<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">p</font> be   <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="Maroon">q</font> be   <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="Maroon">p1</font> be   <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="Maroon">p2</font> be   <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>;<br/>

<b>assume </b><a NAME="E1:55"/><i><font color="Green">E50</font></i>: 
 <a href="jordan3.html#R2" target="_self">LE</a> <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">p1</font>,<font color="Maroon">p2</font>
 ;<br/>

<a NAME="E2:55"/><b>then </b><i><font color="Green">E51</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">p2</font> &amp; ( for <font color="Olive">r1</font>, <font color="Olive">r2</font> being  <a href="real_1.html#NM1">Real</a>  st 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">r1</font> &amp; <font color="Olive">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Olive">r1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Olive">r1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">r2</font> &amp; <font color="Olive">r2</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Olive">r2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Olive">r2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span> holds <br/><font color="Olive">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">r2</font> ) )
 
<b>by </b><i><a class="txt" href="jordan3.html#E6:55"><i><font color="Green">E53</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">s1</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:55"/><i><font color="Green">E52</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s1</font> &amp; <font color="Maroon">s1</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="sppol_1.html#T21">SPPOL_1:21</a></i>;<br/>
<b>consider </b><font color="Maroon">s2</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E6:55"/><i><font color="Green">E53</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s2</font> &amp; <font color="Maroon">s2</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="jordan3.html#T21" target="_self">Th21</a>, <a class="ref" href="sppol_1.html#T21">SPPOL_1:21</a></i>;<br/>
<a NAME="E7:55"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">s1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s2</font>
 
<b>by </b><i><a class="ref" href="jordan3.html#T19" target="_self">Th19</a>, , , <a class="txt" href="jordan3.html#E6:55"><i><font color="Green">E53</font></i></a></i>;<br/>
<a NAME="E8:55"/><i><font color="Green">E62</font></i>: 
1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/>
<div><i><font color="Green">E63</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="55_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:55_1_1"/>
( 1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or 1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1_1"><b>case </b></a><a NAME="E1:55_1_1_1"/><i><font color="Green">E64</font></i>: 
1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:55_1_1_1"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="jordan3.html#E8:55"><i><font color="Green">E62</font></i></a>, <a class="ref" href="xreal_1.html#T50">XREAL_1:50</a></i>;<br/><b>set </b><font color="Maroon">s</font> = <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span>;<br/><a NAME="E3:55_1_1_1"/><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="jordan3.html#E9:55"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jordan3.html#E3:55_1_1_1"><i><font color="Green">E66</font></i></a>, <a class="ref" href="real_2.html#T125">REAL_2:125</a></i>;<br/><a NAME="E4:55_1_1_1"/><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font>
 <b>by </b><i><a class="txt" href="jordan3.html#E2:55_1_1_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E5:55_1_1_1"/><i><font color="Green">E68</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font>
 <b>by </b><i><a class="txt" href="jordan3.html#E2:55_1_1_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><i><font color="Green">E69</font></i>: 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan3.html#E2:55_1_1_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="xcmplx_1.html#T128">XCMPLX_1:128</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span>

