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 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> <font color="Maroon" title="c16">p</font>
 
;<br/>
<a NAME="E15:25"/>
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 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> <font color="Maroon" title="c16">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:25"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>;<br/>
<a NAME="E16:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">B13</font></span>: 
 <a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 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> <font color="Maroon" title="c16">p</font>
 
;<br/>
<a NAME="E17:25"/><span class="lab"><font color="Green" title="E29">I2</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>;<br/>
<a NAME="E18:25"/><span class="lab"><font color="Green" title="E30">A14</font></span>: 
 for <font color="Olive" title="b1">t</font> being   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  st  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">t</font> holds <br/>( <font color="Olive" title="b1">t</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Olive" title="b1">t</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c22">t</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">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="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c22">t</font> implies ( <font color="Maroon" title="c22">t</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Maroon" title="c22">t</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:25_1"/><span class="lab"><font color="Green" title="E31">A15</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c22">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c22">t</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> &amp; <font color="Maroon" title="c22">t</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y</font> )</span><br/>

<a NAME="E2:25_1"/>
<font color="Maroon" title="c16">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c16">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:25"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="ref" href="memstr_0.html#T7" title="MEMSTR_0:th.7">MEMSTR_0:7</a></span>;<br/>
<a NAME="E3:25_1"/><span class="kw">then </span>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c16">p</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:25"><span class="lab"><font color="Green" title="E29">I2</font></span></a>, <a class="ref" href="memstr_0.html#T4" title="MEMSTR_0:th.4">MEMSTR_0:4</a></span>;<br/>
<a NAME="E4:25_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T32" title="FUNCT_4:th.32">FUNCT_4:32</a></span>;<br/>
<a NAME="E5:25_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font>
 
;<br/>
<a NAME="E6:25_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A16</font></span>: 
<font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c22">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25_1"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c22">t</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> 9</span>)</span> = 
<font color="Maroon" title="c16">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:25"><span class="lab"><font color="Green" title="E27">B12</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c16">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>

<br/>.= 
<font color="Maroon" title="c17">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a>, <a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c22">t</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c22">t</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> 10</span>)</span> = 
<font color="Maroon" title="c16">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:25_1"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E16:25"><span class="lab"><font color="Green" title="E28">B13</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
<font color="Maroon" title="c16">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span>

<br/>.= 
<font color="Maroon" title="c18">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="ref" href="funct_4.html#T63" title="FUNCT_4:th.63">FUNCT_4:63</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">let </span><font color="Maroon" title="c22">P1</font>, <font color="Maroon" title="c23">P2</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D10" title="EXTPRO_1:def.10">EXTPRO_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <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="c22">P1</font> or  not  <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="c23">P2</font> or  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>1</sub></font> or  not  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>2</sub></font> or  for <font color="Olive">b<sub>3</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E19:25"/><span class="lab"><font color="Green" title="E31">A17</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="c22">P1</font> &amp;  <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="c23">P2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   holds <br/>(  not  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>1</sub></font> or  not  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>2</sub></font> or  for <font color="Olive">b<sub>3</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">let </span><font color="Maroon" title="c24">s1</font>, <font color="Maroon" title="c25">s2</font> be   <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">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="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c24">s1</font> or  not  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c25">s2</font> or  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E20:25"/><span class="lab"><font color="Green" title="E32">A18</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c24">s1</font>
 <span class="kw">and </span><br/><a NAME="E21:25"/><span class="lab"><font color="Green" title="E33">A19</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c25">s2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span></span><br/>

