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

<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">c</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:35"/>
( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> )
 ;<br/>

<a NAME="E2:35"/><b>then </b>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K2">.]</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_2.html#T13">RCOMP_2:13</a></i>;<br/>
<a NAME="E3:35"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="seq_4.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K2">.]</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T14">RCOMP_1:14</a></i>;<br/>
<a NAME="E4:35"/>
( <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="seq_4.html#K1">}</a></span> &amp; <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="seq_4.html#K1">}</a></span> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:35"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T70">XBOOLE_1:70</a></i>;<br/>
<a NAME="E6:35"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p3"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K2">.]</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="seq_4.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E7:35"/>
<span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K1">.]</a></span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">b</font></span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K2">.]</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T88">XBOOLE_1:88</a></i>;<br/>


</div>
