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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="rat_1.html#NM1">Rational</a>;<br/>



<b>assume </b><a NAME="E1:81"/><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = 0 as   <a href="rat_1.html#NM1">Rational</a> ;<br/>
<a NAME="E3:81"/><i><font color="Green">E68</font></i>: 
1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="prepower.html#E1:81"><i><font color="Green">E67</font></i></a>, <a class="txt" href="prepower.html#E56"><i><font color="Green">Lemma38</font></i></a>, <a class="ref" href="real_2.html#T151">REAL_2:151</a></i>;<br/>
<a NAME="E4:81"/><b>then </b><i><font color="Green">E69</font></i>: 
1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
;<br/>
<a NAME="E5:81"/>
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="prepower.html#E1:81"><i><font color="Green">E67</font></i></a>, <a class="txt" href="prepower.html#E3:81"><i><font color="Green">E68</font></i></a>, <a class="ref" href="prepower.html#T75" target="_self">Th75</a></i>;<br/>
<a NAME="E6:81"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="prepower.html#E4:81"><i><font color="Green">E69</font></i></a>, <a class="ref" href="prepower.html#T58" target="_self">Th58</a></i>;<br/>
<a NAME="E7:81"/><b>then </b>
1 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i><a class="txt" href="prepower.html#E1:81"><i><font color="Green">E67</font></i></a>, <a class="ref" href="prepower.html#T68" target="_self">Th68</a></i>;<br/>
<b>hence </b><a NAME="E8:81"/>
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K8" target="_self">#Q</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 1
 <b>by </b><i><a class="ref" href="real_2.html#T117">REAL_2:117</a></i>;<br/>


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