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<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/>







<b>assume </b><a NAME="E1:34"/>
( ( <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">c<sub>5</sub></font> ) or ( <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">c<sub>5</sub></font> ) or ( <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR2" target="_self">&lt;`</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>5</sub></font> ) or ( <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>5</sub></font> ) )
 ;<br/>

<a NAME="E2:34"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="card_1.html#T13">CARD_1:13</a></i>;<br/>
<a NAME="E3:34"/><b>then </b><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="card_2.html#K1">+`</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="card_2.html#K1">+`</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>4</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="card_2.html#D1">CARD_2:def 1</a>, <a class="ref" href="ordinal3.html#T21">ORDINAL3:21</a></i>;<br/>
<b>hence </b><a NAME="E4:34"/>
<font color="Maroon">c<sub>2</sub></font> <a href="card_2.html#K1">+`</a> <font color="Maroon">c<sub>4</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>3</sub></font> <a href="card_2.html#K1">+`</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="card_1.html#T27">CARD_1:27</a></i>;<br/>

<b>thus </b><a NAME="E5:34"/>
<font color="Maroon">c<sub>4</sub></font> <a href="card_2.html#K1">+`</a> <font color="Maroon">c<sub>2</sub></font> <a href="card_1.html#NR1" target="_self">&lt;=`</a> <font color="Maroon">c<sub>3</sub></font> <a href="card_2.html#K1">+`</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="card_4.html#E3:34"><i><font color="Green">E24</font></i></a>, <a class="ref" href="card_1.html#T27">CARD_1:27</a></i>;<br/>


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