<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green">E12</font></i>: 
 <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> 
 ;<br/>

<b>assume </b><a NAME="E2:11"/>
<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>
 ;<br/>

<a NAME="E3:11"/><b>then </b><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T24">ORDINAL1:24</a></i>;<br/>
<div><i><font color="Green">E14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:11_1"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</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="wellord1.html#K1">-Seg</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="wellord2.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E3:11_1"/><i><font color="Green">E17</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="E4:11_1"/><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#K1">-Seg</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="wellord1.html#T13">WELLORD1:13</a></i>;<br/><a NAME="E5:11_1"/><b>then </b><i><font color="Green">E18</font></i>: 
 <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</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="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>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="wellord2.html#E2:11_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="wellord2.html#T8" target="_self">Th8</a></i>;<br/><a NAME="E6:11_1"/>
 <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="E7:11_1"/><b>then </b>
not  <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font>, <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>1</sub></font> <a href="wellord1.html#R4">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="wellord2.html#E1:11_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="wellord2.html#E3:11_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="wellord2.html#E5:11_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="wellord1.html#T57">WELLORD1:57</a></i>;<br/><b>hence </b><a NAME="E8:11_1"/>
contradiction
 <b>by </b><i><a class="txt" href="wellord2.html#E1:11"><i><font color="Green">E12</font></i></a>, <a class="ref" href="wellord1.html#T50">WELLORD1:50</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:11"/><b>then </b><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</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="wellord1.html#K1">-Seg</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="wellord2.html#E3:11"><i><font color="Green">E13</font></i></a>, <a class="ref" href="wellord2.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E6:11"/><i><font color="Green">E16</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>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="wellord2.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E7:11"/><b>then </b>
<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="wellord1.html#K1">-Seg</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="wellord1.html#T13">WELLORD1:13</a></i>;<br/>
<a NAME="E8:11"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="wellord2.html#K1" target="_self">RelIncl</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</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="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>1</sub></font></span>)</span> <a href="wellord1.html#K1">-Seg</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="wellord2.html#E5:11"><i><font color="Green">E15</font></i></a>, <a class="ref" href="wellord2.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E9:11"/>
 <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#T7" target="_self">Th7</a></i>;<br/>
<b>hence </b><a NAME="E10:11"/>
contradiction
 <b>by </b><i><a class="txt" href="wellord2.html#E1:11"><i><font color="Green">E12</font></i></a>, <a class="txt" href="wellord2.html#E3:11"><i><font color="Green">E13</font></i></a>, <a class="txt" href="wellord2.html#E4:11"><i><font color="Green">E14</font></i></a>, <a class="txt" href="wellord2.html#E6:11"><i><font color="Green">E16</font></i></a>, <a class="txt" href="wellord2.html#E8:11"><i><font color="Green">E17</font></i></a>, <a class="ref" href="wellord1.html#T57">WELLORD1:57</a></i>;<br/>


</div>
