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

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:179"/><i><font color="Green">E83</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 holds <br/><font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:179"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E3:179"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="xreal_1.html#E2:179"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xreal_1.html#T157" target="_self">Th157</a></i>;<br/>
<a NAME="E4:179"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2
 
<b>by </b><i><a class="ref" href="xreal_1.html#T85" target="_self">Th85</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:179_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 or ( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) or ( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_1"><b>suppose </b></a><a NAME="E1:179_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:179_1_1"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T133" target="_self">Th133</a></i>;<br/><b>hence </b><a NAME="E3:179_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:179"><i><font color="Green">E83</font></i></a>, <a class="txt" href="xreal_1.html#E2:179"><i><font color="Green">E84</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_2"><b>suppose </b></a><b>that </b><a NAME="E1:179_1_2"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:179_1_2"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><a NAME="E3:179_1_2"/>
2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179"><i><font color="Green">E84</font></i></a>, <a class="txt" href="xreal_1.html#E136"><i><font color="Green">Lemma65</font></i></a></i>;<br/><a NAME="E4:179_1_2"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179_1_2"><i><font color="Green">E88</font></i></a>, <a class="txt" href="xreal_1.html#E129"><i><font color="Green">Lemma63</font></i></a></i>;<br/><a NAME="E5:179_1_2"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179_1_2"><i><font color="Green">E88</font></i></a>, <a class="txt" href="xreal_1.html#E1:179_1_2"><i><font color="Green">E87</font></i></a>, <a class="txt" href="xreal_1.html#E219"><i><font color="Green">Lemma81</font></i></a></i>;<br/><a NAME="E6:179_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179"><i><font color="Green">E84</font></i></a>, <a class="txt" href="xreal_1.html#E2:179_1_2"><i><font color="Green">E88</font></i></a>, <a class="txt" href="xreal_1.html#E129"><i><font color="Green">Lemma63</font></i></a></i>;<br/><a NAME="E7:179_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T157" target="_self">Th157</a></i>;<br/><a NAME="E8:179_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T85" target="_self">Th85</a></i>;<br/><a NAME="E9:179_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T79">XCMPLX_1:79</a></i>;<br/><a NAME="E10:179_1_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1
 <b>by </b><i><a class="txt" href="xreal_1.html#E5:179_1_2"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xreal_1.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E11:179_1_2"/><b>then </b><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:179"><i><font color="Green">E83</font></i></a>, <a class="txt" href="xreal_1.html#E4:179_1_2"><i><font color="Green">E89</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:179_1_2_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_2_1_1"><b>suppose </b></a><a NAME="E1:179_1_2_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:179_1_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:179_1_2"><i><font color="Green">E87</font></i></a>, <a class="ref" href="xreal_1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:179_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179_1_2"><i><font color="Green">E88</font></i></a>, <a class="ref" href="xcmplx_1.html#T93">XCMPLX_1:93</a></i>;<br/><b>hence </b><a NAME="E4:179_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="xreal_1.html#E3:179"><i><font color="Green">E85</font></i></a>, <a class="txt" href="xreal_1.html#E11:179_1_2"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xreal_1.html#T85" target="_self">Th85</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_2_1_2"><b>suppose </b></a><a NAME="E1:179_1_2_1_2"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:179_1_2_1_2"/>
