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

<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be   <a href="ordinal1.html#V3" title="ORDINAL1:attr.3">ordinal</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">b</font> iff  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <font color="Maroon" title="c2">b</font> )</span><br/>



<a NAME="E1:17"/>
( <font color="Maroon" title="c2">b</font> <a href="matroid0.html#NR1" title="MATROID0:NR.1">c/=</a> <font color="Maroon" title="c1">a</font> iff  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <font color="Maroon" title="c2">b</font> <a href="matroid0.html#NR1" title="MATROID0:NR.1">c/=</a>  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <font color="Maroon" title="c1">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal6.html#T11" target="_self" title="ORDINAL6:th.11">LemE1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:17"/>
( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">b</font> iff  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ordinal5.html#K3" title="ORDINAL5:func.3">epsilon_</a> <font color="Maroon" title="c2">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal6.html#T4" target="_self" title="ORDINAL6:th.4">EXCH1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
