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<b>let </b><font color="Maroon" title="c1">r1</font>, <font color="Maroon" title="c2">r2</font>, <font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">s2</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">r2</font> &amp; <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">s2</font> implies <span class="p1"><a href="sppol_2.html#K1" title="SPPOL_2:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font></span><a href="sppol_2.html#K1" title="SPPOL_2:func.1">.]</a></span> is <a href="jordan1.html#V2" title="JORDAN1:attr.2">Jordan</a> )</span><br/>







<b>assume </b><a NAME="E1:107"/><i><font color="Green" title="E82">A1</font></i>: 
( <font color="Maroon" title="c1">r1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">r2</font> &amp; <font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">s2</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="sppol_2.html#K1" title="SPPOL_2:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font></span><a href="sppol_2.html#K1" title="SPPOL_2:func.1">.]</a></span> is <a href="jordan1.html#V2" title="JORDAN1:attr.2">Jordan</a></span><br/>

<a NAME="E2:107"/><b>then </b>
<span class="p1"><a href="sppol_2.html#K1" title="SPPOL_2:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font></span><a href="sppol_2.html#K1" title="SPPOL_2:func.1">.]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">p</font> where <font color="Olive" title="b1">p</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : ( ( <font color="Olive" title="b1">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r1</font> &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">s1</font> ) or ( <font color="Olive" title="b1">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">r1</font> &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font> ) or ( <font color="Olive" title="b1">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">r2</font> &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c1">r1</font> &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> ) or ( <font color="Olive" title="b1">p</font> <a href="euclid.html#K21" title="EUCLID:func.21">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">r2</font> &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Olive" title="b1">p</font> <a href="euclid.html#K22" title="EUCLID:func.22">`2</a>  <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c3">s1</font> ) ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="sppol_2.html#T58" title="SPPOL_2:th.58">SPPOL_2:58</a></i>;<br/>
<b>hence </b><a NAME="E3:107"/>
<span class="p1"><a href="sppol_2.html#K1" title="SPPOL_2:func.1">[.</a><span class="default"><font color="Maroon" title="c1">r1</font>,<font color="Maroon" title="c2">r2</font>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font></span><a href="sppol_2.html#K1" title="SPPOL_2:func.1">.]</a></span> is <a href="jordan1.html#V2" title="JORDAN1:attr.2">Jordan</a>
 <b>by </b><i><a class="txt" href="#E1:107"><i><font color="Green" title="E82">A1</font></i></a>, <a class="ref" href="jordan1.html#T48" title="JORDAN1:th.48">JORDAN1:48</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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