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

<a NAME="E1:107_1_1"/>
 <a href="ami_1.html#K7" target="_self">sproduct</a> the <a href="ami_1.html#U5" target="_self">Object-Kind</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E3:107_1_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_3.html#K4">product</a> the <a href="ami_1.html#U5" target="_self">Object-Kind</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E4:107_1_1"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="ami_1.html#T30" target="_self">Th30</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="ami_1.html#E3:107_1_1"><i><font color="Green">E60</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">(<span class="default"><a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as    <a href="ami_1.html#M1" target="_self">FinPartState</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="ami_1.html#T62" target="_self">Th62</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E7:107_1_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E8:107_1_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="ami_1.html#V9" target="_self">halting</a>
 
<b>by </b><i><a class="txt" href="ami_1.html#E1:107"><i><font color="Green">E59</font></i></a>, <a class="txt" href="ami_1.html#E4:107_1_1"><i><font color="Green">E61</font></i></a>, <a class="ref" href="ami_1.html#D26" target="_self">Def26</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:107_1_1"/><i><font color="Green">E63</font></i>: 
(  <a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="ami_1.html#K8" target="_self">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5" target="_self">halt</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="ami_1.html#D22" target="_self">Def22</a></i>;<br/>
<a NAME="E11:107_1_1"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="ami_1.html#V9" target="_self">halting</a>
 
<b>by </b><i><a class="txt" href="ami_1.html#E1:107"><i><font color="Green">E59</font></i></a>, <a class="txt" href="ami_1.html#E7:107_1_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="ami_1.html#D26" target="_self">Def26</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E13:107_1_1"/><i><font color="Green">E64</font></i>: 
(  <a href="ami_1.html#K12" target="_self">Result</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#K10" target="_self">Computation</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font> &amp;  <a href="ami_1.html#K8" target="_self">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5" target="_self">halt</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="ami_1.html#D22" target="_self">Def22</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="107_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_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_1"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font> or <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>9</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_1_1_1_1_1"/><b>then </b>
 <a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" target="_self">Computation</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="ami_1.html#E10:107_1_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="ami_1.html#T52" target="_self">Th52</a></i>;<br/><b>hence </b><a NAME="E3:107_1_1_1_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_1.html#E1:107"><i><font color="Green">E59</font></i></a>, <a class="txt" href="ami_1.html#E4:107_1_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="ami_1.html#E7:107_1_1"><i><font color="Green">E62</font></i></a>, <a class="txt" href="ami_1.html#E13:107_1_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="ami_1.html#D25" target="_self">Def25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="107_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:107_1_1_1_1_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><div class="add"><a NAME="E2:107_1_1_1_1_2"/><b>then </b>
 <a href="ami_1.html#K12" target="_self">Result</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#K10" target="_self">Computation</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="ami_1.html#E13:107_1_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="ami_1.html#T52" target="_self">Th52</a></i>;<br/><b>hence </b><a NAME="E3:107_1_1_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="ami_1.html#E1:107"><i><font color="Green">E59</font></i></a>, <a class="txt" href="ami_1.html#E4:107_1_1"><i><font color="Green">E61</font></i></a>, <a class="txt" href="ami_1.html#E7:107_1_1"><i><font color="Green">E62</font></i></a>, <a class="txt" href="ami_1.html#E10:107_1_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="ami_1.html#D25" target="_self">Def25</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E15:107_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="relat_1.html#K7">|</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 ;<br/>


</div>
