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<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">S</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">h</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">E34</font></i>: 
<font color="Maroon">h</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">S</font>
 <b>and </b><br/><a NAME="E4:107_1_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">s</font> <a href="funct_4.html#NR1" target="_self">&lt;=</a> <font color="Maroon">h</font>
 <b>by </b><i><a class="ref" href="ami_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">h</font> = <font color="Maroon">h</font> as   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">R</font> = <span class="p1">(<span class="default"><a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">h</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">s</font></span>)</span> as    <a href="ami_1.html#M1" target="_self">FinPartState</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="ami_1.html#T11" target="_self">Th11</a></i>;<br/>
<b>take </b>
<font color="Maroon">R</font>
;<br/>

<b>let </b><font color="Maroon">s'</font> be   <a href="ami_1.html#NM4">State</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E7:107_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">s</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">s'</font>
 ;<br/>

<a NAME="E8:107_1_1"/>
<font color="Maroon">h</font> is <a href="ami_1.html#V9" target="_self">halting</a>
 
<b>by </b><i>, , <a class="ref" href="ami_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>then consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E10:107_1_1"/><i><font color="Green">E65</font></i>: 
(  <a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">h</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">h</font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">k1</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">h</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5" target="_self">halt</a> <font color="Maroon">S</font> )
 <b>by </b><i><a class="ref" href="ami_1.html#D13" target="_self">Def13</a></i>;<br/>
<a NAME="E11:107_1_1"/>
<font color="Maroon">s'</font> is <a href="ami_1.html#V9" target="_self">halting</a>
 
<b>by </b><i>, <a class="ref" href="ami_1.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_1.html#T8" target="_self">Th8</a></i>;<br/>
<b>then consider </b><font color="Maroon">k2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E13:107_1_1"/><i><font color="Green">E66</font></i>: 
(  <a href="ami_1.html#K12" target="_self">Result</a> <font color="Maroon">s'</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">s'</font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">k2</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">s'</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5" target="_self">halt</a> <font color="Maroon">S</font> )
 <b>by </b><i><a class="ref" href="ami_1.html#D13" target="_self">Def13</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">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k2</font> or <font color="Maroon">k1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">k2</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">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k2</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">h</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">h</font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">k2</font>
 <b>by </b><i><a class="ref" href="ami_1.html#T15" target="_self">Th15</a>, <a class="ref" href="ami_1.html#D11" target="_self">Def11</a></i>;<br/><b>hence </b><a NAME="E3:107_1_1_1_1_1"/>
<font color="Maroon">R</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">s'</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">s</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="ami_1.html#T14" target="_self">Th14</a>, , <a class="ref" href="ami_1.html#T7" target="_self">Th7</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">k1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">k2</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">s'</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">s'</font></span>)</span> <a href="ami_1.html#K11" target="_self">.</a> <font color="Maroon">k1</font>
 <b>by </b><i>, <a class="ref" href="ami_1.html#D11" target="_self">Def11</a></i>;<br/><b>hence </b><a NAME="E3:107_1_1_1_1_2"/>
<font color="Maroon">R</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">s'</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">s</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="ami_1.html#T14" target="_self">Th14</a>, <a class="ref" href="ami_1.html#T15" target="_self">Th15</a>, <a class="ref" href="ami_1.html#T7" target="_self">Th7</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">R</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">s'</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">s</font></span>)</span>
 ;<br/>


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