<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:30"/>
 <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:30_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Y</font>
 ;<br/>

<b>hence </b><a NAME="E2:30_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="classes1.html#D4" target="_self">Def4</a>, </i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:30"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Y</font></span>)</span> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">Y</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="card_1.html#T27">CARD_1:27</a>, <a class="ref" href="card_1.html#T30">CARD_1:30</a></i>;<br/>
<b>hence </b><a NAME="E4:30"/>
 <a href="card_1.html#K1">Card</a> <font color="Maroon">Y</font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="classes1.html#K1" target="_self">Tarski-Class</a> <font color="Maroon">X</font></span>)</span>
 ;<br/>


</div>
