<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c3">L</font>, <font color="Maroon" title="c4">M</font>, <font color="Maroon" title="c5">N</font> be   <a href="card_1.html#NM1" title="CARD_1:NM.1">Cardinal</a>;<br/>







<b>assume </b><a NAME="E1:34"/>
( ( <font color="Maroon" title="c2">K</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c4">M</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c5">N</font> ) or ( <font color="Maroon" title="c2">K</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c4">M</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c5">N</font> ) or ( <font color="Maroon" title="c2">K</font> <a href="card_1.html#NR2" title="CARD_1:NR.2">&lt;`</a> <font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c4">M</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c5">N</font> ) or ( <font color="Maroon" title="c2">K</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c4">M</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c5">N</font> ) )
 ;<br/>

<a NAME="E2:34"/><b>then </b>
( <font color="Maroon" title="c2">K</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c4">M</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c5">N</font> &amp; <font color="Maroon" title="c2">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">K</font> &amp; <font color="Maroon" title="c3">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">L</font> &amp; <font color="Maroon" title="c4">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c5">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">N</font> )
 
<b>by </b><i><a class="ref" href="card_1.html#T13" title="CARD_1:th.13">CARD_1:13</a></i>;<br/>
<a NAME="E3:34"/><b>then </b><i><font color="Green" title="E25">A1</font></i>: 
( <font color="Maroon" title="c2">K</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c4">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">K</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c4">M</font></span>)</span> &amp; <font color="Maroon" title="c3">L</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c5">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">L</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c5">N</font></span>)</span> &amp; <font color="Maroon" title="c2">K</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c4">M</font> <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">L</font> <a href="ordinal2.html#K10" title="ORDINAL2:func.10">+^</a> <font color="Maroon" title="c5">N</font> )
 
<b>by </b><i><a class="ref" href="card_2.html#D1" title="CARD_2:def.1">CARD_2:def 1</a>, <a class="ref" href="ordinal3.html#T21" title="ORDINAL3:th.21">ORDINAL3:21</a></i>;<br/>
<b>hence </b><a NAME="E4:34"/>
<font color="Maroon" title="c2">K</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c4">M</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c3">L</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c5">N</font>
 <b>by </b><i><a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a></i>;<br/>

<b>thus </b><a NAME="E5:34"/>
<font color="Maroon" title="c4">M</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c2">K</font> <a href="card_1.html#NR1" title="CARD_1:NR.1">&lt;=`</a> <font color="Maroon" title="c3">L</font> <a href="card_2.html#K1" title="CARD_2:func.1">+`</a> <font color="Maroon" title="c5">N</font>
 <b>by </b><i><a class="txt" href="card_4.html#E3:34"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a></i>;<br/>


</div>
