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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E12">A1</font></i>: 
 <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font>, <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 ;<br/>

<b>assume </b><a NAME="E2:11"/>
<font color="Maroon" title="c1">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">B</font>
 ;<br/>

<a NAME="E3:11"/><b>then </b><i><font color="Green" title="E13">A2</font></i>: 
( <font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font> or <font color="Maroon" title="c2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T24" title="ORDINAL1:th.24">ORDINAL1:24</a></i>;<br/>
<div><i><font color="Green" title="E14">A3</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" title="E15">A4</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">B</font>
 ;<br/><a NAME="E2:11_1"/><b>then </b><i><font color="Green" title="E16">A5</font></i>: 
<font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="ref" href="wellord2.html#T10" target="_self" title="WELLORD2:th.10">Th10</a></i>;<br/><a NAME="E3:11_1"/><i><font color="Green" title="E17">A6</font></i>: 
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="ref" href="wellord2.html#D1" target="_self" title="WELLORD2:def.1">Def1</a></i>;<br/><a NAME="E4:11_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="ref" href="wellord1.html#T13" title="WELLORD1:th.13">WELLORD1:13</a></i>;<br/><a NAME="E5:11_1"/><b>then </b><i><font color="Green" title="E18">A7</font></i>: 
 <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c1">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="wellord2.html#E2:11_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="wellord2.html#T8" target="_self" title="WELLORD2:th.8">Th8</a></i>;<br/><a NAME="E6:11_1"/>
 <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>
 <b>by </b><i><a class="ref" href="wellord2.html#T7" target="_self" title="WELLORD2:th.7">Th7</a></i>;<br/><a NAME="E7:11_1"/><b>then </b>
not  <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font>, <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font> <a href="wellord1.html#R4" title="WELLORD1:pred.4">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="wellord2.html#E1:11_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="wellord2.html#E3:11_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="txt" href="wellord2.html#E5:11_1"><i><font color="Green" title="E18">A7</font></i></a>, <a class="ref" href="wellord1.html#T57" title="WELLORD1:th.57">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" title="E12">A1</font></i></a>, <a class="ref" href="wellord1.html#T50" title="WELLORD1:th.50">WELLORD1:50</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:11"/><b>then </b><i><font color="Green" title="E15">A8</font></i>: 
<font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="txt" href="wellord2.html#E3:11"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="wellord2.html#T10" target="_self" title="WELLORD2:th.10">Th10</a></i>;<br/>
<a NAME="E6:11"/><i><font color="Green" title="E16">A9</font></i>: 
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="wellord2.html#D1" target="_self" title="WELLORD2:def.1">Def1</a></i>;<br/>
<a NAME="E7:11"/><b>then </b>
<span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="ref" href="wellord1.html#T13" title="WELLORD1:th.13">WELLORD1:13</a></i>;<br/>
<a NAME="E8:11"/><b>then </b><i><font color="Green" title="E17">A10</font></i>: 
 <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="wellord1.html#K1" title="WELLORD1:func.1">-Seg</a> <font color="Maroon" title="c2">B</font></span>)</span>
 
<b>by </b><i><a class="txt" href="wellord2.html#E5:11"><i><font color="Green" title="E15">A8</font></i></a>, <a class="ref" href="wellord2.html#T8" target="_self" title="WELLORD2:th.8">Th8</a></i>;<br/>
<a NAME="E9:11"/>
 <a href="wellord2.html#K1" title="WELLORD2:func.1">RelIncl</a> <font color="Maroon" title="c1">A</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>
 
<b>by </b><i><a class="ref" href="wellord2.html#T7" target="_self" title="WELLORD2:th.7">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" title="E12">A1</font></i></a>, <a class="txt" href="wellord2.html#E3:11"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="wellord2.html#E4:11"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="wellord2.html#E6:11"><i><font color="Green" title="E16">A9</font></i></a>, <a class="txt" href="wellord2.html#E8:11"><i><font color="Green" title="E17">A10</font></i></a>, <a class="ref" href="wellord1.html#T57" title="WELLORD1:th.57">WELLORD1:57</a></i>;<br/>


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