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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <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">a<sub>1</sub></font>;<br/>
<a NAME="E1:150_1_1"/><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> <font color="Maroon">S</font> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>) <a href="hidden.html#R2">in</a>  <a href="margrel1.html#K6">BOOLEAN</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="150_1_1_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="E1:150_1_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="150_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="E1:150_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> or  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="150_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:150_1_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 ;<br/><div class="add"><a NAME="E2:150_1_1_1_1_1"/><b>then </b>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">x</font>) <a href="hidden.html#R1">=</a> 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="E3:150_1_1_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">x</font>) <a href="hidden.html#R2">in</a>  <a href="margrel1.html#K6">BOOLEAN</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="150_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:150_1_1_1_1_2"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 ;<br/><div class="add"><a NAME="E2:150_1_1_1_1_2"/><b>then </b>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">x</font>) <a href="hidden.html#R1">=</a> 0
 <b>by </b><i>, <a class="ref" href="funct_3.html#D3">FUNCT_3:def 3</a></i>;<br/><b>hence </b><a NAME="E3:150_1_1_1_1_2"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">x</font>) <a href="hidden.html#R2">in</a>  <a href="margrel1.html#K6">BOOLEAN</a> 
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>consider </b><font color="Maroon">IT</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">S</font>, <a href="margrel1.html#K6">BOOLEAN</a> <b> such that </b><br/><a NAME="E3:150_1_1"/><i><font color="Green">E50</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> <font color="Maroon">S</font> holds <br/><font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2">FUNCT_2:sch 2</a>();<br/></i>
<b>reconsider </b><font color="Maroon">IT</font> = <font color="Maroon">IT</font> as   <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> <b>by </b><i><a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>
<b>take </b>
<font color="Maroon">IT</font>
;<br/>

<a NAME="E5:150_1_1"/>
 <a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">IT</font>,<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:150_1_1"/>
for <font color="Olive">s</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font> holds <br/><span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">IT</font>,<font color="Maroon">S</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <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="Olive">s</font>
 <b>by </b><i/>;<br/>


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