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





<b>assume </b><a NAME="E1:79"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 &amp; <font color="Maroon">p</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">q</font> )
 ;<br/>

<a NAME="E2:79"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E3:79"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">p</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">q</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="prepower.html#T26" target="_self">Th26</a>, <a class="ref" href="xreal_1.html#T52">XREAL_1:52</a></i>;<br/>
<a NAME="E4:79"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">q</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:79"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:79"/>
<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> <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">q</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">q</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:79"/><b>then </b>
<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> <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">q</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="ref" href="prepower.html#T26" target="_self">Th26</a>, , </i>;<br/>
<a NAME="E8:79"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">p</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">q</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">q</font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">q</font></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#D3" target="_self">Def3</a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<b>hence </b><a NAME="E9:79"/>
<font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">p</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">a</font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">q</font>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>


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