<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1" title="POWER:func.1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span></span><br/>





<a NAME="E1:23"/>
( 3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; 3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; 3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<b>by </b><i><a class="ref" href="prepower.html#D3" title="PREPOWER:def.3">PREPOWER:def 3</a></i>;<br/>
<a NAME="E2:23"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="series_3.html#T12" target="_self" title="SERIES_3:th.12">Th12</a></i>;<br/>
<a NAME="E3:23"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#T28" title="PREPOWER:th.28">PREPOWER:28</a></i>;<br/>
<a NAME="E4:23"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 3</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p3">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#T28" title="PREPOWER:th.28">PREPOWER:28</a></i>;<br/>
<a NAME="E5:23"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#T28" title="PREPOWER:th.28">PREPOWER:28</a></i>;<br/>
<a NAME="E6:23"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#T31" title="PREPOWER:th.31">PREPOWER:31</a></i>;<br/>
<a NAME="E7:23"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E8:23"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">3 <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#T31" title="PREPOWER:th.31">PREPOWER:31</a></i>;<br/>
<b>hence </b><a NAME="E9:23"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 3 <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1" title="POWER:func.1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c3">c</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="power.html#D1" title="POWER:def.1">POWER:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
