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<b>let </b><font color="Maroon">r1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">r2</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">s1</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">s2</font> be   <a href="real_1.html#NM1">Real</a>;<br/>







<b>assume </b><a NAME="E1:114"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">r1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">r2</font> &amp; <font color="Maroon">s1</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">s2</font> )
 ;<br/>

<a NAME="E2:114"/>
<span class="p1"><a href="sppol_2.html#K1">[.</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">r2</font>,<font color="Maroon">s1</font>,<font color="Maroon">s2</font></span><a href="sppol_2.html#K1">.]</a></span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">p</font> where <font color="Olive">p</font> is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( ( <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> &amp; <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s2</font> &amp; <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s1</font> ) or ( <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r2</font> &amp; <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">r1</font> &amp; <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> ) or ( <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r2</font> &amp; <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">r1</font> &amp; <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> ) or ( <font color="Olive">p</font> <a href="euclid.html#K21">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">r2</font> &amp; <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s2</font> &amp; <font color="Olive">p</font> <a href="euclid.html#K22">`2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s1</font> ) ) </span>}</span> 
 
<b>by </b><i>, <a class="ref" href="sppol_2.html#T58">SPPOL_2:58</a></i>;<br/>
<b>hence </b><a NAME="E3:114"/>
<span class="p1"><a href="sppol_2.html#K1">[.</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">r2</font>,<font color="Maroon">s1</font>,<font color="Maroon">s2</font></span><a href="sppol_2.html#K1">.]</a></span> is <a href="jordan1.html#V2">Jordan</a>
 <b>by </b><i>, <a class="ref" href="jordan1.html#T48">JORDAN1:48</a></i>;<br/>


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