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

<b>let </b><font color="Maroon">N</font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V4">halting</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a> <a href="amistd_1.html#V4">standard</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">N</font>;<br/><b>let </b><font color="Maroon">F</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="ami_3.html#V1">programmed</a> <a href="amistd_1.html#V9">lower</a> <a href="amistd_1.html#V11">unique-halt</a>  <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:120"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span>
 <b>and </b><br/><a NAME="E2:120"/><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E3:120"/><i><font color="Green">E56</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E4:120"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="ref" href="amistd_2.html#D2" target="_self">Def2</a>, <a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<a NAME="E5:120"/><b>then </b><i><font color="Green">E57</font></i>: 
<font color="Maroon">I</font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">F</font>
 
<b>by </b><i>, , <a class="ref" href="amistd_1.html#D23">AMISTD_1:def 23</a></i>;<br/>
<a NAME="E6:120"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K11" target="_self">CutLastLoc</a> <font color="Maroon">F</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">F</font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E7:120"/><b>then </b>
not <font color="Maroon">I</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="realset1.html#K5">{</a><span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">F</font></span>)</span></span><a href="realset1.html#K5">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>hence </b><a NAME="E8:120"/>
contradiction
 <b>by </b><i><a class="ref" href="amistd_2.html#T7" target="_self">Th7</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div>
