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



<b>assume </b><a NAME="E1:11"/>
<font color="Maroon">c<sub>2</sub></font> <a href="wellord1.html#R2" target="_self">well_orders</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:11"/><b>then </b><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R1">is_reflexive_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R6">is_connected_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="wellord1.html#R1" target="_self">is_well_founded_in</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="wellord1.html#D5" target="_self">Def5</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E3:11"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</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>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:11"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="wellord1.html#K1" target="_self">-Seg</a> <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="wellord1.html#E2:11"><i><font color="Green">E12</font></i></a>, <a class="ref" href="wellord1.html#D3" target="_self">Def3</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>thus </b><a NAME="E6:11"/>
<font color="Maroon">c<sub>4</sub></font> <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#E5:11"><i><font color="Green">E14</font></i></a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E7:11"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E8:11"/><b>then </b>
not <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="wellord1.html#K1" target="_self">-Seg</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="wellord1.html#E5:11"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E9:11"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> or  not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</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>2</sub></font> )
 
<b>by </b><i><a class="ref" href="wellord1.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E10:11"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> implies <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>5</sub></font></span><a href="tarski.html#K4">]</a></span> <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#E2:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="wellord1.html#E3:11"><i><font color="Green">E13</font></i></a>, <a class="txt" href="wellord1.html#E5:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="wellord1.html#E7:11"><i><font color="Green">E15</font></i></a>, <a class="ref" href="relat_2.html#D6">RELAT_2:def 6</a></i>;<br/>
<b>hence </b><a NAME="E11:11"/>
<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>5</sub></font></span><a href="tarski.html#K4">]</a></span> <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#E2:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="wellord1.html#E3:11"><i><font color="Green">E13</font></i></a>, <a class="txt" href="wellord1.html#E5:11"><i><font color="Green">E14</font></i></a>, <a class="ref" href="relat_2.html#D1">RELAT_2:def 1</a></i>;<br/>


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