<?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="E1:42"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c</font> )
 ;<br/>

<a NAME="E2:42"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E3:42"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.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">c</font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:42"/>
not <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K2">.]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_4.html#T2" target="_self">Th2</a>, <a class="ref" href="rcomp_2.html#T4">RCOMP_2:4</a></i>;<br/>
<a NAME="E5:42"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</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">c</font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T56">ZFMISC_1:56</a></i>;<br/>
<a NAME="E6:42"/>
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.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">c</font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E7:42"/><b>then </b><i><font color="Green">E50</font></i>: 
<span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.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">c</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="E8:42"/>
<span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K2">.]</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="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K2">.]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_4.html#T2" target="_self">Th2</a>, <a class="ref" href="rcomp_2.html#T12">RCOMP_2:12</a></i>;<br/>
<a NAME="E9:42"/><b>then </b>
<span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</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">c</font></span><a href="seq_4.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K2">.]</a></span>
 
<b>by </b><i><a class="ref" href="borsuk_4.html#T2" target="_self">Th2</a>, <a class="ref" href="rcomp_2.html#T6">RCOMP_2:6</a></i>;<br/>
<a NAME="E10:42"/><b>then </b>
<span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</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">c</font></span><a href="seq_4.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c</font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="rcomp_2.html#T6">RCOMP_2:6</a></i>;<br/>
<a NAME="E11:42"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="subset_1.html#K4">\/</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c</font></span><a href="seq_4.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="seq_4.html#K1">{</a><span class="default"><font color="Maroon">c</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/>
<a NAME="E12:42"/><b>then </b>
<span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</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">c</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">c</font></span><a href="seq_4.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T88">XBOOLE_1:88</a></i>;<br/>
<b>hence </b><a NAME="E13:42"/>
<span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="subset_1.html#K4">\/</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K2">.[</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T88">XBOOLE_1:88</a></i>;<br/>


</div>