;<br/><a NAME="E7:55_1_1_1"/>
1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E8:55_1_1_1"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan3.html#E9:55"><i><font color="Green">E63</font></i></a>, <a class="txt" href="jordan3.html#E2:55_1_1_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E9:55_1_1_1"/><b>then </b><i><font color="Green">E70</font></i>: 
1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan3.html#E2:55_1_1_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>;<br/><span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="jordan3.html#E9:55_1_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="euclid.html#T36">EUCLID:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan3.html#E5:55_1_1_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan3.html#E6:55_1_1_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="euclid.html#T36">EUCLID:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T30">EUCLID:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K4">*</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T37">EUCLID:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">q</font>
<b>by </b><i>, <a class="ref" href="euclid.html#T36">EUCLID:36</a></i>
;<br/><a NAME="E11:55_1_1_1"/><b>then </b>
<font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
 <b>by </b><i><a class="txt" href="jordan3.html#E2:55_1_1_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="euclid.html#T38">EUCLID:38</a></i>;<br/><b>hence </b><a NAME="E12:55_1_1_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font>
 <b>by </b><i><a class="txt" href="jordan3.html#E4:55_1_1_1"><i><font color="Green">E67</font></i></a>, , <a class="ref" href="sppol_1.html#T22">SPPOL_1:22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_1_1_2"><b>case </b></a><a NAME="E1:55_1_1_2"/>
1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:55_1_1_2"/><b>then </b>
1 <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font>
 ;<br/><a NAME="E3:55_1_1_2"/><b>then </b>
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="txt" href="jordan3.html#E8:55"><i><font color="Green">E62</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><b>then </b><font color="Maroon">q</font> = 
<span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default">1 <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="euclid.html#T33">EUCLID:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span> <a href="euclid.html#K17">+</a> <font color="Maroon">p2</font>
<b>by </b><i><a class="ref" href="euclid.html#T33">EUCLID:33</a></i>
<br/>.= 
<font color="Maroon">p2</font>
<b>by </b><i><a class="ref" href="euclid.html#T31">EUCLID:31</a></i>
;<br/><b>hence </b><a NAME="E5:55_1_1_2"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="55_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:55_2_1"/>
( <font color="Maroon">s2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_2_1_1"><b>case </b></a><a NAME="E1:55_2_1_1"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">s2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>set </b><font color="Maroon">s</font> = <font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font>;<br/><a NAME="E2:55_2_1_1"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i>, , <a class="ref" href="real_2.html#T125">REAL_2:125</a></i>;<br/><a NAME="E3:55_2_1_1"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">s2</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E4:55_2_1_1"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">s2</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E5:55_2_1_1"/><i><font color="Green">E75</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">s2</font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span>
 ;<br/><a NAME="E6:55_2_1_1"/>
<font color="Maroon">s2</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font>
 <b>by </b><i>, <a class="txt" href="jordan3.html#E8:55"><i><font color="Green">E62</font></i></a>, , <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E7:55_2_1_1"/><b>then </b><i><font color="Green">E76</font></i>: 
1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>;<br/><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">q</font></span>)</span></span>)</span> = 
<font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K4">*</a> <font color="Maroon">s2</font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="xcmplx_1.html#T128">XCMPLX_1:128</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T36">EUCLID:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p4">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="euclid.html#T36">EUCLID:36</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T30">EUCLID:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s2</font></span>)</span></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K4">*</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T37">EUCLID:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s2</font> <a href="real_1.html#K4">*</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">s1</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T34">EUCLID:34</a></i>
<br/>.= 
<font color="Maroon">s2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p</font>
<b>by </b><i>, <a class="ref" href="euclid.html#T36">EUCLID:36</a></i>
;<br/><a NAME="E9:55_2_1_1"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">s1</font> <a href="real_1.html#K6">/</a> <font color="Maroon">s2</font></span>)</span> <a href="euclid.html#K18">*</a> <font color="Maroon">q</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="euclid.html#T38">EUCLID:38</a></i>;<br/><b>hence </b><a NAME="E10:55_2_1_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">q</font>
 <b>by </b><i>, , <a class="ref" href="sppol_1.html#T22">SPPOL_1:22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="55_2_1_2"><b>case </b></a><a NAME="E1:55_2_1_2"/>
<font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:55_2_1_2"/><b>then </b>
<font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="jordan3.html#T19" target="_self">Th19</a>, , , <a class="txt" href="jordan3.html#E6:55"><i><font color="Green">E53</font></i></a></i>;<br/><b>then </b><font color="Maroon">p</font> = 
<span class="p1">(<span class="default">1 <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span>
<b>by </b><i>, <a class="ref" href="euclid.html#T33">EUCLID:33</a></i>
<br/>.= 
<font color="Maroon">p1</font> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K16">0.REAL</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="euclid.html#T33">EUCLID:33</a></i>
<br/>.= 
<font color="Maroon">p1</font>
<b>by </b><i><a class="ref" href="euclid.html#T31">EUCLID:31</a></i>
;<br/><b>hence </b><a NAME="E4:55_2_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="topreal1.html#T6">TOPREAL1:6</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E11:55"/>
( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p</font>,<font color="Maroon">p2</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="topreal1.html#K3">LSeg</a> <font color="Maroon">p1</font>,<font color="Maroon">q</font> )
 <b>by </b><i/>;<br/>


</div>
