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

<b>let </b><font color="Maroon">h1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">h2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:92_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">h1</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E2:92_1"/><i><font color="Green">E28</font></i>: 
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">F<sub>1</sub></font>() holds <br/>( <font color="Maroon">F<sub>4</sub></font>(<font color="Olive">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()) <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 <b>and </b><br/><a NAME="E3:92_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">h2</font> <a href="hidden.html#R2">in</a>  <a href="modelc_1.html#K32" target="_self">ModelSP</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E4:92_1"/><i><font color="Green">E52</font></i>: 
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">F<sub>1</sub></font>() holds <br/>( <font color="Maroon">F<sub>4</sub></font>(<font color="Olive">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()) <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  )
 ;<br/>

<a NAME="E5:92_1"/><i><font color="Green">E53</font></i>: 
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">F<sub>1</sub></font>() holds <br/><span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h1</font>,<font color="Maroon">F<sub>1</sub></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="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">s</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1_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>assume </b><a NAME="E1:92_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>()
 ;<br/>

<b>set </b><font color="Maroon">f1</font> = <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">f2</font> = <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">F1</font> = <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>());<br/>
<a NAME="E2:92_1_1"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()) <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h1</font>,<font color="Maroon">F<sub>1</sub></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><a class="ref" href="modelc_1.html#D13" target="_self">Def13</a>, </i>;<br/>
<a NAME="E3:92_1_1"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()) <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  iff <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h2</font>,<font color="Maroon">F<sub>1</sub></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/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:92_1_1_1"/>
( <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()) <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a>  or <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()) <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_1_1_1_1"><b>suppose </b></a><a NAME="E1:92_1_1_1_1"/>
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()) <a href="hidden.html#R1">=</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:92_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="92_1_1_1_2"><b>suppose </b></a><a NAME="E1:92_1_1_1_2"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">s</font>,<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()) <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K8">TRUE</a> 
 ;<br/><div class="add"><a NAME="E2:92_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h1</font>,<font color="Maroon">F<sub>1</sub></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#K7">FALSE</a> 
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E3:92_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h1</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h2</font>,<font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<font color="Maroon">h1</font> = 
 <a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h1</font>,<font color="Maroon">F<sub>1</sub></font>()
<b>by </b><i>, </i>
<br/>.= 
 <a href="modelc_1.html#K33" target="_self">Fid</a> <font color="Maroon">h2</font>,<font color="Maroon">F<sub>1</sub></font>()
<b>by </b><i>, <a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>
<br/>.= 
<font color="Maroon">h2</font>
<b>by </b><i><a class="ref" href="modelc_1.html#T1" target="_self">Th1</a>, </i>
;<br/>
<b>hence </b><a NAME="E7:92_1"/>
<font color="Maroon">h1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h2</font>
 ;<br/>


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