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<b>let </b><font color="Maroon" title="c1">r</font>, <font color="Maroon" title="c2">s</font>, <font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</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> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:52"/><i><font color="Green" title="E32">A1</font></i>: 
<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>and </b><br/><a NAME="E2:52"/><i><font color="Green" title="E33">A2</font></i>: 
<span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">[.</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font></span><a href="xxreal_1.html#K1" title="XXREAL_1:func.1">.]</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">t</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> ;<br/><b>assume </b><a NAME="E1:52_1"/>
( <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font> )
 ;<br/><a NAME="E2:52_1"/><b>then </b>
<font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span>
 <b>by </b><i><a class="ref" href="xxreal_1.html#T4" target="_self" title="XXREAL_1:th.4">Th4</a></i>;<br/><b>hence </b><a NAME="E3:52_1"/>
<font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">t</font>
 <b>by </b><i><a class="ref" href="xxreal_1.html#T1" target="_self" title="XXREAL_1:th.1">Th1</a>, <a class="txt" href="xxreal_1.html#E2:52"><i><font color="Green" title="E33">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:52"/>
<font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font>
 <b>by </b><i><a class="txt" href="xxreal_1.html#E1:52"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="xreal_1.html#T230" title="XREAL_1:th.230">XREAL_1:230</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">t</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> ;<br/><b>assume </b><a NAME="E1:52_2"/>
( <font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">t</font> &amp; <font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">s</font> )
 ;<br/><a NAME="E2:52_2"/><b>then </b>
<font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">].</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K4" title="XXREAL_1:func.4">.[</a></span>
 <b>by </b><i><a class="ref" href="xxreal_1.html#T4" target="_self" title="XXREAL_1:th.4">Th4</a></i>;<br/><b>hence </b><a NAME="E3:52_2"/>
<font color="Maroon" title="c5">t</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">q</font>
 <b>by </b><i><a class="ref" href="xxreal_1.html#T1" target="_self" title="XXREAL_1:th.1">Th1</a>, <a class="txt" href="xxreal_1.html#E2:52"><i><font color="Green" title="E33">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:52"/>
<font color="Maroon" title="c2">s</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">q</font>
 <b>by </b><i><a class="txt" href="xxreal_1.html#E1:52"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="xreal_1.html#T231" title="XREAL_1:th.231">XREAL_1:231</a></i>;<br/>


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