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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="polynom3.html#NM1">Polynomial</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/>

<b>assume </b><a NAME="E1:94"/><i><font color="Green">E67</font></i>: 
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/>

<a NAME="E2:94"/><b>then </b><i><font color="Green">E68</font></i>: 
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <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/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:94_1"/>
(  <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2 or  <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="polynom5.html#E2:94"><i><font color="Green">E68</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_1"><b>suppose </b></a><a NAME="E1:94_1_1"/>
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> <b> such that </b><br/><a NAME="E3:94_1_1"/><i><font color="Green">E69</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a>  holds <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#T74" target="_self">Th74</a></i>;<br/><b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span>;<br/><i><font color="Green">E70</font></i>:  <a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> = 
 <a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7">RLVECT_1:def 7</a></i>
<br/>.= 
 <a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="polynom4.html#K2">eval</a> <span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span>,<span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T48" target="_self">Th48</a></i>
<br/>.= 
 <a href="polynom4.html#K2">eval</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T54" target="_self">Th54</a></i>
;<br/><div><i><font color="Green">E71</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/> <a href="polynom4.html#K2">eval</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="polynom4.html#K2">eval</a> <span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T54" target="_self">Th54</a></i>
<br/>.= 
 <a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T48" target="_self">Th48</a></i>
;<br/><a NAME="E2:94_1_1_2"/><b>then </b>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2">eval</a> <span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E3:94_1_1"><i><font color="Green">E69</font></i></a></i>;<br/><b>hence </b><a NAME="E3:94_1_1_2"/>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2">eval</a> <span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E4:94_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="polynom5.html#T32" target="_self">Th32</a></i>;<br/></div><b>end;</b></div><a NAME="E6:94_1_1"/><i><font color="Green">E72</font></i>: 
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94"><i><font color="Green">E67</font></i></a></i>;<br/><a NAME="E7:94_1_1"/>
 <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/><a NAME="E8:94_1_1"/><b>then </b>
 <a href="algseq_1.html#K3">len</a> <span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i><a class="ref" href="polynom5.html#T41" target="_self">Th41</a></i>;<br/><b>then </b><i><font color="Green">E73</font></i>:  <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 2</span>)</span> <a href="real_1.html#K3">+</a> 2
<b>by </b><i><a class="txt" href="polynom5.html#E6:94_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="polynom5.html#T53" target="_self">Th53</a></i>
<br/>.= 
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>

;<br/><b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means ( <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 &amp; <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  );<br/><a NAME="E10:94_1_1"/><i><font color="Green">E74</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_4"><b>proof </b></a><div class="add">

<a NAME="E1:94_1_1_4"/>
<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="txt" href="polynom5.html#E1:94"><i><font color="Green">E67</font></i></a>, <a class="txt" href="polynom5.html#E9:94_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E2:94_1_1_4"/><b>then </b>
<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1
 
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 as   <a href="nat_1.html#NM1">Nat</a> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<a NAME="E4:94_1_1_4"/>
 <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="polynom5.html#E1:94"><i><font color="Green">E67</font></i></a>, <a class="txt" href="polynom5.html#E9:94_1_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>hence </b><a NAME="E5:94_1_1_4"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/>

