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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <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="int_1.html#NM1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:52"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:52_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="52_1_1"><b>suppose </b></a><a NAME="E1:52_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="E2:52_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="prepower.html#D4" target="_self">Def4</a></i>;<br/><b>hence </b><a NAME="E3:52_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</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="prepower.html#E1:52"><i><font color="Green">E41</font></i></a>, <a class="ref" href="prepower.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_2"><b>suppose </b></a><a NAME="E1:52_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="E2:52_1_2"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="prepower.html#K1" target="_self">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K5">"</a> 
 <b>by </b><i><a class="ref" href="prepower.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E3:52_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><a href="prepower.html#K1" target="_self">abs</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="prepower.html#E1:52"><i><font color="Green">E41</font></i></a>, <a class="ref" href="prepower.html#T13" target="_self">Th13</a></i>;<br/><b>hence </b><a NAME="E4:52_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</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="prepower.html#E2:52_1_2"><i><font color="Green">E42</font></i></a>, <a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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