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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="E1:61"/><i><font color="Green" title="E41">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="E2:61"/><i><font color="Green" title="E42">A2</font></i>: 
<span class="p1"><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">.[</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</a></span>
 ;<br/>

<a NAME="E3:61"/>
<span class="p1"><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">].</a><span class="default"><font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font></span><a href="xxreal_1.html#K3" title="XXREAL_1:func.3">.]</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>
 
<b>by </b><i><a class="ref" href="xxreal_1.html#T23" target="_self" title="XXREAL_1:th.23">Th23</a></i>;<br/>
<a NAME="E4:61"/><b>then </b><i><font color="Green" title="E43">A3</font></i>: 
<span class="p1"><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">.[</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>
 
<b>by </b><i><a class="txt" href="xxreal_1.html#E2:61"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:61"/>
<font color="Maroon" title="c1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">[.</a><span class="default"><font color="Maroon" title="c1">r</font>,<font color="Maroon" title="c2">s</font></span><a href="xxreal_1.html#K2" title="XXREAL_1:func.2">.[</a></span>
 
<b>by </b><i><a class="txt" href="xxreal_1.html#E1:61"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="xxreal_1.html#T3" target="_self" title="XXREAL_1:th.3">Th3</a></i>;<br/>
<b>hence </b><a NAME="E6:61"/>
<font color="Maroon" title="c3">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">r</font>
 <b>by </b><i><a class="txt" href="xxreal_1.html#E2:61"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="xxreal_1.html#T2" target="_self" title="XXREAL_1:th.2">Th2</a></i>;<br/>

<b>thus </b><a NAME="E7:61"/>
<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#E1:61"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="xxreal_1.html#E4:61"><i><font color="Green" title="E43">A3</font></i></a>, <a class="ref" href="xxreal_1.html#T52" target="_self" title="XXREAL_1:th.52">Th52</a></i>;<br/>


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