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<b>let </b><font color="Maroon">a</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">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:49"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 )
 ;<br/>

<a NAME="E2:49"/><i><font color="Green">E34</font></i>: 
1 <a href="real_1.html#K6">/</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="real_1.html#K2">"</a> 
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>;<br/>
<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">n</font> <a href="real_1.html#K2">"</a>  as   <a href="rat_1.html#NM1">Rational</a> ;<br/>
<a NAME="E4:49"/><i><font color="Green">E35</font></i>: 
1 <a href="real_1.html#K6">/</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="power.html#E2:49"><i><font color="Green">E34</font></i></a>, <a class="txt" href="power.html#E4:49"><i><font color="Green">E35</font></i></a>, <a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_1_1"/>
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0 )
 </span><b>by </b><i><a class="txt" href="power.html#E2:49"><i><font color="Green">E34</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1_1"><b>suppose </b></a><a NAME="E1:49_1_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><font color="Maroon">a</font> <a href="power.html#K3" target="_self">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">n</font></span>)</span> = 
<font color="Maroon">a</font> <a href="prepower.html#K8">#Q</a> <font color="Maroon">p</font>
<b>by </b><i><a class="txt" href="power.html#E4:49"><i><font color="Green">E35</font></i></a>, <a class="ref" href="power.html#T2" target="_self">Th2</a></i>
<br/>.= 
<font color="Maroon">n</font> <a href="prepower.html#K4">-Root</a> <font color="Maroon">a</font>
<b>by </b><i><a class="txt" href="power.html#E2:49"><i><font color="Green">E34</font></i></a>, , <a class="ref" href="prepower.html#T61">PREPOWER:61</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1_2"><b>suppose </b></a><a NAME="E1:49_1_1_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><font color="Maroon">a</font> <a href="power.html#K3" target="_self">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">n</font></span>)</span> = 
0
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">n</font> <a href="prepower.html#K4">-Root</a> <font color="Maroon">a</font>
<b>by </b><i><a class="txt" href="power.html#E2:49"><i><font color="Green">E34</font></i></a>, <a class="txt" href="power.html#E1:49_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:49"/>
<font color="Maroon">a</font> <a href="power.html#K3" target="_self">to_power</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="power.html#K1" target="_self">-root</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="txt" href="power.html#E2:49"><i><font color="Green">E34</font></i></a>, </i>;<br/>


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