<a NAME="E6:94_1_1_4"/>
 <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<b>hence </b><a NAME="E7:94_1_1_4"/>
<span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="algseq_1.html#T25">ALGSEQ_1:25</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E12:94_1_1"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>4</sub></font>]
 <b>and </b><br/><a NAME="E13:94_1_1"/><i><font color="Green">E76</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font>
 <b>from </b><i><a class="ref" href="nat_1.html#S5">NAT_1:sch 5</a>(<a class="txt" href="polynom5.html#E10:94_1_1"><i><font color="Green">E74</font></i></a>);<br/></i><a NAME="E14:94_1_1"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a> <b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green">E75</font></i></a></i>;<br/><a NAME="E16:94_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="algseq_1.html#T22">ALGSEQ_1:22</a></i>;<br/><a NAME="E17:94_1_1"/><b>then </b><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="comptrig.html#M1">CRoot</a> of <font color="Maroon">c<sub>5</sub></font>, <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>;<br/><b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a>  = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span>;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a> <b> such that </b><br/><a NAME="E20:94_1_1"/><i><font color="Green">E79</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E21:94_1_1"/><i><font color="Green">E80</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1">FINSEQ_2:sch 1</a>();<br/></i><a NAME="E22:94_1_1"/>
<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1"><i><font color="Green">E78</font></i></a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E23:94_1_1"/><b>then </b><i><font color="Green">E81</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E20:94_1_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><div><i><font color="Green">E82</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_5"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:94_1_1_5"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:94_1_1_5"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algseq_1.html#K3">len</a> <span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E20:94_1_1"><i><font color="Green">E79</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E3:94_1_1_5"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E21:94_1_1"><i><font color="Green">E80</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_6"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E1:94_1_1_6"/><i><font color="Green">E83</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 ;<br/><b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font>;<br/><b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="complfld.html#K1">F_Complex</a> <b> such that </b><br/><a NAME="E3:94_1_1_6"/><i><font color="Green">E84</font></i>: 
 <a href="polynom4.html#K2">eval</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E4:94_1_1_6"/><i><font color="Green">E85</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span>
 <b>and </b><br/><a NAME="E5:94_1_1_6"/><i><font color="Green">E86</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>10</sub></font> holds <br/><font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom4.html#D2">POLYNOM4:def 2</a></i>;<br/><a NAME="E6:94_1_1_6"/>
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E14:94_1_1"><i><font color="Green">E77</font></i></a>, <a class="txt" href="polynom5.html#E17:94_1_1"><i><font color="Green">E78</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green">E85</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E7:94_1_1_6"/><b>then </b><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E8:94_1_1_6"/><b>then </b><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/><a NAME="E9:94_1_1_6"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green">E75</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green">E85</font></i></a>, <a class="ref" href="algseq_1.html#T22">ALGSEQ_1:22</a></i>;<br/><a NAME="E10:94_1_1_6"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E11:94_1_1_6"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E9:94_1_1_6"><i><font color="Green">E89</font></i></a>, <a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>;<br/><a NAME="E12:94_1_1_6"/><b>then </b><i><font color="Green">E90</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E13:94_1_1_6"/><i><font color="Green">E91</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="finseq_5.html#T20">FINSEQ_5:20</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>11</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:94_1_1_6_1"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E2:94_1_1_6_1"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 ;<br/><a NAME="E3:94_1_1_6_1"/><i><font color="Green">E94</font></i>: 
