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







<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">b</font>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green">E34</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="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_2.html#K2">.]</a></span>
 ;<br/>

<a NAME="E3:17"/>
(  not <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> is <a href="xboole_0.html#V1">empty</a> or  not <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_2.html#K2">.]</a></span> is <a href="xboole_0.html#V1">empty</a> )
 
<b>by </b><i>, <a class="ref" href="rcomp_2.html#T4">RCOMP_2:4</a></i>;<br/>
<a NAME="E4:17"/><b>then </b>
( <font color="Maroon">a</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">s</font> )
 
<b>by </b><i>, <a class="ref" href="rcomp_2.html#T10">RCOMP_2:10</a></i>;<br/>
<a NAME="E5:17"/><b>then </b>
(  <a href="pscomp_1.html#K3">inf</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> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="pscomp_1.html#K3">inf</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp;  <a href="pscomp_1.html#K2">sup</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> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp;  <a href="pscomp_1.html#K2">sup</a> <span class="p1"><a href="rcomp_2.html#K2">].</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="rcomp_2.html#K2">.]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:17"/>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> )
 <b>by </b><i/>;<br/>


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