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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="hidden.html#M1">set</a> ;<br/>



<b>thus </b><a NAME="E1:13"/>
(  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> implies  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="card_1.html#T34">CARD_1:34</a></i>;<br/>

<b>assume </b><a NAME="E2:13"/><i><font color="Green">E12</font></i>: 
(  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E3:13"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> or  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T24">ORDINAL1:24</a></i>;<br/>
<a NAME="E4:13"/><b>then </b>
( (  <a href="card_1.html#K2">nextcard</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">Card</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">c<sub>2</sub></font> ) or (  <a href="card_1.html#K2">nextcard</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">Card</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>1</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K2">nextcard</a> <font color="Maroon">c<sub>1</sub></font> ) )
 
<b>by </b><i><a class="ref" href="card_1.html#D6">CARD_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E5:13"/>
contradiction
 <b>by </b><i><a class="txt" href="card_4.html#E2:13"><i><font color="Green">E12</font></i></a>, <a class="ref" href="ordinal1.html#T22">ORDINAL1:22</a></i>;<br/>


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