<a NAME="E22:25"/>
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c24">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:25"><span class="lab"><font color="Green" title="E32">A18</font></span></a></span>;<br/>
<a NAME="E23:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">B20</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c24">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T50" title="MEMSTR_0:th.50">MEMSTR_0:50</a></span>;<br/>
<a NAME="E24:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">C20</font></span>: 
<font color="Maroon" title="c24">s1</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T29" title="MEMSTR_0:th.29">MEMSTR_0:29</a></span>;<br/>
<a NAME="E25:25"/><span class="lab"><font color="Green" title="E36">A23</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="c22">P1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:25"><span class="lab"><font color="Green" title="E31">A17</font></span></a></span>;<br/>
<a NAME="E26:25"/>
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c25">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:25"><span class="lab"><font color="Green" title="E33">A19</font></span></a></span>;<br/>
<a NAME="E27:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">B24</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">Start-At</a> (<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c25">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T50" title="MEMSTR_0:th.50">MEMSTR_0:50</a></span>;<br/>
<a NAME="E28:25"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">C24</font></span>: 
<font color="Maroon" title="c25">s2</font> is  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T29" title="MEMSTR_0:th.29">MEMSTR_0:29</a></span>;<br/>
<a NAME="E29:25"/><span class="lab"><font color="Green" title="E39">A26</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="c23">P2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:25"><span class="lab"><font color="Green" title="E31">A17</font></span></a></span>;<br/>
<a NAME="E30:25"/><span class="lab"><font color="Green" title="E40">A27</font></span>: 
<font color="Maroon" title="c24">s1</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:25"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E20:25"><span class="lab"><font color="Green" title="E32">A18</font></span></a></span>;<br/>
<a NAME="E31:25"/><span class="lab"><font color="Green" title="E41">A28</font></span>: 
<font color="Maroon" title="c24">s1</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:25"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E20:25"><span class="lab"><font color="Green" title="E32">A18</font></span></a></span>;<br/>
<a NAME="E32:25"/><span class="lab"><font color="Green" title="E42">A29</font></span>: 
<font color="Maroon" title="c25">s2</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:25"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E21:25"><span class="lab"><font color="Green" title="E33">A19</font></span></a></span>;<br/>
<a NAME="E33:25"/><span class="lab"><font color="Green" title="E43">A30</font></span>: 
<font color="Maroon" title="c25">s2</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:25"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E21:25"><span class="lab"><font color="Green" title="E33">A19</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c26">s4</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4);<br/>
<span class="kw">set </span><font color="Maroon" title="c27">t4</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4);<br/>
<a NAME="E34:25"/><span class="lab"><font color="Green" title="E44">A32</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E24:25"><span class="lab"><font color="Green" title="E35">C20</font></span></a></span>;<br/>
<a NAME="E35:25"/><span class="lab"><font color="Green" title="E45">A33</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E24:25"><span class="lab"><font color="Green" title="E35">C20</font></span></a></span>;<br/>
<a NAME="E36:25"/><span class="lab"><font color="Green" title="E46">A34</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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> 7
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E24:25"><span class="lab"><font color="Green" title="E35">C20</font></span></a></span>;<br/>
<a NAME="E37:25"/><span class="lab"><font color="Green" title="E47">A35</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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">7 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E24:25"><span class="lab"><font color="Green" title="E35">C20</font></span></a></span>;<br/>
<a NAME="E38:25"/><span class="lab"><font color="Green" title="E48">A36</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">s1</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> 9</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E24:25"><span class="lab"><font color="Green" title="E35">C20</font></span></a></span>;<br/>
<a NAME="E39:25"/><span class="lab"><font color="Green" title="E49">A37</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">s1</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> 10</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E24:25"><span class="lab"><font color="Green" title="E35">C20</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E50">A38</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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">7 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:25"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="ref" href="scmp_gcd.html#T1" target="_self" title="SCMP_GCD:th.1">Th5</a></span>
<br/>.= 
<font color="Maroon" title="c18">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:25"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E20:25"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E39:25"><span class="lab"><font color="Green" title="E49">A37</font></span></a></span>
;<br/>
<a NAME="E41:25"/><span class="lab"><font color="Green" title="E51">A39</font></span>: 
 <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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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">7 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:25"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="ref" href="scmp_gcd.html#T1" target="_self" title="SCMP_GCD:th.1">Th5</a></span>;<br/>
<a NAME="E42:25"/><span class="lab"><font color="Green" title="E52">A41</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="txt" href="#E28:25"><span class="lab"><font color="Green" title="E38">C24</font></span></a></span>;<br/>
<a NAME="E43:25"/><span class="lab"><font color="Green" title="E53">A42</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="txt" href="#E28:25"><span class="lab"><font color="Green" title="E38">C24</font></span></a></span>;<br/>
<a NAME="E44:25"/><span class="lab"><font color="Green" title="E54">A43</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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> 7
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="txt" href="#E28:25"><span class="lab"><font color="Green" title="E38">C24</font></span></a></span>;<br/>
<a NAME="E45:25"/><span class="lab"><font color="Green" title="E55">A44</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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">7 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="txt" href="#E28:25"><span class="lab"><font color="Green" title="E38">C24</font></span></a></span>;<br/>
<a NAME="E46:25"/><span class="lab"><font color="Green" title="E56">A45</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">s2</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> 9</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="txt" href="#E28:25"><span class="lab"><font color="Green" title="E38">C24</font></span></a></span>;<br/>
