<?xml version="1.0"?>
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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>, <font color="Maroon">c<sub>3</sub></font> be   <a href="rat_1.html#NM1">Rational</a>;<br/>





<b>assume </b><a NAME="E1:69"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> =  <a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E2:69"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E1:69"><i><font color="Green">E55</font></i></a>, <a class="ref" href="prepower.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E3:69"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E1:69"><i><font color="Green">E55</font></i></a>, <a class="ref" href="prepower.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E4:69"/><i><font color="Green">E58</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 
<b>by </b><i><a class="txt" href="prepower.html#E1:69"><i><font color="Green">E55</font></i></a>, <a class="ref" href="prepower.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E5:69"/><i><font color="Green">E59</font></i>: 
 <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="rat_1.html#T29">RAT_1:29</a></i>;<br/>
<a NAME="E6:69"/><i><font color="Green">E60</font></i>: 
 <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="rat_1.html#T29">RAT_1:29</a></i>;<br/>
<a NAME="E7:69"/><i><font color="Green">E61</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E3:69"><i><font color="Green">E57</font></i></a>, <a class="ref" href="prepower.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E8:69"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E2:69"><i><font color="Green">E56</font></i></a>, <a class="ref" href="prepower.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E9:69"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="txt" href="prepower.html#E5:69"><i><font color="Green">E59</font></i></a>, <a class="txt" href="prepower.html#E6:69"><i><font color="Green">E60</font></i></a>, <a class="ref" href="real_2.html#T138">REAL_2:138</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> =  <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> =  <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<a NAME="E12:69"/><i><font color="Green">E64</font></i>: 
 <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="rat_1.html#D3">RAT_1:def 3</a></i>;<br/>
<a NAME="E13:69"/><i><font color="Green">E65</font></i>: 
 <a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="rat_1.html#D3">RAT_1:def 3</a></i>;<br/>
<a NAME="E14:69"/><b>then </b><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E12:69"><i><font color="Green">E64</font></i></a>, <a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="rat_1.html#T37">RAT_1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rat_1.html#T37">RAT_1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E12:69"><i><font color="Green">E64</font></i></a>, <a class="txt" href="prepower.html#E13:69"><i><font color="Green">E65</font></i></a>, <a class="ref" href="xcmplx_1.html#T117">XCMPLX_1:117</a></i>
;<br/>
<b>then consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E17:69"/><i><font color="Green">E67</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</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"><span class="p2">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2">numerator</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>10</sub></font> &amp; <span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="prepower.html#E14:69"><i><font color="Green">E66</font></i></a>, <a class="ref" href="rat_1.html#T60">RAT_1:60</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="int_1.html#NM1">Integer</a> ;<br/>
<a NAME="E19:69"/><i><font color="Green">E68</font></i>: 
 <a href="rat_1.html#K1">denominator</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</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="rat_1.html#T27">RAT_1:27</a></i>;<br/>
<a NAME="E20:69"/><i><font color="Green">E69</font></i>: 
 <a href="rat_1.html#K1">denominator</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="rat_1.html#T27">RAT_1:27</a></i>;<br/>
<a NAME="E21:69"/>
<span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E9:69"><i><font color="Green">E63</font></i></a>, <a class="txt" href="prepower.html#E17:69"><i><font color="Green">E67</font></i></a></i>;<br/>
<a NAME="E22:69"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E19:69"><i><font color="Green">E68</font></i></a>, <a class="ref" href="xreal_1.html#T141">XREAL_1:141</a></i>;<br/>
<a NAME="E23:69"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E20:69"><i><font color="Green">E69</font></i></a>, <a class="ref" href="xcmplx_1.html#T90">XCMPLX_1:90</a></i>;<br/>
<a NAME="E24:69"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E25:69"/><i><font color="Green">E71</font></i>: 
 <a href="rat_1.html#K1">denominator</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="rat_1.html#T29">RAT_1:29</a></i>;<br/>
<a NAME="E26:69"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p1">(<span class="default"><a href="rat_1.html#K2">numerator</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="prepower.html#E1:69"><i><font color="Green">E55</font></i></a>, <a class="ref" href="prepower.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E27:69"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K8" target="_self">#Q</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</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="txt" href="prepower.html#E1:69"><i><font color="Green">E55</font></i></a>, <a class="ref" href="prepower.html#T63" target="_self">Th63</a></i>;<br/>
