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<b>let </b><font color="Maroon">F</font> be   <a href="card_3.html#NM1">Cardinal-Function</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">M</font> = <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as   <a href="card_1.html#NM1">Cardinal</a> <b>by </b><i/>;<br/>
<a NAME="E3:38"/>
( <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> &amp; <font color="Maroon">M</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">M</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="card_1.html#D5">CARD_1:def 5</a>, <a class="ref" href="card_2.html#T13">CARD_2:13</a></i>;<br/>
<a NAME="E4:38"/><b>then </b>
( <font color="Maroon">M</font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <span class="p1">(<span class="default"><a href="card_3.html#K2" target="_self">disjoin</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">M</font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i>, , <a class="ref" href="card_1.html#T21">CARD_1:21</a></i>;<br/>
<b>hence </b><a NAME="E5:38"/>
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_3.html#K2" target="_self">disjoin</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/>


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