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

<b>let </b><font color="Maroon">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CLS</font>, <font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CLS</font>, <font color="Maroon">c</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CLS</font>;<br/>

<b>thus </b><a NAME="E1:22"/>
( <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">RR</font> implies ( ( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:22_1"/>
<span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">RR</font>
 ;<br/>

<b>then consider </b><font color="Maroon">i</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">k</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:22_1"/><i><font color="Green">E19</font></i>: 
<span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">i</font>,<font color="Maroon">j</font>,<font color="Maroon">k</font></span><a href="domain_1.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:22_1"/><i><font color="Green">E20</font></i>: 
( ( <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> or <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> ) &amp; <font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">k</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> )
 ;<br/>
<a NAME="E5:22_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> )
 
<b>by </b><i><a class="txt" href="collsp.html#E3:22_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="mcart_1.html#T28">MCART_1:28</a></i>;<br/>
<b>hence </b><a NAME="E6:22_1"/>
( ( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> )
 <b>by </b><i><a class="txt" href="collsp.html#E4:22_1"><i><font color="Green">E20</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:22"/>
( ( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font> implies <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">RR</font> )
 ;<br/>


</div>
