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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:36"/>
( <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>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="wellord2.html#R2">are_equipotent</a>  )
 ;<br/>

<a NAME="E2:36"/><b>then </b>
(  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="card_1.html#T21" target="_self">Th21</a>, <a class="ref" href="card_1.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E3:36"/><b>then </b>
(  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1" target="_self">Card</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E4:36"/>
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="wellord2.html#R2">are_equipotent</a>  &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="wellord2.html#R2">are_equipotent</a>  )
 <b>by </b><i><a class="ref" href="card_1.html#T21" target="_self">Th21</a></i>;<br/>


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