( 0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E4:94_1_1_6_1"/><b>then </b><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E5:94_1_1_6_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E2:94_1_1_6_1"><i><font color="Green">E93</font></i></a>, <a class="txt" href="polynom5.html#E3:94_1_1_6_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E6:94_1_1_6_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <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="E7:94_1_1_6_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><a NAME="E8:94_1_1_6_1"/><b>then </b><i><font color="Green">E96</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E9:94_1_1_6_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E9:94_1_1_6"><i><font color="Green">E89</font></i></a>, <a class="txt" href="polynom5.html#E3:94_1_1_6_1"><i><font color="Green">E94</font></i></a>, <a class="ref" href="finseq_1.html#T80">FINSEQ_1:80</a></i>;<br/><a NAME="E10:94_1_1_6_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <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="E11:94_1_1_6_1"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E12:94_1_1_6_1"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E4:94_1_1_6_1"><i><font color="Green">E95</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font> = 
<font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="finseq_4.html#T85">FINSEQ_4:85</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="txt" href="polynom5.html#E13:94_1_1_6"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom5.html#E1:94_1_1_6_1"><i><font color="Green">E92</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E5:94_1_1_6"><i><font color="Green">E86</font></i></a>, <a class="txt" href="polynom5.html#E13:94_1_1_6"><i><font color="Green">E91</font></i></a>, <a class="txt" href="polynom5.html#E1:94_1_1_6_1"><i><font color="Green">E92</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E13:94_1_1"><i><font color="Green">E76</font></i></a>, <a class="txt" href="polynom5.html#E8:94_1_1_6_1"><i><font color="Green">E96</font></i></a>, <a class="txt" href="polynom5.html#E12:94_1_1_6_1"><i><font color="Green">E97</font></i></a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
;<br/></div><b>end;</b></div><b>then </b><i><font color="Green">E92</font></i>:  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1_6"><i><font color="Green">E90</font></i></a>, <a class="ref" href="polynom2.html#T5">POLYNOM2:5</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> 1
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1_6"><i><font color="Green">E90</font></i></a>, <a class="ref" href="finseq_4.html#T85">FINSEQ_4:85</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1_6"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom5.html#E13:94_1_1_6"><i><font color="Green">E91</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E5:94_1_1_6"><i><font color="Green">E86</font></i></a>, <a class="txt" href="polynom5.html#E12:94_1_1_6"><i><font color="Green">E90</font></i></a>, <a class="txt" href="polynom5.html#E13:94_1_1_6"><i><font color="Green">E91</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default">1 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,0</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D8">GROUP_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0
<b>by </b><i><a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>
;<br/><i><font color="Green">E93</font></i>: <font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> = 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E7:94_1_1_6"><i><font color="Green">E87</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E5:94_1_1_6"><i><font color="Green">E86</font></i></a>, <a class="txt" href="polynom5.html#E7:94_1_1_6"><i><font color="Green">E87</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comptrig.html#T15">COMPTRIG:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="comptrig.html#D2">COMPTRIG:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="complfld.html#T78">COMPLFLD:78</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="complfld.html#T64">COMPLFLD:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="complfld.html#T66">COMPLFLD:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="comptrig.html#T16">COMPTRIG:16</a></i>
;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span>;<br/><a NAME="E17:94_1_1_6"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="power.html#T39">POWER:39</a></i>;<br/><a NAME="E18:94_1_1_6"/><i><font color="Green">E95</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="power.html#T39">POWER:39</a></i>;<br/><a NAME="E19:94_1_1_6"/>
0 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="tbsp_1.html#T2">TBSP_1:2</a></i>;<br/><a NAME="E20:94_1_1_6"/><b>then </b><i><font color="Green">E96</font></i>: 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E21:94_1_1_6"/><i><font color="Green">E97</font></i>: 
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default">0,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="hidden.html#R1">=</a> 0 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
 <b>by </b><i><a class="ref" href="hahnban1.html#D1">HAHNBAN1:def 1</a></i>;<br/> <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a>  = 
 <a href="complex1.html#K5">0c</a> 
<b>by </b><i><a class="ref" href="complfld.html#T9">COMPLFLD:9</a></i>
<br/>.= 
0