<a NAME="E47:25"/><span class="lab"><font color="Green" title="E57">A46</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">s2</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> 10</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmp_gcd.html#T11" target="_self" title="SCMP_GCD:th.11">Th15</a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="txt" href="#E28:25"><span class="lab"><font color="Green" title="E38">C24</font></span></a></span>;<br/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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">7 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:25"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="ref" href="scmp_gcd.html#T1" target="_self" title="SCMP_GCD:th.1">Th5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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="kw">by</span> <span class="lab"><a class="txt" href="#E18:25"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E21:25"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E40:25"><span class="lab"><font color="Green" title="E50">A38</font></span></a>, <a class="txt" href="#E47:25"><span class="lab"><font color="Green" title="E57">A46</font></span></a></span>
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c28">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E50:25"/><span class="lab"><font color="Green" title="E58">A47</font></span>: 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c22">P1</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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>
 <span class="kw">and </span><br/><a NAME="E51:25"/><span class="lab"><font color="Green" title="E59">A48</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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>
 <span class="kw">and </span><br/><a NAME="E52:25"/><span class="lab"><font color="Green" title="E60">A49</font></span>: 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c23">P2</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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>
 <span class="kw">and </span><br/><a NAME="E53:25"/><span class="lab"><font color="Green" title="E61">A50</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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>
 <span class="kw">and </span><br/><a NAME="E54:25"/><span class="lab"><font color="Green" title="E62">A51</font></span>: 
 for <font color="Olive" title="b1">j</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS: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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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="Olive" title="b1">j</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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="Olive" title="b1">j</font></span>)</span> )
 <span class="kw">and </span><br/><a NAME="E55:25"/><span class="lab"><font color="Green" title="E63">A52</font></span>: 
 for <font color="Olive" title="b1">k</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/>  for <font color="Olive" title="b2">c</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>   st <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c28">n</font> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b2">c</font> holds <br/>(  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<font color="Olive" title="b1">k</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b2">c</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E2:25"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E18:25"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E21:25"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E30:25"><span class="lab"><font color="Green" title="E40">A27</font></span></a>, <a class="txt" href="#E34:25"><span class="lab"><font color="Green" title="E44">A32</font></span></a>, <a class="txt" href="#E35:25"><span class="lab"><font color="Green" title="E45">A33</font></span></a>, <a class="txt" href="#E36:25"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="txt" href="#E38:25"><span class="lab"><font color="Green" title="E48">A36</font></span></a>, <a class="txt" href="#E40:25"><span class="lab"><font color="Green" title="E50">A38</font></span></a>, <a class="txt" href="#E41:25"><span class="lab"><font color="Green" title="E51">A39</font></span></a>, <a class="txt" href="#E42:25"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="txt" href="#E43:25"><span class="lab"><font color="Green" title="E53">A42</font></span></a>, <a class="txt" href="#E44:25"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="txt" href="#E46:25"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="txt" href="scmp_gcd.html#E26"><span class="lab"><font color="Green" title="E19">Lm8</font></span></a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E64">A53</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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"><span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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></span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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> <span class="p2">(<span class="default">7 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:25"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="txt" href="#E51:25"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="ref" href="scmp_gcd.html#T1" target="_self" title="SCMP_GCD:th.1">Th5</a>, <a class="ref" href="scmpds_1.html#D21" title="SCMPDS_1:def.21">SCMPDS_1:def 21</a></span>
<br/>.= 
2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:25"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="txt" href="#E37:25"><span class="lab"><font color="Green" title="E47">A35</font></span></a>, <a class="txt" href="#E54:25"><span class="lab"><font color="Green" title="E62">A51</font></span></a>, <a class="ref" href="scmpds_1.html#D21" title="SCMPDS_1:def.21">SCMPDS_1:def 21</a></span>
;<br/>
<span class="lab"><font color="Green" title="E65">A54</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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"><span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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></span>)</span>,<a href="scmpds_1.html#K23" title="SCMPDS_1:func.23">RetIC</a>)</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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> <span class="p2">(<span class="default">7 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:25"><span class="lab"><font color="Green" title="E54">A43</font></span></a>, <a class="txt" href="#E53:25"><span class="lab"><font color="Green" title="E61">A50</font></span></a>, <a class="ref" href="scmp_gcd.html#T1" target="_self" title="SCMP_GCD:th.1">Th5</a>, <a class="ref" href="scmpds_1.html#D21" title="SCMPDS_1:def.21">SCMPDS_1:def 21</a></span>
<br/>.= 
2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:25"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="txt" href="#E45:25"><span class="lab"><font color="Green" title="E55">A44</font></span></a>, <a class="txt" href="#E54:25"><span class="lab"><font color="Green" title="E62">A51</font></span></a>, <a class="ref" href="scmpds_1.html#D21" title="SCMPDS_1:def.21">SCMPDS_1:def 21</a></span>
;<br/>
<a NAME="E58:25"/><span class="lab"><font color="Green" title="E66">A55</font></span>: 
<font color="Maroon" title="c22">P1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">P1</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>;<br/>
<span class="lab"><font color="Green" title="E67">A57</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<font color="Maroon" title="c22">P1</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<font color="Maroon" title="c28">n</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<font color="Maroon" title="c28">n</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E50:25"><span class="lab"><font color="Green" title="E58">A47</font></span></a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E68">A58</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<font color="Maroon" title="c28">n</font>)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p0">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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></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
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></span>
<br/>.= 
2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:25"><span class="lab"><font color="Green" title="E64">A53</font></span></a>, <a class="ref" href="absvalue.html#T29" title="ABSVALUE:th.29">ABSVALUE:29</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E69">A59</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c22">P1</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>) = 
<font color="Maroon" title="c22">P1</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:25"><span class="lab"><font color="Green" title="E66">A55</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c22">P1</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4

