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

<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">R</font> being  <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>  st <font color="Olive" title="b1">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  holds <br/><font color="Olive" title="b1">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c1">Y</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  implies <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c1">Y</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:40"/>
<font color="Maroon" title="c2">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c1">Y</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> </span><br/>

<a NAME="E2:40"/><span class="kw">then </span>
( <font color="Maroon" title="c2">R</font> is  <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>  &amp; <font color="Maroon" title="c2">R</font> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a>  &amp; <font color="Maroon" title="c2">R</font> is  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  &amp; <font color="Maroon" title="c2">R</font> is  <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a>  &amp; <font color="Maroon" title="c2">R</font> is  <a href="wellord1.html#V1" title="WELLORD1:attr.1">well_founded</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="wellord1.html#D4" target="_self" title="WELLORD1:def.4">Def4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:40"/>
( <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c1">Y</font> is  <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>  &amp; <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c1">Y</font> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a>  &amp; <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c1">Y</font> is  <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a>  &amp; <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c1">Y</font> is  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  &amp; <font color="Maroon" title="c2">R</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <font color="Maroon" title="c1">Y</font> is  <a href="wellord1.html#V1" title="WELLORD1:attr.1">well_founded</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="wellord1.html#T22" target="_self" title="WELLORD1:th.22">Th22</a>, <a class="ref" href="wellord1.html#T23" target="_self" title="WELLORD1:th.23">Th23</a>, <a class="ref" href="wellord1.html#T24" target="_self" title="WELLORD1:th.24">Th24</a>, <a class="ref" href="wellord1.html#T25" target="_self" title="WELLORD1:th.25">Th25</a>, <a class="ref" href="wellord1.html#T31" target="_self" title="WELLORD1:th.31">Th31</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="wellord1.html#D4" target="_self" title="WELLORD1:def.4">WELLORD1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
