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<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">f</font> be   <a href="modelc_1.html#NM2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K50" target="_self">CTLModel</a> <font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font></span>)</span>;<br/>







<b>set </b><font color="Maroon">g</font> =  <a href="modelc_1.html#K27" target="_self">EX</a> <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">H</font> =  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font>;<br/>
<a NAME="E1:180"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</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#K27" target="_self">EX</a> <font color="Maroon">f</font></span>)</span> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K52" target="_self">Pred</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_1"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:180_1"/>
<font color="Maroon">x</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#K27" target="_self">EX</a> <font color="Maroon">f</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon">s</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:180_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E4:180_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">s</font> <a href="modelc_1.html#R3" target="_self">|=</a>  <a href="modelc_1.html#K27" target="_self">EX</a> <font color="Maroon">f</font>
 ;<br/>
<b>consider </b><font color="Maroon">s1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E6:180_1"/><i><font color="Green">E52</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">s1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 <b>and </b><br/><a NAME="E7:180_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">s1</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E48"><i><font color="Green">Lemma138</font></i></a>, </i>;<br/>
<a NAME="E8:180_1"/>
<font color="Maroon">s1</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:180_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K52" target="_self">Pred</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E47"><i><font color="Green">Lemma137</font></i></a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:180"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K52" target="_self">Pred</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font> holds <br/><font color="Olive">x</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#K27" target="_self">EX</a> <font color="Maroon">f</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="180_2"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:180_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K52" target="_self">Pred</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font>
 ;<br/>

<b>then consider </b><font color="Maroon">s</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:180_2"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 <b>and </b><br/><a NAME="E4:180_2"/><i><font color="Green">E55</font></i>: 
 ex <font color="Olive">s1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font> st <br/>( <font color="Olive">s1</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">s</font>,<font color="Olive">s1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> )
 ;<br/>
<b>consider </b><font color="Maroon">s1</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E6:180_2"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">s1</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font>
 <b>and </b><br/><a NAME="E7:180_2"/><i><font color="Green">E57</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">s1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E48"><i><font color="Green">Lemma138</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">s2</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E9:180_2"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font>
 <b>and </b><br/><a NAME="E10:180_2"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">s2</font> <a href="modelc_1.html#R3" target="_self">|=</a> <font color="Maroon">f</font>
 <b>by </b><i/>;<br/>
<a NAME="E11:180_2"/>
<font color="Maroon">s</font> <a href="modelc_1.html#R3" target="_self">|=</a>  <a href="modelc_1.html#K27" target="_self">EX</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , <a class="ref" href="modelc_1.html#D24" target="_self">Def24</a>, </i>;<br/>
<b>hence </b><a NAME="E12:180_2"/>
<font color="Maroon">x</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#K27" target="_self">EX</a> <font color="Maroon">f</font></span>)</span>
 <b>by </b><i><a class="txt" href="modelc_1.html#E47"><i><font color="Green">Lemma137</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:180"/>
 <a href="modelc_1.html#K53" target="_self">SIGMA</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K27" target="_self">EX</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K52" target="_self">Pred</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" target="_self">SIGMA</a> <font color="Maroon">f</font></span>)</span>,<font color="Maroon">R</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E46"><i><font color="Green">Lemma136</font></i></a>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


</div>
