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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="E1:80"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="wellord1.html#R2">well_orders</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:80"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:80"/>
( <font color="Maroon">c<sub>3</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>3</sub></font> <a href="relat_2.html#R8">is_transitive_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R4">is_antisymmetric_in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R6">is_connected_in</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="orders_2.html#E1:80"><i><font color="Green">E52</font></i></a>, <a class="ref" href="wellord1.html#D5">WELLORD1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E4:80"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R1">is_reflexive_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R8">is_transitive_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R4">is_antisymmetric_in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="relat_2.html#R6">is_connected_in</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="orders_2.html#E2:80"><i><font color="Green">E53</font></i></a>, <a class="txt" href="orders_2.html#E182"><i><font color="Green">Lemma50</font></i></a>, <a class="ref" href="orders_1.html#T93">ORDERS_1:93</a>, <a class="ref" href="orders_1.html#T94">ORDERS_1:94</a>, <a class="ref" href="orders_1.html#T95">ORDERS_1:95</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="wellord1.html#D5">WELLORD1:def 5</a><br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="wellord1.html#D3">WELLORD1:def 3</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E5:80"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E6:80"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E7:80"/>
( <font color="Maroon">c<sub>4</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="wellord1.html#R1">is_well_founded_in</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="orders_2.html#E1:80"><i><font color="Green">E52</font></i></a>, <a class="txt" href="orders_2.html#E2:80"><i><font color="Green">E53</font></i></a>, <a class="txt" href="orders_2.html#E5:80"><i><font color="Green">E54</font></i></a>, <a class="ref" href="wellord1.html#D5">WELLORD1:def 5</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E8:80"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="wellord1.html#K1">-Seg</a> <font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="orders_2.html#E6:80"><i><font color="Green">E55</font></i></a>, <a class="ref" href="wellord1.html#D3">WELLORD1:def 3</a></i>;<br/>


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