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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="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:17"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> is <a href="wellord1.html#V2">well-ordering</a>
 
<b>by </b><i><a class="ref" href="wellord2.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E3:17"/><i><font color="Green">E18</font></i>: 
 <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font> is <a href="wellord1.html#V2">well-ordering</a>
 
<b>by </b><i><a class="ref" href="wellord2.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E4:17"/><i><font color="Green">E19</font></i>: 
 <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="wellord2.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E5:17"/><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="wellord2.html#E1:17"><i><font color="Green">E16</font></i></a>, <a class="ref" href="wellord2.html#T8" target="_self">Th8</a></i>;<br/>
<div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1"/>
 <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">c<sub>1</sub></font> <a href="wellord1.html#R4">are_isomorphic</a> 
 ;<br/><a NAME="E2:17_1"/><b>then </b>
 <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font>, <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font> <a href="wellord1.html#R4">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="wellord2.html#E5:17"><i><font color="Green">E20</font></i></a>, <a class="ref" href="wellord1.html#T50">WELLORD1:50</a></i>;<br/><b>hence </b><a NAME="E3:17_1"/>
 <a href="wellord2.html#K2" target="_self">order_type_of</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="wellord2.html#E2:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="wellord2.html#D2" target="_self">Def2</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E1:17_2"/><i><font color="Green">E22</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; <span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord1.html#K2">|_2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord1.html#K1">-Seg</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">c<sub>1</sub></font> <a href="wellord1.html#R4">are_isomorphic</a>  )
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="ordinal1.html#NM2">Ordinal</a> <b>by </b><i><a class="txt" href="wellord2.html#E1:17_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/><a NAME="E3:17_2"/><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord1.html#K1">-Seg</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="wellord2.html#E1:17_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="wellord2.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E4:17_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="wellord2.html#E1:17_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/><a NAME="E5:17_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="wellord1.html#K2">|_2</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="wellord2.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E6:17_2"/><b>then </b>
 <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font>, <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>4</sub></font> <a href="wellord1.html#R4">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="wellord2.html#E5:17"><i><font color="Green">E20</font></i></a>, <a class="txt" href="wellord2.html#E1:17_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="wellord2.html#E3:17_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="wellord1.html#T50">WELLORD1:50</a></i>;<br/><b>hence </b><a NAME="E7:17_2"/>
 <a href="wellord2.html#K2" target="_self">order_type_of</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="wellord2.html#E2:17"><i><font color="Green">E17</font></i></a>, <a class="txt" href="wellord2.html#E4:17_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="wellord2.html#D2" target="_self">Def2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:17"/>
 <a href="wellord2.html#K2" target="_self">order_type_of</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="wellord2.html#E1:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="wellord2.html#E3:17"><i><font color="Green">E18</font></i></a>, <a class="txt" href="wellord2.html#E4:17"><i><font color="Green">E19</font></i></a>, <a class="txt" href="wellord2.html#E6:17"><i><font color="Green">E21</font></i></a>, <a class="ref" href="wellord1.html#T64">WELLORD1:64</a></i>;<br/>


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