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

<b>assume </b><a NAME="E1:12"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="wellord1.html#V2" target="_self">well-ordering</a>
 ;<br/>

<a NAME="E2:12"/><b>then </b><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V1">reflexive</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V6">connected</a> &amp; <font color="Maroon">c<sub>1</sub></font> is <a href="wellord1.html#V1" target="_self">well_founded</a> )
 
<b>by </b><i><a class="ref" href="wellord1.html#D4" target="_self">Def4</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E3:12"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:12"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="wellord1.html#K1" target="_self">-Seg</a> <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="wellord1.html#E2:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="wellord1.html#D2" target="_self">Def2</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E6:12"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="wellord1.html#E5:12"><i><font color="Green">E15</font></i></a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E7:12"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E8:12"/><b>then </b>
not <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="wellord1.html#K1" target="_self">-Seg</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E5:12"><i><font color="Green">E15</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E9:12"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> or  not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="wellord1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E10:12"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> implies <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="wellord1.html#E2:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="wellord1.html#E3:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="wellord1.html#E5:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="wellord1.html#E7:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="wellord1.html#E4"><i><font color="Green">Lemma4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E11:12"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="wellord1.html#E2:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="wellord1.html#E3:12"><i><font color="Green">E14</font></i></a>, <a class="txt" href="wellord1.html#E5:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="wellord1.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>


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