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<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><a NAME="E1:157"/><i><font color="Green">E78</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; 0 <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#R1">&lt;=</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:157_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 </span><b>by </b><i><a class="txt" href="xreal_1.html#E1:157"><i><font color="Green">E78</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1"><b>case </b></a><a NAME="E1:157_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:157_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:157"><i><font color="Green">E78</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_2"><b>case </b></a><a NAME="E1:157_1_1_2"/><i><font color="Green">E79</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"><a NAME="E2:157_1_1_2"/><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> <a href="xcmplx_0.html#K5">"</a> 
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:157"><i><font color="Green">E78</font></i></a>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/><a NAME="E3:157_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="xcmplx_0.html#K5">"</a> 
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:157"><i><font color="Green">E78</font></i></a>, <a class="txt" href="xreal_1.html#E1:157_1_1_2"><i><font color="Green">E79</font></i></a>, <a class="txt" href="xreal_1.html#E124"><i><font color="Green">Lemma61</font></i></a></i>;<br/><b>hence </b><a NAME="E4:157_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="xreal_1.html#E1:157"><i><font color="Green">E78</font></i></a>, <a class="ref" href="xreal_1.html#T1" target="_self">Th1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:157"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/>


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