<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">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="scmp_gcd.html#E15"><span class="lab"><font color="Green" title="E9">Lm1</font></span></a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a></span>
;<br/>
<a NAME="E62:25"/><span class="lab"><font color="Green" title="E70">A61</font></span>: 
<font color="Maroon" title="c23">P2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">P2</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p3">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>;<br/>
<span class="lab"><font color="Green" title="E71">A63</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<font color="Maroon" title="c23">P2</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<font color="Maroon" title="c28">n</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<font color="Maroon" title="c28">n</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:25"><span class="lab"><font color="Green" title="E60">A49</font></span></a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E72">A64</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p4">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<font color="Maroon" title="c28">n</font>)</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="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p0">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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></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
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></span>
<br/>.= 
2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:25"><span class="lab"><font color="Green" title="E65">A54</font></span></a>, <a class="ref" href="absvalue.html#T29" title="ABSVALUE:th.29">ABSVALUE:29</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E73">A65</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c23">P2</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>) = 
<font color="Maroon" title="c23">P2</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:25"><span class="lab"><font color="Green" title="E70">A61</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c23">P2</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 4

<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">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="scmp_gcd.html#E15"><span class="lab"><font color="Green" title="E9">Lm1</font></span></a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a></span>
;<br/>
<a NAME="E66:25"/><span class="lab"><font color="Green" title="E74">A68</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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> 9</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:25"><span class="lab"><font color="Green" title="E37">B24</font></span></a>, <a class="txt" href="#E30:25"><span class="lab"><font color="Green" title="E40">A27</font></span></a>, <a class="txt" href="#E32:25"><span class="lab"><font color="Green" title="E42">A29</font></span></a>, <a class="txt" href="scmp_gcd.html#E27"><span class="lab"><font color="Green" title="E20">Lm9</font></span></a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E23:25"><span class="lab"><font color="Green" title="E34">B20</font></span></a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a></span>;<br/>
<a NAME="E67:25"/><span class="lab"><font color="Green" title="E75">A69</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</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> 10</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:25"><span class="lab"><font color="Green" title="E37">B24</font></span></a>, <a class="txt" href="#E31:25"><span class="lab"><font color="Green" title="E41">A28</font></span></a>, <a class="txt" href="#E33:25"><span class="lab"><font color="Green" title="E43">A30</font></span></a>, <a class="txt" href="scmp_gcd.html#E27"><span class="lab"><font color="Green" title="E20">Lm9</font></span></a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E23:25"><span class="lab"><font color="Green" title="E34">B20</font></span></a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E76">A70</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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> 9</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:25"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:25"><span class="lab"><font color="Green" title="E63">A52</font></span></a>, <a class="txt" href="#E66:25"><span class="lab"><font color="Green" title="E74">A68</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E63:25"><span class="lab"><font color="Green" title="E71">A63</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></span>
;<br/>
<span class="lab"><font color="Green" title="E77">A71</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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> 10</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:25"><span class="lab"><font color="Green" title="E67">A57</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:25"><span class="lab"><font color="Green" title="E63">A52</font></span></a>, <a class="txt" href="#E67:25"><span class="lab"><font color="Green" title="E75">A69</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E63:25"><span class="lab"><font color="Green" title="E71">A63</font></span></a>, <a class="ref" href="ami_3.html#T10" title="AMI_3:th.10">AMI_3:10</a>, <a class="ref" href="scmpds_2.html#T58" title="SCMPDS_2:th.58">SCMPDS_2:58</a></span>
;<br/>
<div><span class="lab"><font color="Green" title="E78">A72</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_14"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c29">j</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></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> 10</span>)</span> )</span><br/><a NAME="E1:25_14"/><span class="lab"><font color="Green" title="E79">A73</font></span>: 
( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">n</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 or <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 )
 ;<br/><div><span class="lab"><font color="Green" title="E80">A74</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="25_14_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:25_14_1"/><span class="lab"><font color="Green" title="E81">A75</font></span>: 
<font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( ( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3 &amp; <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3 ) or ( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4 ) )</span><br/><a NAME="E2:25_14_1"/><span class="lab"><font color="Green" title="E82">A76</font></span>: 
( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 3 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 )
