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<a NAME="E1:39_1_1"/>
2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">X</font>
 
<b>by </b><i><a class="ref" href="pencil_1.html#T4" title="PENCIL_1:th.4">PENCIL_1:4</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:39_1_1"/><i><font color="Green" title="E32">A1</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">y</font> )
 <b>by </b><i><a class="ref" href="pencil_1.html#T2" title="PENCIL_1:th.2">PENCIL_1:2</a></i>;<br/>
<a NAME="E4:39_1_1"/><i><font color="Green" title="E33">A2</font></i>: 
( <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pencil_4.html#K9" title="PENCIL_4:func.9">PairSet</a> <font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c2">X</font> &amp; <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pencil_4.html#K9" title="PENCIL_4:func.9">PairSet</a> <font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c2">X</font> )
 
<b>by </b><i><a class="txt" href="#E3:39_1_1"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="pencil_4.html#D9" target="_self" title="PENCIL_4:def.9">Def9</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:39_1_1_1"/><i><font color="Green" title="E34">A3</font></i>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:39_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">t</font>
 <b>by </b><i><a class="txt" href="#E3:39_1_1"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T10" title="ZFMISC_1:th.10">ZFMISC_1:10</a></i>;<br/><b>hence </b><a NAME="E3:39_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:39_1_1"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="#E1:39_1_1_1"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T10" title="ZFMISC_1:th.10">ZFMISC_1:10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E6:39_1_1"/><b>then </b>
2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="pencil_4.html#K9" title="PENCIL_4:func.9">PairSet</a> <font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c2">X</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E4:39_1_1"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="pencil_1.html#T2" title="PENCIL_1:th.2">PENCIL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E7:39_1_1"/>
not  <a href="pencil_4.html#K9" title="PENCIL_4:func.9">PairSet</a> <font color="Maroon" title="c1">t</font>,<font color="Maroon" title="c2">X</font> is <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>
 <b>by </b><i><a class="ref" href="pencil_1.html#T4" title="PENCIL_1:th.4">PENCIL_1:4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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