2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179"><i><font color="Green">E84</font></i></a>, <a class="txt" href="xreal_1.html#E136"><i><font color="Green">Lemma65</font></i></a></i>;<br/><a NAME="E3:179_1_2_1_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179_1_2"><i><font color="Green">E88</font></i></a>, <a class="txt" href="xreal_1.html#E129"><i><font color="Green">Lemma63</font></i></a></i>;<br/><a NAME="E4:179_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179_1_2"><i><font color="Green">E88</font></i></a>, <a class="txt" href="xreal_1.html#E1:179_1_2_1_2"><i><font color="Green">E92</font></i></a>, <a class="ref" href="xreal_1.html#T100" target="_self">Th100</a></i>;<br/><a NAME="E5:179_1_2_1_2"/><b>then </b><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179"><i><font color="Green">E84</font></i></a>, <a class="ref" href="xcmplx_1.html#T93">XCMPLX_1:93</a></i>;<br/><a NAME="E6:179_1_2_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:179_1_2_1_2"><i><font color="Green">E92</font></i></a>, <a class="txt" href="xreal_1.html#E72"><i><font color="Green">Lemma42</font></i></a></i>;<br/><a NAME="E7:179_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="xreal_1.html#E5:179_1_2_1_2"><i><font color="Green">E93</font></i></a>, <a class="ref" href="xreal_1.html#T2" target="_self">Th2</a></i>;<br/><b>hence </b><a NAME="E8:179_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="xreal_1.html#E11:179_1_2"><i><font color="Green">E91</font></i></a>, <a class="txt" href="xreal_1.html#E4:179"><i><font color="Green">E86</font></i></a>, <a class="ref" href="xreal_1.html#T2" target="_self">Th2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_3"><b>suppose </b></a><b>that </b><a NAME="E1:179_1_3"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:179_1_3"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/><a NAME="E3:179_1_3"/>
2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="xreal_1.html#E136"><i><font color="Green">Lemma65</font></i></a></i>;<br/><a NAME="E4:179_1_3"/><b>then </b><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179"><i><font color="Green">E84</font></i></a>, <a class="txt" href="xreal_1.html#E129"><i><font color="Green">Lemma63</font></i></a></i>;<br/><a NAME="E5:179_1_3"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="xreal_1.html#E1:179_1_3"><i><font color="Green">E87</font></i></a>, <a class="txt" href="xreal_1.html#E220"><i><font color="Green">Lemma82</font></i></a></i>;<br/><a NAME="E6:179_1_3"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179"><i><font color="Green">E84</font></i></a>, <a class="txt" href="xreal_1.html#E2:179_1_3"><i><font color="Green">E88</font></i></a>, <a class="txt" href="xreal_1.html#E129"><i><font color="Green">Lemma63</font></i></a></i>;<br/><a NAME="E7:179_1_3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T157" target="_self">Th157</a></i>;<br/><a NAME="E8:179_1_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="ref" href="xreal_1.html#T85" target="_self">Th85</a></i>;<br/><a NAME="E9:179_1_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K3">*</a> 2</span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T79">XCMPLX_1:79</a></i>;<br/><a NAME="E10:179_1_3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1
 <b>by </b><i><a class="txt" href="xreal_1.html#E5:179_1_3"><i><font color="Green">E90</font></i></a>, <a class="ref" href="xreal_1.html#T2" target="_self">Th2</a></i>;<br/><a NAME="E11:179_1_3"/><b>then </b><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:179"><i><font color="Green">E83</font></i></a>, <a class="txt" href="xreal_1.html#E4:179_1_3"><i><font color="Green">E89</font></i></a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:179_1_3_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_3_1_1"><b>suppose </b></a><a NAME="E1:179_1_3_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:179_1_3_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2
 <b>by </b><i><a class="txt" href="xreal_1.html#E2:179_1_3"><i><font color="Green">E88</font></i></a>, <a class="ref" href="xcmplx_1.html#T93">XCMPLX_1:93</a></i>;<br/><b>hence </b><a NAME="E3:179_1_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="xreal_1.html#E3:179"><i><font color="Green">E85</font></i></a>, <a class="txt" href="xreal_1.html#E11:179_1_3"><i><font color="Green">E91</font></i></a>, <a class="ref" href="xreal_1.html#T85" target="_self">Th85</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="179_1_3_1_2"><b>suppose </b></a><a NAME="E1:179_1_3_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:179_1_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:179_1_3"><i><font color="Green">E87</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

</div>
