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

<b>assume </b><a NAME="E1:2_1_1"/><i><font color="Green">E22</font></i>: 
( not <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">A</font> is <a href="ordinal1.html#V4">being_limit_ordinal</a> )
 ;<br/>

<b>assume </b><a NAME="E2:2_1_1"/>
<font color="Maroon">A</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<a NAME="E3:2_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a> 
 
<b>by </b><i><a class="ref" href="card_4.html#T7">CARD_4:7</a></i>;<br/>
<a NAME="E4:2_1_1"/>
not <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="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E5:2_1_1"/><b>then </b>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T26">ORDINAL1:26</a></i>;<br/>
<a NAME="E6:2_1_1"/><b>then </b>
 <a href="ordinal1.html#K5">omega</a>  <a href="ordinal1.html#R1">c=</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="ordinal1.html#D12">ORDINAL1:def 12</a></i>;<br/>
<a NAME="E7:2_1_1"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:2_1_1"/>
contradiction
 ;<br/>


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