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

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="ami_3.html#M1">Data-Location</a> ;<br/>



<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>
<b>assume </b><a NAME="E1:47"/>
not  <a href="ami_7.html#K3" target="_self">Out_\_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="ami_1.html#NM1">Object</a> of <a href="ami_3.html#K1">SCM</a> <b> such that </b><br/><a NAME="E3:47"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="ami_7.html#K3" target="_self">Out_\_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a>  or <font color="Maroon">c<sub>5</sub></font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a>  or <font color="Maroon">c<sub>5</sub></font> is    <a href="ami_3.html#M1">Data-Location</a>  )
 </span><b>by </b><i><a class="ref" href="ami_6.html#T3">AMI_6:3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_1"><b>suppose </b></a><a NAME="E1:47_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:47_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="ami_7.html#T23" target="_self">Th23</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_2"><b>suppose </b></a><a NAME="E1:47_1_2"/>
<font color="Maroon">c<sub>5</sub></font> is   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:47_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="ami_7.html#T22" target="_self">Th22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_3"><b>suppose </b></a><a NAME="E1:47_1_3"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="ami_3.html#M1">Data-Location</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="ami_3.html#M1">Data-Location</a>  ;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 as    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">c<sub>6</sub></font> <b>by </b><i><a class="txt" href="ami_7.html#E40"><i><font color="Green">Lemma32</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/><b>set </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_1_3_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_3_1_1"><b>suppose </b></a><a NAME="E1:47_1_3_1_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:47_1_3_1_1"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
 <b>by </b><i><a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>;<br/><i><font color="Green">E39</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:47_1_3_1_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:47_1_3_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="ami_7.html#E39"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_3_1_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:47_1_3_1_1_2"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_3_1_1_2_1"><b>suppose </b></a><a NAME="E1:47_1_3_1_1_2_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:47_1_3_1_1_2_1"/><b>then </b><i><font color="Green">E41</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E2:47_1_3_1_1"><i><font color="Green">E38</font></i></a></i>;<br/><i><font color="Green">E42</font></i>: <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:47_1_3_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="ami_7.html#E3:47_1_3_1_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="ami_7.html#E1:47_1_3_1_1_2_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="ami_7.html#E39"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
<br/>.= 
2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font>

;<br/><a NAME="E4:47_1_3_1_1_2_1"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:47_1_3_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="ami_7.html#E2:47_1_3_1_1_2_1"><i><font color="Green">E41</font></i></a>, <a class="txt" href="ami_7.html#E3:47_1_3_1_1_2_1"><i><font color="Green">E42</font></i></a></i>;<br/><b>hence </b><a NAME="E5:47_1_3_1_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_3_1_1_2_2"><b>suppose </b></a><a NAME="E1:47_1_3_1_1_2_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div class="add"><a NAME="E2:47_1_3_1_1_2_2"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:47_1_3_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="ami_7.html#E3:47_1_3_1_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="ami_7.html#E1:47_1_3_1_1_2_2"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>;<br/><a NAME="E3:47_1_3_1_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:47_1_3_1_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="ami_7.html#E2:47_1_3_1_1"><i><font color="Green">E38</font></i></a></i>;<br/><b>hence </b><a NAME="E4:47_1_3_1_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="47_1_3_1_2"><b>suppose </b></a><a NAME="E1:47_1_3_1_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:47_1_3_1_2"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
 <b>by </b><i><a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>;<br/><span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:47_1_3_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ami_3.html#T9">AMI_3:9</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="ami_7.html#E39"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>
;<br/><a NAME="E4:47_1_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="ami_1.html#K4">Exec</a> <span class="p2">(<span class="default"><a href="ami_3.html#K4">AddTo</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="ami_7.html#E2:47_1_3_1_2"><i><font color="Green">E38</font></i></a></i>;<br/><b>hence </b><a NAME="E5:47_1_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ami_7.html#E3:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

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