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_14_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:25_14_1_1"/>
( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3 or <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:25_14_1"><span class="lab"><font color="Green" title="E82">A76</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_14_1_1_1"><span class="kw">case </span></a><a NAME="E1:25_14_1_1_1"/>
<font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:25_14_1_1_1"/>
<font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_14_1_1_2"><span class="kw">case </span></a><a NAME="E1:25_14_1_1_2"/>
<font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4 )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:25_14_1_1_2"/>
( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4 )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25_14_1"><span class="lab"><font color="Green" title="E81">A75</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_14_2"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:25_14_2"/>
( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3 or ( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4 ) or <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25_14"><span class="lab"><font color="Green" title="E79">A73</font></span></a>, <a class="txt" href="#E2:25_14"><span class="lab"><font color="Green" title="E80">A74</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_14_2_1"><span class="kw">suppose </span></a><a NAME="E1:25_14_2_1"/>
<font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 3
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></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> 10</span>)</span> )</span><br/><div class="add"><a NAME="E2:25_14_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A77</font></span>: 
<font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 4
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:25_14_2_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:25"><span class="lab"><font color="Green" title="E37">B24</font></span></a>, <a class="txt" href="#E30:25"><span class="lab"><font color="Green" title="E40">A27</font></span></a>, <a class="txt" href="#E32:25"><span class="lab"><font color="Green" title="E42">A29</font></span></a>, <a class="txt" href="scmp_gcd.html#E27"><span class="lab"><font color="Green" title="E20">Lm9</font></span></a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E23:25"><span class="lab"><font color="Green" title="E34">B20</font></span></a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> )</span><br/><span class="kw">thus </span><a NAME="E4:25_14_2_1"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:25"><span class="lab"><font color="Green" title="E37">B24</font></span></a>, <a class="txt" href="#E30:25"><span class="lab"><font color="Green" title="E40">A27</font></span></a>, <a class="txt" href="#E32:25"><span class="lab"><font color="Green" title="E42">A29</font></span></a>, <a class="txt" href="#E2:25_14_2_1"><span class="lab"><font color="Green" title="E81">A77</font></span></a>, <a class="txt" href="scmp_gcd.html#E27"><span class="lab"><font color="Green" title="E20">Lm9</font></span></a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E23:25"><span class="lab"><font color="Green" title="E34">B20</font></span></a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span></span><br/><span class="kw">thus </span><a NAME="E5:25_14_2_1"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:25"><span class="lab"><font color="Green" title="E37">B24</font></span></a>, <a class="txt" href="#E31:25"><span class="lab"><font color="Green" title="E41">A28</font></span></a>, <a class="txt" href="#E33:25"><span class="lab"><font color="Green" title="E43">A30</font></span></a>, <a class="txt" href="#E2:25_14_2_1"><span class="lab"><font color="Green" title="E81">A77</font></span></a>, <a class="txt" href="scmp_gcd.html#E27"><span class="lab"><font color="Green" title="E20">Lm9</font></span></a>, <a class="txt" href="#E25:25"><span class="lab"><font color="Green" title="E36">A23</font></span></a>, <a class="txt" href="#E23:25"><span class="lab"><font color="Green" title="E34">B20</font></span></a>, <a class="txt" href="#E29:25"><span class="lab"><font color="Green" title="E39">A26</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_14_2_2"><span class="kw">suppose </span></a><a NAME="E1:25_14_2_2"/><span class="lab"><font color="Green" title="E81">A78</font></span>: 
( <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 4 &amp; <font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></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> 10</span>)</span> )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c30">j1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:25_14_2_2"/><span class="lab"><font color="Green" title="E82">A79</font></span>: 
<font color="Maroon" title="c29">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c30">j1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c31">j1</font> = <font color="Maroon" title="c30">j1</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><a NAME="E5:25_14_2_2"/><span class="lab"><font color="Green" title="E83">A82</font></span>: 
<font color="Maroon" title="c31">j1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c28">n</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:25_14_2_2"><span class="lab"><font color="Green" title="E81">A78</font></span></a>, <a class="txt" href="#E3:25_14_2_2"><span class="lab"><font color="Green" title="E82">A79</font></span></a>, <a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><span class="kw">thus </span> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</font>)</span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<font color="Maroon" title="c31">j1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25_14_2_2"><span class="lab"><font color="Green" title="E82">A79</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<font color="Maroon" title="c31">j1</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:25"><span class="lab"><font color="Green" title="E63">A52</font></span></a>, <a class="txt" href="#E66:25"><span class="lab"><font color="Green" title="E74">A68</font></span></a>, <a class="txt" href="#E5:25_14_2_2"><span class="lab"><font color="Green" title="E83">A82</font></span></a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25_14_2_2"><span class="lab"><font color="Green" title="E82">A79</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> )</span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<font color="Maroon" title="c31">j1</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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25_14_2_2"><span class="lab"><font color="Green" title="E82">A79</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<font color="Maroon" title="c31">j1</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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:25"><span