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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xxreal_0.html#V2">positive</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</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="E1:33"/><i><font color="Green">E20</font></i>: 
 <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:33_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_1"><b>suppose </b></a><a NAME="E1:33_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:33_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="series_3.html#E1:33"><i><font color="Green">E20</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/><b>hence </b><a NAME="E3:33_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="square_1.html#K3">^2</a> 
 <b>by </b><i><a class="ref" href="square_1.html#T77">SQUARE_1:77</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="33_1_2"><b>suppose </b></a><a NAME="E1:33_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:33_1_2"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="series_3.html#E1:33"><i><font color="Green">E20</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/><a NAME="E3:33_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="square_1.html#K3">^2</a> 
 <b>by </b><i><a class="ref" href="square_1.html#T77">SQUARE_1:77</a></i>;<br/><b>hence </b><a NAME="E4:33_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="square_1.html#K3">^2</a> 
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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