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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/>

<b>assume </b><a NAME="E1:26"/>
not <font color="Maroon">c<sub>2</sub></font> is <a href="finset_1.html#V1">finite</a>
 ;<br/>

<a NAME="E2:26"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a> 
 
<b>by </b><i><a class="ref" href="card_4.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E3:26"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K11">*^</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="card_4.html#T30" target="_self">Th30</a></i>;<br/>
<b>then </b> <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <span class="p2">(<span class="default"><a href="ordinal1.html#K1">succ</a> 1</span>)</span></span>)</span> <a href="card_2.html#K2">*`</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_2.html#T25">CARD_2:25</a></i>
<br/>.= 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ordinal1.html#K1">succ</a> 1</span>)</span> <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="card_2.html#T25">CARD_2:25</a></i>
<br/>.= 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="ordinal2.html#K11">*^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ordinal2.html#T53">ORDINAL2:53</a></i>
<br/>.= 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="ordinal2.html#T56">ORDINAL2:56</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font> <a href="card_2.html#K1">+`</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="card_2.html#D1">CARD_2:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E5:26"/>
<font color="Maroon">c<sub>2</sub></font> <a href="card_2.html#K1">+`</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>


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