class="lab"><font color="Green" title="E63">A52</font></span></a>, <a class="txt" href="#E66:25"><span class="lab"><font color="Green" title="E74">A68</font></span></a>, <a class="txt" href="#E5:25_14_2_2"><span class="lab"><font color="Green" title="E83">A82</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25_14_2_2"><span class="lab"><font color="Green" title="E82">A79</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<font color="Maroon" title="c31">j1</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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25_14_2_2"><span class="lab"><font color="Green" title="E82">A79</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<font color="Maroon" title="c31">j1</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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:25"><span class="lab"><font color="Green" title="E63">A52</font></span></a>, <a class="txt" href="#E67:25"><span class="lab"><font color="Green" title="E75">A69</font></span></a>, <a class="txt" href="#E5:25_14_2_2"><span class="lab"><font color="Green" title="E83">A82</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25_14_2_2"><span class="lab"><font color="Green" title="E82">A79</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="25_14_2_3"><span class="kw">suppose </span></a><a NAME="E1:25_14_2_3"/>
<font color="Maroon" title="c29">j</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 5
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></font>)</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Olive">b<sub>1</sub></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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Olive">b<sub>1</sub></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> 10</span>)</span> )</span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c30">j1</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:25_14_2_3"/><span class="lab"><font color="Green" title="E81">A83</font></span>: 
<font color="Maroon" title="c29">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c30">j1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c31">j1</font> = <font color="Maroon" title="c30">j1</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><a NAME="E5:25_14_2_3"/><span class="lab"><font color="Green" title="E82">A86</font></span>: 
<font color="Maroon" title="c29">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 4
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:25_14_2_3"><span class="lab"><font color="Green" title="E81">A83</font></span></a></span>;<br/><span class="kw">hence </span> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</font>)</span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j1</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:25"><span class="lab"><font color="Green" title="E68">A58</font></span></a>, <a class="txt" href="#E61:25"><span class="lab"><font color="Green" title="E69">A59</font></span></a>, <a class="txt" href="#E64:25"><span class="lab"><font color="Green" title="E72">A64</font></span></a>, <a class="ref" href="extpro_1.html#T5" title="EXTPRO_1:th.5">EXTPRO_1:5</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j1</font></span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:25"><span class="lab"><font color="Green" title="E73">A65</font></span></a>, <a class="ref" href="extpro_1.html#T5" title="EXTPRO_1:th.5">EXTPRO_1:5</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>
<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:25_14_2_3"><span class="lab"><font color="Green" title="E82">A86</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> &amp; <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> )</span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j1</font></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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:25_14_2_3"><span class="lab"><font color="Green" title="E82">A86</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:25"><span class="lab"><font color="Green" title="E69">A59</font></span></a>, <a class="txt" href="#E68:25"><span class="lab"><font color="Green" title="E76">A70</font></span></a>, <a class="ref" href="extpro_1.html#T5" title="EXTPRO_1:th.5">EXTPRO_1:5</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j1</font></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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:25"><span class="lab"><font color="Green" title="E73">A65</font></span></a>, <a class="ref" href="extpro_1.html#T5" title="EXTPRO_1:th.5">EXTPRO_1:5</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 9</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:25_14_2_3"><span class="lab"><font color="Green" title="E82">A86</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span> = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,4)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j1</font></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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:25_14_2_3"><span class="lab"><font color="Green" title="E82">A86</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:25"><span class="lab"><font color="Green" title="E69">A59</font></span></a>, <a class="txt" href="#E69:25"><span class="lab"><font color="Green" title="E77">A71</font></span></a>, <a class="ref" href="extpro_1.html#T5" title="EXTPRO_1:th.5">EXTPRO_1:5</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,4)</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c28">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c31">j1</font></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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E65:25"><span class="lab"><font color="Green" title="E73">A65</font></span></a>, <a class="ref" href="extpro_1.html#T5" title="EXTPRO_1:th.5">EXTPRO_1:5</a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c29">j</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> 10</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:25_14_2_3"><span class="lab"><font color="Green" title="E82">A86</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c29">A</font> = <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>;<br/>
<a NAME="E71:25"/><span class="lab"><font color="Green" title="E79">A89</font></span>: 
 <a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</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> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T48" title="MEMSTR_0:th.48">MEMSTR_0:48</a></span>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> = 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c16">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T45" title="MEMSTR_0:th.45">MEMSTR_0:45</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c16">p</font></span>)</span>

