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<b>let </b><font color="Maroon" title="c1">q1</font>, <font color="Maroon" title="c2">q2</font>, <font color="Maroon" title="c3">p1</font>, <font color="Maroon" title="c4">p2</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>







<b>assume </b><a NAME="E1:22"/>
<span class="p1"><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">].</a><span class="default"><font color="Maroon" title="c1">q1</font>,<font color="Maroon" title="c2">q2</font></span><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">.]</a></span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <span class="p1"><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">].</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font></span><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">.]</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:22"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">].</a><span class="default"><font color="Maroon" title="c1">q1</font>,<font color="Maroon" title="c2">q2</font></span><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">.]</a></span> &amp; <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">].</a><span class="default"><font color="Maroon" title="c3">p1</font>,<font color="Maroon" title="c4">p2</font></span><a href="rcomp_2.html#K2" title="RCOMP_2:func.2">.]</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">x2</font> = <font color="Maroon" title="c5">x</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="txt" href="rcomp_2.html#E3:22"><i><font color="Green" title="E5">A1</font></i></a></i>;<br/>
<a NAME="E5:22"/><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c1">q1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">x2</font> &amp; <font color="Maroon" title="c6">x2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">q2</font> )
 
<b>by </b><i><a class="txt" href="rcomp_2.html#E3:22"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="rcomp_2.html#T4" target="_self" title="RCOMP_2:th.4">Th4</a></i>;<br/>
<a NAME="E6:22"/>
( <font color="Maroon" title="c3">p1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">x2</font> &amp; <font color="Maroon" title="c6">x2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">p2</font> )
 
<b>by </b><i><a class="txt" href="rcomp_2.html#E3:22"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="rcomp_2.html#T4" target="_self" title="RCOMP_2:th.4">Th4</a></i>;<br/>
<b>hence </b><a NAME="E7:22"/>
<font color="Maroon" title="c2">q2</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">p1</font>
 <b>by </b><i><a class="txt" href="rcomp_2.html#E5:22"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>


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