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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="xxreal_0.html#V2">positive</a> <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<a NAME="E1:42"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="series_3.html#T15">SERIES_3:15</a></i>;<br/>
<a NAME="E2:42"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/>
<a NAME="E3:42"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T92">XCMPLX_1:92</a></i>;<br/>
<a NAME="E4:42"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/>
<a NAME="E5:42"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K2">-root</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>;<br/>
<a NAME="E6:42"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3 <a href="nat_1.html#K2">*</a> 1
 
<b>by </b><i><a class="ref" href="power.html#T7">POWER:7</a></i>;<br/>
<b>hence </b><a NAME="E7:42"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 3
 ;<br/>


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