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

<b>consider </b><font color="Maroon" title="c2">li</font>, <font color="Maroon" title="c3">ri</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E2:31_1_1"/><i><font color="Green" title="E19">A1</font></i>: 
( <font color="Maroon" title="c2">li</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Gi</font> &amp; <font color="Maroon" title="c3">ri</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Gi</font> &amp; <font color="Maroon" title="c2">li</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">ri</font> &amp; ( for <font color="Olive" title="b1">xi</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">xi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Gi</font> &amp; <font color="Maroon" title="c2">li</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">xi</font> holds <br/> not <font color="Olive" title="b1">xi</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">ri</font> ) )
 <b>by </b><i><a class="ref" href="chain_1.html#T14" target="_self" title="CHAIN_1:th.14">Th14</a></i>;<br/>
<b>take </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">li</font>,<font color="Maroon" title="c3">ri</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
;<br/>

<b>take </b>
<font color="Maroon" title="c2">li</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c3">ri</font>
;<br/>

<b>thus </b><a NAME="E3:31_1_1"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">li</font>,<font color="Maroon" title="c3">ri</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">li</font>,<font color="Maroon" title="c3">ri</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> &amp; <font color="Maroon" title="c2">li</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Gi</font> &amp; <font color="Maroon" title="c3">ri</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Gi</font> &amp; ( ( <font color="Maroon" title="c2">li</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">ri</font> &amp; ( for <font color="Olive" title="b1">xi</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">xi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Gi</font> &amp; <font color="Maroon" title="c2">li</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">xi</font> holds <br/> not <font color="Olive" title="b1">xi</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">ri</font> ) ) or ( <font color="Maroon" title="c3">ri</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c2">li</font> &amp; ( for <font color="Olive" title="b1">xi</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">xi</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">Gi</font> holds <br/>( not <font color="Maroon" title="c2">li</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">xi</font> &amp; not <font color="Olive" title="b1">xi</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c3">ri</font> ) ) ) ) )
 <b>by </b><i><a class="txt" href="chain_1.html#E2:31_1_1"><i><font color="Green" title="E19">A1</font></i></a></i>;<br/>


</div>
