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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<a NAME="E1:56"/>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="card_1.html#T52">CARD_1:52</a></i>;<br/>
<a NAME="E2:56"/><b>then </b>
 <a href="classes1.html#K4">Rank</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="classes1.html#T34">CLASSES1:34</a></i>;<br/>
<b>hence </b><a NAME="E3:56"/>
(  <a href="classes1.html#K4">Rank</a> <font color="Maroon">c<sub>1</sub></font> is <a href="finset_1.html#V1">finite</a> implies  <a href="classes1.html#K4">Rank</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="finset_1.html#V1">finite</a> )
 <b>by </b><i><a class="ref" href="finset_1.html#T24">FINSET_1:24</a></i>;<br/>


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