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

<b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be  <a href="partfun1.html#V1">total</a>  <a href="relset_1.html#M2">Relation</a> of <font color="Maroon">S</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">BASSIGN</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">S</font></span>)</span>;<br/><b>let </b><font color="Maroon">T</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/>







<b>set </b><font color="Maroon">f</font> =  <a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font>;<br/>
<b>set </b><font color="Maroon">U</font> =  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>;<br/>
<a NAME="E1:153"/><i><font color="Green">E27</font></i>: 
 <a href="modelc_1.html#K53" target="_self">SIGMA</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">s</font> where <font color="Olive">s</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font> : <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>,<font color="Maroon">S</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  </span>}</span> 
 
<b>by </b><i/>;<br/>
<a NAME="E2:153"/>
for <font color="Olive">s</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">s</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span> iff <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="153_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E1:153_1"/>
( <font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span> implies <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="153_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:153_1_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">t</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:153_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>and </b><br/><a NAME="E4:153_1_1"/><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>,<font color="Maroon">S</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 <b>by </b><i/>;<br/>
<a NAME="E5:153_1_1"/>
<span class="p1">(<span class="default"><a href="funct_3.html#K5">chi</a> <font color="Maroon">T</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E6:153_1_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="funct_3.html#T42">FUNCT_3:42</a></i>;<br/>


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

<b>assume </b><a NAME="E2:153_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 ;<br/>

<b>then </b><span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> = 
<span class="p1">(<span class="default"><a href="funct_3.html#K5">chi</a> <font color="Maroon">T</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
<b>by </b><i/>
<br/>.= 
1
<b>by </b><i>, <a class="ref" href="funct_3.html#D3">FUNCT_3:def 3</a></i>
;<br/>
<b>hence </b><a NAME="E4:153_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:153"/>
 <a href="modelc_1.html#K53" target="_self">SIGMA</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K54" target="_self">Tau</a> <font color="Maroon">T</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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