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<b>take </b><font color="Maroon" title="c1">p</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> 1,1</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a> &amp; not <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a> )</span><br/>

<a NAME="E1:31_1_1"/>
<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> 1,1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_4.html#K3" title="AMI_4:func.3">Euclide-Function</a> 
 
<b>by </b><i><a class="ref" href="ami_4.html#T11" title="AMI_4:th.11">AMI_4:11</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c2">s</font> being   <a href="ami_1.html#NM8" title="AMI_1:NM.8">FinPartState</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <b> such that </b><br/><a NAME="E3:31_1_1"/><i><font color="Green" title="E19">A1</font></i>: 
<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> 1,1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font>
 <b>and </b><br/><a NAME="E4:31_1_1"/><i><font color="Green" title="E20">A2</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Maroon" title="c2">s</font> is   <a href="ami_1.html#NM9" title="AMI_1:NM.9">pre-program</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
 <b>and </b><br/><a NAME="E5:31_1_1"/>
<a href="ami_4.html#K3" title="AMI_4:func.3">Euclide-Function</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ami_1.html#K19" title="AMI_1:func.19">Result</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Algorithm</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <font color="Maroon" title="c2">s</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#D29" title="AMI_1:def.29">AMI_1:def 29</a>, <a class="ref" href="ami_4.html#T13" title="AMI_4:th.13">AMI_4:13</a></i>;<br/>
<b>thus </b><a NAME="E6:31_1_1"/>
<font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V10" title="AMI_1:attr.10">autonomic</a>
 <b>by </b><i><a class="txt" href="#E3:31_1_1"><i><font color="Green" title="E19">A1</font></i></a>, <a class="txt" href="#E4:31_1_1"><i><font color="Green" title="E20">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c1">p</font> is <a href="ami_1.html#V15" title="AMI_1:attr.15">programmed</a></span><br/>

<b>take </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D40" title="AMI_1:def.40">AMI_1:def 40</a>,<a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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> <font color="Maroon" title="c1">p</font> &amp; not  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  )</span><br/>

<a NAME="E7:31_1_1"/><i><font color="Green" title="E21">A3</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p4">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Algorithm</a> </span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>,<span class="p3">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> 1</span>)</span> <a href="ami_3.html#K14" title="AMI_3:func.14">--&gt;</a> 1,1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E8:31_1_1"/><i><font color="Green" title="E22">A4</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Algorithm</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Algorithm</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>;<br/>
<a NAME="E9:31_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E10:31_1_1"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E11:31_1_1"/><b>then </b>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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"><span class="p2">(<span class="default"><a href="ami_1.html#K28" title="AMI_1:func.28">Start-At</a> <span class="p3">(<span class="default"><a href="ami_3.html#K12" title="AMI_3:func.12">il.</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <a href="ami_4.html#K2" title="AMI_4:func.2">Euclide-Algorithm</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="#E8:31_1_1"><i><font color="Green" title="E22">A4</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E12:31_1_1"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</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> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="#E7:31_1_1"><i><font color="Green" title="E21">A3</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span><br/>

<b>assume </b><a NAME="E13:31_1_1"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>hence </b><a NAME="E14:31_1_1"/>
contradiction
 <b>by </b><i><a class="ref" href="ami_3.html#T4" title="AMI_3:th.4">AMI_3:4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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