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<b>take </b><font color="Maroon">p</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <a href="ami_4.html#K1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="ami_3.html#K18">--&gt;</a> 1,1</span>)</span>;<br/>

<a NAME="E1:69_1_1"/>
<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="ami_3.html#K18">--&gt;</a> 1,1 <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <a href="ami_4.html#K2">Euclide-Function</a> 
 
<b>by </b><i><a class="ref" href="ami_4.html#T11">AMI_4:11</a></i>;<br/>
<b>then consider </b><font color="Maroon">s</font> being    <a href="ami_1.html#M1">FinPartState</a> of  <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:69_1_1"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="ami_3.html#K18">--&gt;</a> 1,1 <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E4:69_1_1"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <a href="ami_4.html#K1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">s</font> is   <a href="ami_1.html#NM6">pre-program</a> of  <a href="ami_3.html#K1">SCM</a> 
 <b>and </b><br/><a NAME="E5:69_1_1"/>
<a href="ami_4.html#K2">Euclide-Function</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="tarski.html#R1">c=</a>  <a href="ami_1.html#K18">Result</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <a href="ami_4.html#K1">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K17">+*</a> <font color="Maroon">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#D29">AMI_1:def 29</a>, <a class="ref" href="ami_4.html#T13">AMI_4:13</a></i>;<br/>
<b>thus </b><a NAME="E6:69_1_1"/>
<font color="Maroon">p</font> is <a href="ami_1.html#V11">autonomic</a>
 <b>by </b><i>, <a class="ref" href="ami_5.html#T22" target="_self">Th22</a></i>;<br/>

<b>take </b>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="ami_3.html#D13">AMI_3:def 13</a><br/>

<a NAME="E7:69_1_1"/><i><font color="Green">E45</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <a href="ami_4.html#K1">Euclide-Algorithm</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 0</span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K15">dl.</a> 1</span>)</span> <a href="ami_3.html#K18">--&gt;</a> 1,1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E8:69_1_1"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <a href="ami_4.html#K1">Euclide-Algorithm</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <a href="ami_4.html#K1">Euclide-Algorithm</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E9:69_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> </span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="ami_3.html#T34">AMI_3:34</a></i>;<br/>
<a NAME="E10:69_1_1"/><b>then </b>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E11:69_1_1"/><b>then </b>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K16">il.</a> 0</span>)</span></span>)</span> <a href="ami_1.html#K17">+*</a> <a href="ami_4.html#K1">Euclide-Algorithm</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="ami_5.html#T23" target="_self">Th23</a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E12:69_1_1"/>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>

<b>assume </b><a NAME="E13:69_1_1"/>
 <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <a href="ami_3.html#K1">SCM</a> 
 ;<br/>

<b>hence </b><a NAME="E14:69_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scm_1.html#T7">SCM_1:7</a></i>;<br/>


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