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<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="E1:33"/><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="E2:33"/><b>then </b>
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K1">.[</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_2.html#T3">RCOMP_2:3</a></i>;<br/>
<a NAME="E3:33"/><b>then </b><i><font color="Green">E32</font></i>: 
<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="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K1">.[</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E4:33"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_2.html#T17">RCOMP_2:17</a></i>;<br/>
<a NAME="E5:33"/>
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E6:33"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K2">.[</a></span> <a href="xboole_0.html#R1">misses</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K1">.[</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E7:33"/>
<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="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">b</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">b</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/>
<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#K9">/\</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K1">.[</a></span> = 
<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="subset_1.html#K9">/\</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K1">.[</a></span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T78">XBOOLE_1:78</a></i>
<br/>.= 
<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="borsuk_4.html#T1" target="_self">Th1</a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<b>hence </b><a NAME="E9:33"/>
<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#K9">/\</a> <span class="p1"><a href="rcomp_2.html#K1">[.</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="rcomp_2.html#K1">.[</a></span> <a href="hidden.html#R1">=</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>
 ;<br/>


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