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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be  <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font> implies <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> is <a href="xxreal_2.html#V2" title="XXREAL_2:attr.2">right_end</a> )</span><br/>



<b>assume </b><a NAME="E1:71"/><i><font color="Green" title="E49">Z</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span> is <a href="xxreal_2.html#V2" title="XXREAL_2:attr.2">right_end</a></span><br/>

<a NAME="E2:71"/>
<font color="Maroon" title="c2">y</font> <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">x</font>,<font color="Maroon" title="c2">y</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span>
 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E49">Z</font></i></a>, <a class="ref" href="xxreal_1.html#T2" title="XXREAL_1:th.2">XXREAL_1:2</a></i>;<br/>
<b>hence </b><a NAME="E3:71"/>
 <a href="xxreal_2.html#K1" title="XXREAL_2:func.1">sup</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</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">x</font>,<font color="Maroon" title="c2">y</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span>
 <b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E49">Z</font></i></a>, <a class="ref" href="xxreal_2.html#T30" target="_self" title="XXREAL_2:th.30">Th30</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xxreal_2.html#D6" target="_self" title="XXREAL_2:def.6">XXREAL_2:def 6</a> <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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