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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E1:9"/>
 <a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V4" target="_self">antisymmetric</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="relat_2.html#D4" target="_self">RELAT_2:def 4</a>,<a class="ref" href="relat_2.html#D12" target="_self">RELAT_2:def 12</a><br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:9_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>hence </b><a NAME="E2:9_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="relat_1.html#D10">RELAT_1:def 10</a></i>;<br/>


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

<b>thus </b><a NAME="E2:9"/>
 <a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V1" target="_self">reflexive</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_2"><b>proof </b></a><div class="add">

<a NAME="E1:9_2"/>
(  <a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V3" target="_self">symmetric</a> &amp;  <a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V8" target="_self">transitive</a> )
 
<b>by </b><i><a class="ref" href="relat_2.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E2:9_2"/>
 <a href="relat_1.html#K6">id</a> <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V1" target="_self">reflexive</a>
 <b>by </b><i><a class="ref" href="relat_2.html#T22" target="_self">Th22</a></i>;<br/>


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


</div>
