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<b>let </b><font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>







<b>assume </b><a NAME="E1:11"/><i><font color="Green">E47</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">X</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k</font>
 ;<br/>

<b>assume </b><a NAME="E2:11"/>
not  <a href="card_fin.html#K1" target="_self">Choose</a> <font color="Maroon">X</font>,<font color="Maroon">k</font>,<font color="Maroon">x1</font>,<font color="Maroon">x2</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>

<b>then consider </b><font color="Maroon">z</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:11"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="card_fin.html#K1" target="_self">Choose</a> <font color="Maroon">X</font>,<font color="Maroon">k</font>,<font color="Maroon">x1</font>,<font color="Maroon">x2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="tarski.html#K2">}</a></span><b> such that </b><br/><a NAME="E6:11"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x1</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> )
 <b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E7:11"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="card_1.html#T80">CARD_1:80</a></i>;<br/>


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