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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="relat_1.html#NM1">Relation</a>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:41"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="wellord1.html#V2" target="_self">well-ordering</a> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>and </b><br/><a NAME="E2:41"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="wellord1.html#K1" target="_self">-Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<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> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E3:41"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="relat_2.html#V6">connected</a>
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:41"><i><font color="Green">E39</font></i></a>, <a class="ref" href="wellord1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E4:41"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="relat_2.html#V1">reflexive</a>
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:41"><i><font color="Green">E39</font></i></a>, <a class="ref" href="wellord1.html#D4" target="_self">Def4</a></i>;<br/>
<b>assume </b><a NAME="E5:41"/><i><font color="Green">E43</font></i>: 
not <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> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E6:41"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="wellord1.html#E4:41"><i><font color="Green">E42</font></i></a>, <a class="txt" href="wellord1.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E7:41"/><b>then </b>
<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> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E1:41"><i><font color="Green">E39</font></i></a>, <a class="txt" href="wellord1.html#E3:41"><i><font color="Green">E41</font></i></a>, <a class="txt" href="wellord1.html#E5:41"><i><font color="Green">E43</font></i></a>, <a class="txt" href="wellord1.html#E4"><i><font color="Green">Lemma4</font></i></a></i>;<br/>
<a NAME="E8:41"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> <a href="wellord1.html#K1" target="_self">-Seg</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E6:41"><i><font color="Green">E44</font></i></a>, <a class="ref" href="wellord1.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E9:41"/>
contradiction
 <b>by </b><i><a class="txt" href="wellord1.html#E2:41"><i><font color="Green">E40</font></i></a></i>;<br/>


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