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

<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>



<b>assume </b><a NAME="E1:32"/>
<font color="Maroon">R</font> is <a href="wellord1.html#V2" target="_self">well-ordering</a>
 ;<br/>

<a NAME="E2:32"/><b>then </b>
( <font color="Maroon">R</font> is <a href="relat_2.html#V1">reflexive</a> &amp; <font color="Maroon">R</font> is <a href="relat_2.html#V8">transitive</a> &amp; <font color="Maroon">R</font> is <a href="relat_2.html#V6">connected</a> &amp; <font color="Maroon">R</font> is <a href="relat_2.html#V4">antisymmetric</a> &amp; <font color="Maroon">R</font> is <a href="wellord1.html#V1" target="_self">well_founded</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:32"/>
( <font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">Y</font> is <a href="relat_2.html#V1">reflexive</a> &amp; <font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">Y</font> is <a href="relat_2.html#V8">transitive</a> &amp; <font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">Y</font> is <a href="relat_2.html#V4">antisymmetric</a> &amp; <font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">Y</font> is <a href="relat_2.html#V6">connected</a> &amp; <font color="Maroon">R</font> <a href="wellord1.html#K2" target="_self">|_2</a> <font color="Maroon">Y</font> is <a href="wellord1.html#V1" target="_self">well_founded</a> )
 <b>by </b><i><a class="txt" href="wellord1.html#E3"><i><font color="Green">Lemma21</font></i></a>, <a class="txt" href="wellord1.html#E4"><i><font color="Green">Lemma22</font></i></a>, , <a class="ref" href="wellord1.html#D1" target="_self">Def1</a>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="wellord1.html#D4" target="_self">WELLORD1:def 4</a><br/>


</div>
