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

<b>reconsider </b><font color="Maroon">c<sub>1</sub></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="ami_3.html#K1" target="_self">SCM</a>  <b>by </b><i><a class="ref" href="ami_2.html#T2">AMI_2:2</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>1</sub></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="E2:30_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="ami_1.html#V3">halting</a>
 <b>by </b><i><a class="txt" href="ami_3.html#E28"><i><font color="Green">Lemma16</font></i></a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="ami_3.html#K1" target="_self">SCM</a> ;<br/>

<b>assume </b><a NAME="E3:30_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="ami_1.html#V3">halting</a>
 ;<br/>

<b>assume </b><a NAME="E4:30_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:30_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></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">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Olive">b<sub>1</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a> ex <font color="Olive">b<sub>2</sub></font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Olive">b<sub>2</sub></font> or ex <font color="Olive">b<sub>1</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a> ex <font color="Olive">b<sub>2</sub></font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Olive">b<sub>2</sub></font> )
 </span><b>by </b><i><a class="txt" href="ami_3.html#E37"><i><font color="Green">Lemma25</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_1"><b>suppose </b></a><a NAME="E1:30_1_1_1_1"/>
<font color="Maroon">c<sub>2</sub></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="E2:30_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E4:30_1_1"><i><font color="Green">E27</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_2"><b>suppose </b></a><a NAME="E1:30_1_1_1_2"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K3" target="_self">:=</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E3:30_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ami_3.html#E29"><i><font color="Green">Lemma17</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_3"><b>suppose </b></a><a NAME="E1:30_1_1_1_3"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K4" target="_self">AddTo</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E3:30_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ami_3.html#E30"><i><font color="Green">Lemma18</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_4"><b>suppose </b></a><a NAME="E1:30_1_1_1_4"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K5" target="_self">SubFrom</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E3:30_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ami_3.html#E31"><i><font color="Green">Lemma19</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_5"><b>suppose </b></a><a NAME="E1:30_1_1_1_5"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K6" target="_self">MultBy</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1_5"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E3:30_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ami_3.html#E32"><i><font color="Green">Lemma20</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_6"><b>suppose </b></a><a NAME="E1:30_1_1_1_6"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K7" target="_self">Divide</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1_6"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E3:30_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ami_3.html#E33"><i><font color="Green">Lemma21</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_7"><b>suppose </b></a><a NAME="E1:30_1_1_1_7"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K8" target="_self">goto</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1_7"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E3:30_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ami_3.html#E34"><i><font color="Green">Lemma22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_8"><b>suppose </b></a><a NAME="E1:30_1_1_1_8"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a> ex <font color="Olive">b<sub>2</sub></font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K9" target="_self">=0_goto</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1_8"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E3:30_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ami_3.html#E35"><i><font color="Green">Lemma23</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="30_1_1_1_9"><b>suppose </b></a><a NAME="E1:30_1_1_1_9"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="ami_3.html#M1" target="_self">Data-Location</a> ex <font color="Olive">b<sub>2</sub></font> being  <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1" target="_self">SCM</a>  st <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="ami_3.html#K10" target="_self">&gt;0_goto</a> <font color="Olive">b<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:30_1_1_1_9"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_3.html#E3:30_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="ami_3.html#E36"><i><font color="Green">Lemma24</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
