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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<b>assume </b><a NAME="E1:111"/><i><font color="Green">E90</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#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:111"/><b>then </b><i><font color="Green">E91</font></i>: 
1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="prepower.html#E56"><i><font color="Green">Lemma38</font></i></a>, <a class="ref" href="real_2.html#T152">REAL_2:152</a></i>;<br/>
<a NAME="E3:111"/>
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K12" target="_self">#R</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E1:111"><i><font color="Green">E90</font></i></a>, <a class="ref" href="prepower.html#T95" target="_self">Th95</a></i>;<br/>
<a NAME="E4:111"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K12" target="_self">#R</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K5">"</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/>
<a NAME="E5:111"/><b>then </b><i><font color="Green">E92</font></i>: 
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#K12" target="_self">#R</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>;<br/>
<a NAME="E6:111"/>
<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#K12" target="_self">#R</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" 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#K12" target="_self">#R</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="prepower.html#E1:111"><i><font color="Green">E90</font></i></a>, <a class="txt" href="prepower.html#E2:111"><i><font color="Green">E91</font></i></a>, <a class="ref" href="prepower.html#T96" target="_self">Th96</a></i>;<br/>
<a NAME="E7:111"/><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#K12" target="_self">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" 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#K12" target="_self">#R</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="prepower.html#E1:111"><i><font color="Green">E90</font></i></a>, <a class="ref" href="prepower.html#T93" target="_self">Th93</a></i>;<br/>
<a NAME="E8:111"/><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#K12" target="_self">#R</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 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#K12" target="_self">#R</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="prepower.html#E1:111"><i><font color="Green">E90</font></i></a>, <a class="ref" href="prepower.html#T93" target="_self">Th93</a></i>;<br/>
<b>hence </b><a NAME="E9:111"/>
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K12" target="_self">#R</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K12" target="_self">#R</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="prepower.html#E5:111"><i><font color="Green">E92</font></i></a>, <a class="ref" href="real_2.html#T155">REAL_2:155</a></i>;<br/>


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