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



<b>assume </b><a NAME="E1:69"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E2:69"/><i><font color="Green">E32</font></i>: 
 <a href="rat_1.html#K1">denominator</a> <font color="Maroon">p</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="rat_1.html#T29">RAT_1:29</a></i>;<br/>
<a NAME="E3:69"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">a</font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">p</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, </i>;<br/>
<b>thus </b><font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">p</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rat_1.html#T87">RAT_1:87</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">p</font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rat_1.html#T87">RAT_1:87</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">p</font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">p</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="prepower.html#T4" target="_self">Th4</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T22" target="_self">Th22</a>, <a class="ref" href="prepower.html#T24" target="_self">Th24</a>, </i>
;<br/>


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