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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="E1:38"/>
(  <a href="card_5.html#K1" target="_self">cf</a> 0 <a href="card_1.html#NR1" target="_self">&lt;=`</a> 0 &amp; 0 <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_5.html#K1" target="_self">cf</a> 0 )
 
<b>by </b><i><a class="ref" href="card_5.html#D2" target="_self">Def2</a>, <a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<b>hence </b><a NAME="E2:38"/>
 <a href="card_5.html#K1" target="_self">cf</a> 0 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>

<a NAME="E3:38"/><i><font color="Green">E26</font></i>: 
(  <a href="card_1.html#K1">Card</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> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <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> &amp;  <a href="card_1.html#K1">Card</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="zfrefle1.html#R4">is_cofinal_with</a>  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp;  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">c<sub>1</sub></font> <a href="zfrefle1.html#R4">is_cofinal_with</a> 1 )
 
<b>by </b><i><a class="ref" href="card_5.html#D2" target="_self">Def2</a>, <a class="ref" href="card_1.html#T52">CARD_1:52</a>, <a class="ref" href="card_1.html#D5">CARD_1:def 5</a>, <a class="ref" href="zfrefle1.html#T25">ZFREFLE1:25</a></i>;<br/>
<a NAME="E4:38"/><b>then </b>
 <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="ordinal1.html#R1">c=</a> 1
 
<b>by </b><i><a class="ref" href="card_5.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E5:38"/><b>then </b>
(  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 or (  <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="xboole_0.html#K1">{}</a>  <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="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">c<sub>1</sub></font> ) )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T10">ORDINAL1:10</a>, <a class="ref" href="ordinal3.html#T19">ORDINAL3:19</a>, <a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<b>hence </b><a NAME="E6:38"/>
 <a href="card_5.html#K1" target="_self">cf</a> <span class="p1">(<span class="default"><a href="card_1.html#K1">Card</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="card_5.html#E3:38"><i><font color="Green">E26</font></i></a>, <a class="ref" href="zfrefle1.html#T28">ZFREFLE1:28</a></i>;<br/>


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