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

<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">C</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">D</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">E</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">F</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">J</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">M</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">N</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">h</font> be   <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">A'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">B'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">C'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">D'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">E'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">F'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">J'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">M'</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">N'</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:37"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">N</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">N</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">N</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">N</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">F</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">N</font> &amp; <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">J</font> &amp; <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">F</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">N</font> &amp; <font color="Maroon">J</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">M</font> &amp; <font color="Maroon">J</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">N</font> &amp; <font color="Maroon">M</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">N</font> &amp; <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span> )
 ;<br/>

<a NAME="E2:37"/><i><font color="Green">E29</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">A</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5">CQC_LANG:5</a></i>;<br/>
<a NAME="E3:37"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>proof </b></a><div class="add">

<a NAME="E1:37_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:37_1"/><b>then </b>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E3:37_1"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A'</font>
 <b>by </b><i><a class="ref" href="cqc_lang.html#T6">CQC_LANG:6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:37"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><b>proof </b></a><div class="add">

<a NAME="E1:37_2"/>
not <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">B'</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E3:37_2"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B'</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E5:37"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_3"><b>proof </b></a><div class="add">

<a NAME="E1:37_3"/>
not <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:37_3"/><b>then </b>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/>
<b>hence </b><a NAME="E3:37_3"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C'</font>
 <b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:37"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_4"><b>proof </b></a><div class="add">

<a NAME="E1:37_4"/>
not <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">D'</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E3:37_4"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D'</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E7:37"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_5"><b>proof </b></a><div class="add">

<a NAME="E1:37_5"/>
not <font color="Maroon">E</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">E'</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E3:37_5"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E'</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E8:37"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_6"><b>proof </b></a><div class="add">

<a NAME="E1:37_6"/>
not <font color="Maroon">F</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">F'</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E3:37_6"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F'</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E9:37"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">J'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_7"><b>proof </b></a><div class="add">

<a NAME="E1:37_7"/>
not <font color="Maroon">J</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">J'</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, </i>
;<br/>
<b>hence </b><a NAME="E3:37_7"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">J'</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E10:37"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_8"><b>proof </b></a><div class="add">

<a NAME="E1:37_8"/>
not <font color="Maroon">M</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">M</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">M</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">M'</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="bvfunc14.html#T15">BVFUNC14:15</a></i>
;<br/>
<b>hence </b><a NAME="E3:37_8"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M'</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E11:37"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">N'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_9"><b>proof </b></a><div class="add">

<a NAME="E1:37_9"/>
not <font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">A'</font></span>)</span>
 
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="txt" href="bvfunc24.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">N</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">B'</font></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">C'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">D</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">D'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p0">(<span class="default"><font color="Maroon">E</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">E'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p5">(<span class="default"><font color="Maroon">F</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">F'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p4">(<span class="default"><font color="Maroon">J</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">J'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">M'</font></span>)</span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p2">(<span class="default"><font color="Maroon">N</font> <a href="cqc_lang.html#K3">.--&gt;</a> <font color="Maroon">N'</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">N</font>
<b>by </b><i><a class="txt" href="bvfunc24.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon">N'</font>
<b>by </b><i><a class="ref" href="yellow14.html#T3">YELLOW14:3</a></i>
;<br/>
<b>hence </b><a NAME="E3:37_9"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">N'</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E12:37"/>
( <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A'</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B'</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C'</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D'</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E'</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F'</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <font color="Maroon">J'</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M'</font> &amp; <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">N'</font> )
 <b>by </b><i><a class="txt" href="bvfunc24.html#E5:37"><i><font color="Green">E32</font></i></a>, <a class="txt" href="bvfunc24.html#E6:37"><i><font color="Green">E33</font></i></a>, <a class="txt" href="bvfunc24.html#E7:37"><i><font color="Green">E34</font></i></a>, <a class="txt" href="bvfunc24.html#E8:37"><i><font color="Green">E35</font></i></a>, <a class="txt" href="bvfunc24.html#E9:37"><i><font color="Green">E36</font></i></a>, <a class="txt" href="bvfunc24.html#E10:37"><i><font color="Green">E37</font></i></a>, , </i>;<br/>


</div>
