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<a NAME="E1:41_1_1"/>
2 <a href="tarski.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="pencil_1.html#T4">PENCIL_1:4</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:41_1_1"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="pencil_1.html#T2">PENCIL_1:2</a></i>;<br/>
<a NAME="E4:41_1_1"/><i><font color="Green">E29</font></i>: 
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">t</font>,<font color="Maroon">x</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="pencil_4.html#K9" target="_self">PairSet</a> <font color="Maroon">t</font>,<font color="Maroon">X</font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">t</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="pencil_4.html#K9" target="_self">PairSet</a> <font color="Maroon">t</font>,<font color="Maroon">X</font> )
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_1_1_1"/><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">t</font>,<font color="Maroon">x</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">t</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span>
 ;<br/><a NAME="E2:41_1_1_1"/><b>then </b>
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T10">ZFMISC_1:10</a></i>;<br/><b>hence </b><a NAME="E3:41_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T10">ZFMISC_1:10</a>, <a class="ref" href="pencil_4.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:41_1_1"/><b>then </b>
2 <a href="tarski.html#R1">c=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="pencil_4.html#K9" target="_self">PairSet</a> <font color="Maroon">t</font>,<font color="Maroon">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pencil_1.html#T2">PENCIL_1:2</a>, </i>;<br/>
<b>hence </b><a NAME="E7:41_1_1"/>
not  <a href="pencil_4.html#K9" target="_self">PairSet</a> <font color="Maroon">t</font>,<font color="Maroon">X</font> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i><a class="ref" href="pencil_1.html#T4">PENCIL_1:4</a></i>;<br/>


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