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

<a NAME="E1:4"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="relat_2.html#R4">is_antisymmetric_in</a>  <a href="relat_1.html#K3">field</a> <a href="xboole_0.html#K1">{}</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</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">RELAT_2:def 4</a><br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:4_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</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="xboole_0.html#K1">{}</a>  &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>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>hence </b><a NAME="E2:4_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:4"/>
 <a href="xboole_0.html#K1">{}</a>  is <a href="relat_2.html#V4">antisymmetric</a>
 <b>by </b><i><a class="ref" href="relat_2.html#D12">RELAT_2:def 12</a></i>;<br/>


</div>
