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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>



<b>assume </b><a NAME="E1:32"/>
<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:()"><i><font color="Red">::  thesis: </font></i></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="E2:32"/><b>then </b>
( <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> )
 
<b>by </b><i><a class="ref" href="wellord1.html#D4" target="_self" title="WELLORD1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:32"/>
( <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> )
 <b>by </b><i><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></i>; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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