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<div class="add">

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> =  <a href="modelc_1.html#K56" title="MODELC_1:func.56">SigFaxTau</a> <font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="modelc_1.html#K5" title="MODELC_1:func.5">CastBool</a> $1,<font color="Maroon" title="c1">S</font></span>)</span>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>;<br/>
<a NAME="E1:168_1_1"/><i><font color="Green" title="E127">A1</font></i>: 
for <font color="Olive" title="b1">G</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">G</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font>
 
;<br/>
<b>consider </b><font color="Maroon" title="c5">IT</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font>, <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E3:168_1_1"/><i><font color="Green" title="E128">A2</font></i>: 
for <font color="Olive" title="b1">G</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font> holds <br/><font color="Maroon" title="c5">IT</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">G</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S2" title="FUNCT_2:sch.2">FUNCT_2:sch 2</a>(<a class="txt" href="modelc_1.html#E1:168_1_1"><i><font color="Green" title="E127">A1</font></i></a>);<br/></i>
<a NAME="E4:168_1_1"/><i><font color="Green" title="E129">A3</font></i>: 
for <font color="Olive" title="b1">G</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K56" title="MODELC_1:func.56">SigFaxTau</a> <font color="Maroon" title="c4">f</font>,<font color="Olive" title="b1">G</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="168_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">G</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>;<br/>

<a NAME="E1:168_1_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c6">G</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K56" title="MODELC_1:func.56">SigFaxTau</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">G</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
 
<b>by </b><i><a class="ref" href="modelc_1.html#D5" target="_self" title="MODELC_1:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E2:168_1_1_1"/>
<font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K56" title="MODELC_1:func.56">SigFaxTau</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">G</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E3:168_1_1"><i><font color="Green" title="E128">A2</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:168_1_1"/>
<font color="Maroon" title="c5">IT</font> is <a href="cohsp_1.html#V6" title="COHSP_1:attr.6">V202</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="168_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:168_1_1_2"/>
for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">G2</font> holds <br/><font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">G2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="168_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">G1</font>, <font color="Maroon" title="c7">G2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>;<br/>

<b>assume </b><a NAME="E1:168_1_1_2_1"/><i><font color="Green" title="E130">A4</font></i>: 
<font color="Maroon" title="c6">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">G2</font>
 ;<br/>

<a NAME="E2:168_1_1_2_1"/><i><font color="Green" title="E131">A5</font></i>: 
<font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K56" title="MODELC_1:func.56">SigFaxTau</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">G1</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E4:168_1_1"><i><font color="Green" title="E129">A3</font></i></a></i>;<br/>
<a NAME="E3:168_1_1_2_1"/>
<font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K56" title="MODELC_1:func.56">SigFaxTau</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c7">G2</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
 
<b>by </b><i><a class="txt" href="modelc_1.html#E4:168_1_1"><i><font color="Green" title="E129">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:168_1_1_2_1"/>
<font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">G1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">G2</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E1:168_1_1_2_1"><i><font color="Green" title="E130">A4</font></i></a>, <a class="txt" href="modelc_1.html#E2:168_1_1_2_1"><i><font color="Green" title="E131">A5</font></i></a>, <a class="ref" href="modelc_1.html#T37" target="_self" title="MODELC_1:th.37">Th37</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:168_1_1_2"/>
<font color="Maroon" title="c5">IT</font> is <a href="cohsp_1.html#V6" title="COHSP_1:attr.6">V202</a>
 <b>by </b><i><a class="ref" href="knaster.html#D3" title="KNASTER:def.3">KNASTER:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c6">IT</font> = <font color="Maroon" title="c5">IT</font> as  <a href="cohsp_1.html#V6" title="COHSP_1:attr.6">V202</a> <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font>, <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">S</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c6">IT</font>
;<br/>

<b>thus </b><a NAME="E7:168_1_1"/>
for <font color="Olive" title="b1">G</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Maroon" title="c6">IT</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_1.html#K56" title="MODELC_1:func.56">SigFaxTau</a> <font color="Maroon" title="c4">f</font>,<font color="Olive" title="b1">G</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
 <b>by </b><i><a class="txt" href="modelc_1.html#E4:168_1_1"><i><font color="Green" title="E129">A3</font></i></a></i>;<br/>


</div>