<b>thus </b><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="xcmplx_0.html#K3">*</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>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</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>3</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E1:69"><i><font color="Green">E55</font></i></a>, <a class="ref" href="prepower.html#T54" target="_self">Th54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E2:69"><i><font color="Green">E56</font></i></a>, <a class="txt" href="prepower.html#E4:69"><i><font color="Green">E58</font></i></a>, <a class="txt" href="prepower.html#E5:69"><i><font color="Green">E59</font></i></a>, <a class="ref" href="prepower.html#T31" target="_self">Th31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E2:69"><i><font color="Green">E56</font></i></a>, <a class="txt" href="prepower.html#E5:69"><i><font color="Green">E59</font></i></a>, <a class="txt" href="prepower.html#E6:69"><i><font color="Green">E60</font></i></a>, <a class="ref" href="prepower.html#T35" target="_self">Th35</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p0">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E3:69"><i><font color="Green">E57</font></i></a>, <a class="txt" href="prepower.html#E6:69"><i><font color="Green">E60</font></i></a>, <a class="txt" href="prepower.html#E33"><i><font color="Green">Lemma20</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E5:69"><i><font color="Green">E59</font></i></a>, <a class="txt" href="prepower.html#E6:69"><i><font color="Green">E60</font></i></a>, <a class="txt" href="prepower.html#E7:69"><i><font color="Green">E61</font></i></a>, <a class="ref" href="prepower.html#T34" target="_self">Th34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p4">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E7:69"><i><font color="Green">E61</font></i></a>, <a class="txt" href="prepower.html#E8:69"><i><font color="Green">E62</font></i></a>, <a class="txt" href="prepower.html#E9:69"><i><font color="Green">E63</font></i></a>, <a class="ref" href="prepower.html#T31" target="_self">Th31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T46" target="_self">Th46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K6" target="_self">#Z</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T46" target="_self">Th46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</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>8</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K6" target="_self">#Z</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T55" target="_self">Th55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</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>8</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T55" target="_self">Th55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E1:69"><i><font color="Green">E55</font></i></a>, <a class="ref" href="prepower.html#T54" target="_self">Th54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="rat_1.html#K2">numerator</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K6" target="_self">#Z</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E17:69"><i><font color="Green">E67</font></i></a>, <a class="ref" href="prepower.html#T55" target="_self">Th55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K6" target="_self">#Z</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="prepower.html#E9:69"><i><font color="Green">E63</font></i></a>, <a class="txt" href="prepower.html#E17:69"><i><font color="Green">E67</font></i></a>, <a class="txt" href="prepower.html#E26:69"><i><font color="Green">E72</font></i></a>, <a class="ref" href="prepower.html#T56" target="_self">Th56</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K2">*</a> <span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p3">(<span class="default"><a href="rat_1.html#K2">numerator</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="ref" href="prepower.html#T46" target="_self">Th46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rat_1.html#K1">denominator</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K6" target="_self">#Z</a> <span class="p4">(<span class="default"><a href="rat_1.html#K2">numerator</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="prepower.html#E24:69"><i><font color="Green">E70</font></i></a>, <a class="txt" href="prepower.html#E25:69"><i><font color="Green">E71</font></i></a>, <a class="txt" href="prepower.html#E26:69"><i><font color="Green">E72</font></i></a>, <a class="ref" href="prepower.html#T34" target="_self">Th34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="prepower.html#K4" target="_self">-Root</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K8" target="_self">#Q</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <font color="Maroon">c<sub>10</sub></font>

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="prepower.html#K8" target="_self">#Q</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="prepower.html#E24:69"><i><font color="Green">E70</font></i></a>, <a class="txt" href="prepower.html#E27:69"><i><font color="Green">E73</font></i></a>, <a class="txt" href="prepower.html#E33"><i><font color="Green">Lemma20</font></i></a></i>
;<br/>


</div>
