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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:15"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D8">XBOOLE_0:def 8</a><br/>

<b>hence </b><a NAME="E2:15"/>
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="card_1.html#T80">CARD_1:80</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a><br/>

<b>assume </b><a NAME="E3:15"/><i><font color="Green">E12</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E4:15"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="xboole_0.html#R3">are_c=-comparable</a> 
 
<b>by </b><i><a class="txt" href="trees_1.html#E1:15"><i><font color="Green">E11</font></i></a>, <a class="ref" href="xboole_0.html#D9">XBOOLE_0:def 9</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/>
contradiction
 <b>by </b><i><a class="txt" href="trees_1.html#E1:15"><i><font color="Green">E11</font></i></a>, <a class="txt" href="trees_1.html#E3:15"><i><font color="Green">E12</font></i></a>, <a class="ref" href="trees_1.html#T19" target="_self">Th19</a></i>;<br/>


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