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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>let </b><font color="Maroon">p</font> be   <a href="rat_1.html#NM1">Rational</a>;<br/>





<b>assume </b><a NAME="E1:65"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="real_1.html#K2">"</a>  )
 ;<br/>

<a NAME="E2:65"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E3:65"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K6">/</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="prepower.html#T18" target="_self">Th18</a>, <a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>;<br/>
<b>reconsider </b><font color="Maroon">q</font> = <font color="Maroon">n</font> as   <a href="rat_1.html#NM1">Rational</a> ;<br/>
<a NAME="E5:65"/>
(  <a href="rat_1.html#K2">numerator</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="rat_1.html#K1">denominator</a> <font color="Maroon">q</font> &amp;  <a href="rat_1.html#K1">denominator</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="rat_1.html#K2">numerator</a> <font color="Maroon">q</font> )
 
<b>by </b><i>, <a class="ref" href="prepower.html#T19" target="_self">Th19</a>, <a class="ref" href="rat_1.html#T88">RAT_1:88</a></i>;<br/>
<a NAME="E6:65"/><b>then </b><i><font color="Green">E35</font></i>: 
(  <a href="rat_1.html#K2">numerator</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 1 &amp;  <a href="rat_1.html#K1">denominator</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> )
 
<b>by </b><i><a class="ref" href="rat_1.html#T40">RAT_1:40</a></i>;<br/>
<b>reconsider </b><font color="Maroon">i</font> = 1 as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<b>thus </b><a NAME="E8:65"/>
<font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="prepower.html#K4" target="_self">-Root</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="prepower.html#T20" target="_self">Th20</a>, <a class="txt" href="prepower.html#E6:65"><i><font color="Green">E35</font></i></a></i>;<br/>


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