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<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="ami_1.html#M1">FinPartState</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:54_1_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">F</font> is <a href="realset1.html#V1">trivial</a>
 ;<br/>

<b>let </b><font color="Maroon">f</font> be   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="amistd_1.html#D23">AMISTD_1:def 23</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E2:54_1_1"/>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <font color="Maroon">S</font>
 <b>and </b><br/><a NAME="E3:54_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 ;<br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:54_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="realset1.html#D4">REALSET1:def 4</a></i>;<br/>
<a NAME="E6:54_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">a</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E8:54_1_1"/><i><font color="Green">E57</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="relat_1.html#D1">RELAT_1:def 1</a></i>;<br/>
<a NAME="E9:54_1_1"/><i><font color="Green">E58</font></i>: 
 <a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="amistd_1.html#T51">AMISTD_1:51</a></i>;<br/>
<a NAME="E10:54_1_1"/><i><font color="Green">E59</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, , <a class="ref" href="relat_1.html#T23">RELAT_1:23</a></i>;<br/>
<b>hence </b><font color="Maroon">f</font> = 
<font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
<br/>.= 
 <a href="amistd_1.html#K10">LastLoc</a> <font color="Maroon">F</font>
<b>by </b><i>, <a class="txt" href="amistd_2.html#E1"><i><font color="Green">Lemma36</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
;<br/><br/>


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