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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">Y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">X</font>,<font color="Olive" title="b1">Y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">are_equipotent</a>  holds <br/><font color="Olive" title="b1">Y</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">are_equipotent</a>  implies <font color="Maroon" title="c2">Y</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:3"/><span class="lab"><font color="Green" title="E1">A1</font></span>: 
<font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">Y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">are_equipotent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">Y</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> </span><br/>

<a NAME="E2:3"/><span class="lab"><font color="Green" title="E2">A2</font></span>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="realset1.html#T13" title="REALSET1:th.13">REALSET1:13</a></span>;<br/>
<a NAME="E3:3"/><span class="lab"><font color="Green" title="E3">A3</font></span>: 
<font color="Maroon" title="c2">Y</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3"><span class="lab"><font color="Green" title="E1">A1</font></span></a>, <a class="ref" href="card_1.html#T68" title="CARD_1:th.68">CARD_1:68</a></span>;<br/>
<a NAME="E4:3"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3"><span class="lab"><font color="Green" title="E1">A1</font></span></a>, <a class="ref" href="card_1.html#T21" title="CARD_1:th.21">CARD_1:21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:3"/>
<font color="Maroon" title="c2">Y</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:3"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="txt" href="#E3:3"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="realset1.html#T13" title="REALSET1:th.13">REALSET1:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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