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<b>reconsider </b><font color="Maroon">I</font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> as   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  <b>by </b><i><a class="ref" href="scmfsa_1.html#T4">SCMFSA_1:4</a></i>;<br/>
<b>take </b>
<font color="Maroon">I</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D9">AMI_1:def 9</a><br/>

<b>thus </b><a NAME="E2:107_1_1"/>
<font color="Maroon">I</font> is <a href="ami_1.html#V3">halting</a>
 <b>by </b><i>, <a class="ref" href="ami_3.html#T71">AMI_3:71</a></i>;<br/>

<b>let </b><font color="Maroon">W</font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a> ;<br/>

<b>assume </b><a NAME="E3:107_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">W</font> is <a href="ami_1.html#V3">halting</a>
 ;<br/>

<b>assume </b><a NAME="E4:107_1_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">W</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:107_1_1_1"/>
( <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9" target="_self">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10" target="_self">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11" target="_self">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font> or  ex <font color="Olive">la</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13" target="_self">goto</a> <font color="Olive">la</font> or  ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K14" target="_self">=0_goto</a> <font color="Olive">lb</font> or  ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K15" target="_self">&gt;0_goto</a> <font color="Olive">lb</font> or  ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16" target="_self">:=</a> <font color="Olive">fa</font>,<font color="Olive">b</font> or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">fa</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17" target="_self">:=</a> <font color="Olive">b</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18" target="_self">:=len</a> <font color="Olive">f</font> or  ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19" target="_self">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1"/>
<font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K4">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K8" target="_self">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_3"><b>suppose </b></a><a NAME="E1:107_1_1_1_3"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9" target="_self">AddTo</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_3"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_4"><b>suppose </b></a><a NAME="E1:107_1_1_1_4"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10" target="_self">SubFrom</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T26" target="_self">Th26</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_5"><b>suppose </b></a><a NAME="E1:107_1_1_1_5"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K11" target="_self">MultBy</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_5"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T27" target="_self">Th27</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_6"><b>suppose </b></a><a NAME="E1:107_1_1_1_6"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K12" target="_self">Divide</a> <font color="Olive">a</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_6"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_7"><b>suppose </b></a><a NAME="E1:107_1_1_1_7"/>
 ex <font color="Olive">la</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K13" target="_self">goto</a> <font color="Olive">la</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_7"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#D9" target="_self">Def9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_8"><b>suppose </b></a><a NAME="E1:107_1_1_1_8"/>
 ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K14" target="_self">=0_goto</a> <font color="Olive">lb</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_8"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_9"><b>suppose </b></a><a NAME="E1:107_1_1_1_9"/>
 ex <font color="Olive">lb</font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="scmfsa_2.html#K1" target="_self">SCM+FSA</a>  ex <font color="Olive">da</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">da</font> <a href="scmfsa_2.html#K15" target="_self">&gt;0_goto</a> <font color="Olive">lb</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_9"/>
contradiction
 <b>by </b><i>, <a class="ref" href="scmfsa_2.html#T31" target="_self">Th31</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_10"><b>suppose </b></a><a NAME="E1:107_1_1_1_10"/>
 ex <font color="Olive">b</font>, <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K16" target="_self">:=</a> <font color="Olive">fa</font>,<font color="Olive">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_10"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_11"><b>suppose </b></a><a NAME="E1:107_1_1_1_11"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">fa</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">fa</font>,<font color="Olive">a</font> <a href="scmfsa_2.html#K17" target="_self">:=</a> <font color="Olive">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_11"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_12"><b>suppose </b></a><a NAME="E1:107_1_1_1_12"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="scmfsa_2.html#K18" target="_self">:=len</a> <font color="Olive">f</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_12"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_13"><b>suppose </b></a><a NAME="E1:107_1_1_1_13"/>
 ex <font color="Olive">a</font> being   <a href="scmfsa_2.html#M1" target="_self">Int-Location</a>  ex <font color="Olive">f</font> being   <a href="scmfsa_2.html#M2" target="_self">FinSeq-Location</a>  st <font color="Maroon">W</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="scmfsa_2.html#K19" target="_self">:=&lt;0,...,0&gt;</a> <font color="Olive">a</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:107_1_1_1_13"/>
contradiction
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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