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

<b>assume </b><a NAME="E1:26"/>
not <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_1.html#K2" target="_self">nextcard</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:26"/><b>then </b>
(  <a href="card_1.html#K2" target="_self">nextcard</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font>, <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="wellord2.html#R2">are_equipotent</a>  )
 
<b>by </b><i><a class="ref" href="card_1.html#D5" target="_self">Def5</a>, <a class="ref" href="ordinal1.html#T26">ORDINAL1:26</a></i>;<br/>
<a NAME="E3:26"/><b>then </b>
(  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1">(<span class="default"><a href="card_1.html#K2" target="_self">nextcard</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <span class="p1">(<span class="default"><a href="card_1.html#K2" target="_self">nextcard</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2" target="_self">nextcard</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="card_1.html#K2" target="_self">nextcard</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2" target="_self">nextcard</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K2" target="_self">nextcard</a> <span class="p1">(<span class="default"><a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="card_1.html#D5" target="_self">Def5</a>, <a class="ref" href="card_1.html#T27" target="_self">Th27</a>, <a class="ref" href="card_1.html#T32" target="_self">Th32</a>, <a class="ref" href="card_1.html#T35" target="_self">Th35</a></i>;<br/>
<b>hence </b><a NAME="E4:26"/>
contradiction
 <b>by </b><i><a class="ref" href="ordinal1.html#T7">ORDINAL1:7</a></i>;<br/>


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