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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="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font> =  <a href="modelc_1.html#K62" target="_self">SigFoaxTau</a> <font color="Maroon">g</font>,<font color="Maroon">f</font>,<span class="p1">(<span class="default"><a href="modelc_1.html#K5" target="_self">CastBool</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">S</font></span>)</span>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font>;<br/>
<a NAME="E1:177_1_1"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">H</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">H</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">S</font> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">H</font>) <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">S</font>
 
;<br/>
<b>consider </b><font color="Maroon">IT</font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">S</font>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:177_1_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">H</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">H</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">S</font> holds <br/><font color="Maroon">IT</font> <a href="funct_1.html#K1">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">H</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2">FUNCT_2:sch 2</a>(<a class="ref" href="modelc_1.html#D23" target="_self">Def23</a>);<br/></i>
<a NAME="E4:177_1_1"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">H</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font> holds  <font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K62" target="_self">SigFoaxTau</a> <font color="Maroon">g</font>,<font color="Maroon">f</font>,<font color="Olive">H</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="177_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">H</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/>

<a NAME="E1:177_1_1_1"/>
 <a href="modelc_1.html#K5" target="_self">CastBool</a> <font color="Maroon">H</font>,<font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:177_1_1_1"/>
<font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K62" target="_self">SigFoaxTau</a> <font color="Maroon">g</font>,<font color="Maroon">f</font>,<font color="Maroon">H</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E44"><i><font color="Green">Lemma134</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:177_1_1"/>
<font color="Maroon">IT</font> is <a href="cohsp_1.html#V6">V91</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="177_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:177_1_1_2"/>
for <font color="Olive">H1</font>, <font color="Olive">H2</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font>  st <font color="Olive">H1</font> <a href="tarski.html#R1">c=</a> <font color="Olive">H2</font> holds <br/><font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Olive">H1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Olive">H2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="177_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">H1</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font>, <font color="Maroon">H2</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E1:177_1_1_2_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">H2</font>
 ;<br/>

<a NAME="E2:177_1_1_2_1"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">H1</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K62" target="_self">SigFoaxTau</a> <font color="Maroon">g</font>,<font color="Maroon">f</font>,<font color="Maroon">H1</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E45"><i><font color="Green">Lemma135</font></i></a></i>;<br/>
<a NAME="E3:177_1_1_2_1"/>
<font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">H2</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K62" target="_self">SigFoaxTau</a> <font color="Maroon">g</font>,<font color="Maroon">f</font>,<font color="Maroon">H2</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E45"><i><font color="Green">Lemma135</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:177_1_1_2_1"/>
<font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">H1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">H2</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E46"><i><font color="Green">Lemma136</font></i></a>, <a class="txt" href="modelc_1.html#E40"><i><font color="Green">Lemma130</font></i></a>, <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="E2:177_1_1_2"/>
<font color="Maroon">IT</font> is <a href="cohsp_1.html#V6">V91</a>
 <b>by </b><i><a class="ref" href="knaster.html#D3">KNASTER:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">IT</font> = <font color="Maroon">IT</font> as  <a href="cohsp_1.html#V6">V91</a> <a href="funct_2.html#NM1">Function</a> of  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">S</font>, <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">S</font> ;<br/>
<b>take </b>
<font color="Maroon">IT</font>
;<br/>

<b>thus </b><a NAME="E7:177_1_1"/>
for <font color="Olive">H</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">S</font> holds  <font color="Maroon">IT</font> <a href="funct_2.html#K3">.</a> <font color="Olive">H</font> <a href="hidden.html#R1">=</a>  <a href="modelc_1.html#K62" target="_self">SigFoaxTau</a> <font color="Maroon">g</font>,<font color="Maroon">f</font>,<font color="Olive">H</font>,<font color="Maroon">R</font>,<font color="Maroon">BASSIGN</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E45"><i><font color="Green">Lemma135</font></i></a></i>;<br/>


</div>
