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<b>assume </b><a NAME="E1:124_1_1"/>
<span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> is <a href="xxreal_2.html#V1" title="XXREAL_2:attr.1">left_end</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:124_1_1"/><b>then </b><i><font color="Green" title="E73">A</font></i>: 
 <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span>
 
<b>by </b><i><a class="ref" href="xxreal_2.html#D5" target="_self" title="XXREAL_2:def.5">Def5</a></i>;<br/>
<a NAME="E3:124_1_1"/><b>then </b>
( <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> &amp;  <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">s</font> )
 
<b>by </b><i><a class="ref" href="xxreal_1.html#T2" title="XXREAL_1:th.2">XXREAL_1:2</a></i>;<br/>
<a NAME="E4:124_1_1"/><b>then </b>
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E5:124_1_1"/><b>then </b>
<font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_2.html#K2" title="XXREAL_2:func.2">inf</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span>
 
<b>by </b><i><a class="ref" href="xxreal_2.html#T27" target="_self" title="XXREAL_2:th.27">Th27</a></i>;<br/>
<b>hence </b><a NAME="E6:124_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:124_1_1"><i><font color="Green" title="E73">A</font></i></a>, <a class="ref" href="xxreal_1.html#T2" title="XXREAL_1:th.2">XXREAL_1:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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