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<b>let </b><font color="Maroon">A</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">A</font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<a NAME="E2:38"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="ordinal2.html#T55">ORDINAL2:55</a></i>;<br/>
<a NAME="E3:38"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="ordinal1.html#R1">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E4:38"/><b>then </b>
 <a href="xboole_0.html#K1">{}</a>  <a href="xboole_0.html#R2">c&lt;</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="ordinal3.html#T9" target="_self">Th9</a>, <a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a></i>;<br/>
<a NAME="E5:38"/><b>then </b>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T21">ORDINAL1:21</a></i>;<br/>
<a NAME="E6:38"/><b>then </b><i><font color="Green">E22</font></i>: 
1 <a href="ordinal1.html#R1">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T33">ORDINAL1:33</a>, </i>;<br/>
<div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:38_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> 1
 ;<br/><a NAME="E2:38_1"/><b>then </b>
<font color="Maroon">A</font> <a href="ordinal1.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="ordinal1.html#T34">ORDINAL1:34</a>, </i>;<br/><a NAME="E3:38_1"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/><b>hence </b><a NAME="E4:38_1"/>
contradiction
 <b>by </b><i><a class="txt" href="ordinal3.html#E6:38"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ordinal2.html#T52">ORDINAL2:52</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:38_2"/>
1 <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:38_2"/><b>then </b>
( 1 <a href="ordinal2.html#K11">*^</a> <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> 1 <a href="ordinal2.html#K11">*^</a> <font color="Maroon">B</font> )
 <b>by </b><i><a class="ref" href="ordinal3.html#T9" target="_self">Th9</a>, <a class="ref" href="ordinal2.html#T56">ORDINAL2:56</a>, <a class="ref" href="ordinal2.html#T57">ORDINAL2:57</a></i>;<br/><b>hence </b><a NAME="E3:38_2"/>
contradiction
 <b>by </b><i><a class="txt" href="ordinal3.html#E6:38"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ordinal3.html#T10" target="_self">Th10</a>, <a class="ref" href="ordinal1.html#T7">ORDINAL1:7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:38"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="ordinal3.html#E17"><i><font color="Green">Lemma25</font></i></a>, <a class="ref" href="ordinal1.html#T24">ORDINAL1:24</a></i>;<br/>

<b>hence </b><a NAME="E10:38"/>
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="ordinal3.html#E6:38"><i><font color="Green">E22</font></i></a>, <a class="ref" href="ordinal2.html#T56">ORDINAL2:56</a></i>;<br/>


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