<br/>.= 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:25"><span class="lab"><font color="Green" title="E26">A7</font></span></a>, <a class="txt" href="#E4:25"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="ref" href="memstr_0.html#T7" title="MEMSTR_0:th.7">MEMSTR_0:7</a></span>
;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E80">A92</font></span>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span> = 
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E71:25"><span class="lab"><font color="Green" title="E79">A89</font></span></a>, <a class="ref" href="memstr_0.html#T24" title="MEMSTR_0:th.24">MEMSTR_0:24</a></span>
<br/>.= 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T2" title="ENUMSET1:th.2">ENUMSET1:2</a></span>
;<br/>
<span class="kw">let </span><font color="Maroon" title="c30">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span></span><br/>

<span class="lab"><font color="Green" title="E81">A95</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> = 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c30">k</font>)</span>)</span>

<br/>.= 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c30">k</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:25"><span class="lab"><font color="Green" title="E78">A72</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>

;<br/>
<a NAME="E75:25"/><span class="lab"><font color="Green" title="E82">A96</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c30">k</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> 9</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c30">k</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> 9</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:25"><span class="lab"><font color="Green" title="E78">A72</font></span></a></span>;<br/>
<a NAME="E76:25"/><span class="lab"><font color="Green" title="E83">A97</font></span>: 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c30">k</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> 10</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c30">k</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> 10</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:25"><span class="lab"><font color="Green" title="E78">A72</font></span></a></span>;<br/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> = 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>
<br/>.= 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c30">k</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>
;<br/>
<a NAME="E78:25"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p2">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 9</span>)</span>,<span class="p2">(<span class="default"><a href="scmp_gcd.html#K1" title="SCMP_GCD:func.1">intpos</a> 10</span>)</span></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E74:25"><span class="lab"><font color="Green" title="E81">A95</font></span></a>, <a class="txt" href="#E75:25"><span class="lab"><font color="Green" title="E82">A96</font></span></a>, <a class="txt" href="#E76:25"><span class="lab"><font color="Green" title="E83">A97</font></span></a>, <a class="ref" href="grfunc_1.html#T31" title="GRFUNC_1:th.31">GRFUNC_1:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E79:25"/>
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c22">P1</font>,<font color="Maroon" title="c24">s1</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c23">P2</font>,<font color="Maroon" title="c25">s2</font>,<font color="Maroon" title="c30">k</font>)</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p2">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c16">p</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E73:25"><span class="lab"><font color="Green" title="E80">A92</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
