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

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

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="ami_3.html#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>thus </b><a NAME="E1:51"/>
 <a href="ami_7.html#K3" target="_self">Out_\_Inp</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:51_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>4</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="ami_1.html#NM1">Object</a> of <a href="ami_3.html#K1">SCM</a>  ;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:51_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>  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="51_1_1_1"><b>suppose </b></a><a NAME="E1:51_1_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="E2:51_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:51_1"><i><font color="Green">E40</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="51_1_1_2"><b>suppose </b></a><a NAME="E1:51_1_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="E2:51_1_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:51_1"><i><font color="Green">E40</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="51_1_1_3"><b>suppose </b></a><a NAME="E1:51_1_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="51_1_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:51_1_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="51_1_1_3_1_1"><b>suppose </b></a><a NAME="E1:51_1_1_3_1_1"/>
<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"><b>hence </b><a NAME="E2:51_1_1_3_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_1_1_3_1_2"><b>suppose </b></a><a NAME="E1:51_1_1_3_1_2"/>
<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="E2:51_1_1_3_1_2"/><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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</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> <font color="Maroon">c<sub>1</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</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> <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="ref" href="ami_3.html#T12">AMI_3:12</a></i>;<br/><a NAME="E3:51_1_1_3_1_2"/>
<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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K2">+</a> 0
 <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="E4:51_1_1_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <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"><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>
 ;<br/><b>hence </b><a NAME="E5:51_1_1_3_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="ami_7.html#E1:51_1"><i><font color="Green">E40</font></i></a>, <a class="txt" href="ami_7.html#E2:51_1_1_3_1_2"><i><font color="Green">E41</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>

</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:51"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<a NAME="E3:51"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:51"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> <br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">c<sub>2</sub></font> holds  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Olive">b<sub>2</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">c<sub>2</sub></font>;<br/>



<a NAME="E1:51_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="ami_1.html#K2">IC</a> <a href="ami_3.html#K1">SCM</a> 
 
<b>by </b><i><a class="ref" href="ami_5.html#T20">AMI_5:20</a></i>;<br/>
<a NAME="E2:51_2"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="ami_1.html#K6">IC</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K6">IC</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="ami_7.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E3:51_2"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="ami_3.html#M1">Data-Location</a>  holds <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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="ami_3.html#M1">Data-Location</a> ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:51_2_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>7</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="51_2_1_1_1"><b>suppose </b></a><a NAME="E1:51_2_1_1_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="int_1.html#T77">INT_1:77</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="int_1.html#T77">INT_1:77</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:51_2_1_1_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="51_2_1_1_2"><b>suppose </b></a><a NAME="E1:51_2_1_1_2"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:51_2_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="funct_7.html#T34">FUNCT_7:34</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="ami_3.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="ami_7.html#E1:51_2_1_1_2"><i><font color="Green">E43</font></i></a>, <a class="ref" href="ami_3.html#T12">AMI_3:12</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E4:51_2"/>
for <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">SCM</a>  holds <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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<a NAME="E1:51_2_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ami_5.html#T22">AMI_5:22</a></i>;<br/>
<b>hence </b><a NAME="E2:51_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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="ami_1.html#K13">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="ami_7.html#T4" target="_self">Th4</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:51_2"/>
 <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K4">Exec</a> <span class="p1">(<span class="default"><a href="ami_3.html#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="ami_7.html#K1" target="_self">+*</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E2:51_2"><i><font color="Green">E41</font></i></a>, <a class="txt" href="ami_7.html#E3:51_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="ami_5.html#T26">AMI_5:26</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:51"/>
<font color="Maroon">c<sub>4</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#K7">Divide</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E3:51"><i><font color="Green">E40</font></i></a>, <a class="ref" href="ami_7.html#D4" target="_self">Def4</a></i>;<br/>


</div>