;<br/><a NAME="E23:94_1_1_6"/><b>then </b><i><font color="Green">E98</font></i>: 
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6"><i><font color="Green">E94</font></i></a>, <a class="ref" href="comptrig.html#T8">COMPTRIG:8</a>, <a class="txt" href="polynom5.html#E21:94_1_1_6"><i><font color="Green">E97</font></i></a></i>;<br/><a NAME="E24:94_1_1_6"/><b>then </b><i><font color="Green">E99</font></i>: 
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> the <a href="struct_0.html#U2">Zero</a> of <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="rlvect_1.html#D2">RLVECT_1:def 2</a></i>;<br/><i><font color="Green">E100</font></i>:  <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E23:94_1_1_6"><i><font color="Green">E98</font></i></a>, <a class="ref" href="complfld.html#T66">COMPLFLD:66</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E23:94_1_1_6"><i><font color="Green">E98</font></i></a>, <a class="ref" href="complfld.html#T64">COMPLFLD:64</a></i>
;<br/><a NAME="E26:94_1_1_6"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p2"><a href="finseq_1.html#K9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="finseq_1.html#K9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7">^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E14:94_1_1"><i><font color="Green">E77</font></i></a>, <a class="txt" href="polynom5.html#E17:94_1_1"><i><font color="Green">E78</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green">E85</font></i></a>, <a class="ref" href="polynom4.html#T3">POLYNOM4:3</a></i>;<br/><b>then </b> <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E8:94_1_1_6"><i><font color="Green">E88</font></i></a>, <a class="ref" href="rlvect_1.html#T58">RLVECT_1:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T58">RLVECT_1:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_1.html#K17">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E15:94_1_1_6"><i><font color="Green">E92</font></i></a>, <a class="txt" href="polynom5.html#E16:94_1_1_6"><i><font color="Green">E93</font></i></a>, <a class="ref" href="rlvect_1.html#T61">RLVECT_1:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T41">VECTSP_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D11">RLVECT_1:def 11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E25:94_1_1_6"><i><font color="Green">E100</font></i></a>, <a class="ref" href="vectsp_1.html#T43">VECTSP_1:43</a></i>
;<br/><a NAME="E28:94_1_1_6"/><b>then </b><i><font color="Green">E101</font></i>: 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><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="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p5"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E5:94_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="polynom5.html#E3:94_1_1_6"><i><font color="Green">E84</font></i></a></i>;<br/><a NAME="E29:94_1_1_6"/>
 <a href="complex1.html#K6">1r</a>  <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K3">*</a> <a href="complex1.html#K7">&lt;i&gt;</a> </span>)</span>
 <b>by </b><i><a class="ref" href="complex1.html#D7">COMPLEX1:def 7</a></i>;<br/><b>then </b><i><font color="Green">E102</font></i>: <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> = 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default">1,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="rlvect_1.html#K6">-</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span>
<b>by </b><i><a class="ref" href="complfld.html#T10">COMPLFLD:10</a>, <a class="ref" href="hahnban1.html#D1">HAHNBAN1:def 1</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<span class="p3">(<span class="default">0 <a href="real_1.html#K5">-</a> 0</span>)</span></span><a href="hahnban1.html#K1">**]</a></span></span><a href="complfld.html#K3">.|</a></span>
<b>by </b><i><a class="ref" href="polynom5.html#T6" target="_self">Th6</a></i>
<br/>.= 
 <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#T13">HAHNBAN1:13</a></i>
<br/>.= 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E20:94_1_1_6"><i><font color="Green">E96</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/><a NAME="E31:94_1_1_6"/>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><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="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p5"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="ref" href="complfld.html#T100">COMPLFLD:100</a></i>;<br/><a NAME="E32:94_1_1_6"/><b>then </b>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E28:94_1_1_6"><i><font color="Green">E101</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E33:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="ref" href="complfld.html#T109">COMPLFLD:109</a></i>;<br/><a NAME="E34:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="ref" href="complfld.html#T109">COMPLFLD:109</a></i>;<br/><a NAME="E35:94_1_1_6"/><b>then </b>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E30:94_1_1_6"><i><font color="Green">E102</font></i></a>, <a class="ref" href="xreal_1.html#T22">XREAL_1:22</a></i>;<br/><a NAME="E36:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="hahnban1.html#T13">HAHNBAN1:13</a></i>;<br/><a NAME="E37:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6"><i><font color="Green">E94</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/><a NAME="E38:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E18:94_1_1_6"><i><font color="Green">E95</font></i></a>, <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E39:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E18:94_1_1_6"><i><font color="Green">E95</font></i></a>, <a class="ref" href="xcmplx_1.html#T90">XCMPLX_1:90</a></i>;<br/><a NAME="E40:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T75">XCMPLX_1:75</a></i>;<br/><a NAME="E41:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="power.html#T34">POWER:34</a></i>;<br/><a NAME="E42:94_1_1_6"/><b>then </b><i><font color="Green">E103</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23">VECTSP_1:def 23</a></i>
<br/>.= 
 <a href="rlvect_1.html#K9">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T29">POLYNOM1:29</a></i>
;<br/><a NAME="E44:94_1_1_6"/><b>then </b><i><font color="Green">E104</font></i>: 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#T15" target="_self">Th15</a></i>;<br/><a NAME="E45:94_1_1_6"/><i><font color="Green">E105</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D3">POLYNOM1:def 3</a></i>;<br/><i><font color="Green">E106</font></i>:  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span> = 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self">Def1</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E45:94_1_1_6"><i><font color="Green">E105</font></i></a>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1"><i><font color="Green">E78</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green">E85</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E23:94_1_1"><i><font color="Green">E81</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green">E85</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self">Def1</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_6_10"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:94_1_1_6_10"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span>
 ;<br/><a NAME="E2:94_1_1_6_10"/><b>then </b><i><font color="Green">E108</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:94_1_1_6_10"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E4:94_1_1_6_10"/><b>then </b><i><font color="Green">E109</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><i><font color="Green">E110</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 1
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font>

;<br/><a NAME="E6:94_1_1_6_10"/><i><font color="Green">E111</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E7:94_1_1_6_10"/><b>then </b><i><font color="Green">E112</font></i>: 
 <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E8:94_1_1_6_10"/><i><font color="Green">E113</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E46:94_1_1_6"><i><font color="Green">E106</font></i></a>, <a class="txt" href="polynom5.html#E2:94_1_1_6_10"><i><font color="Green">E108</font></i></a>, <a class="txt" href="polynom5.html#E6:94_1_1_6_10"><i><font color="Green">E111</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E9:94_1_1_6_10"/><i><font color="Green">E114</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <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="xreal_1.html#T8">XREAL_1:8</a></i>;<br/><a NAME="E10:94_1_1_6_10"/>
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E46:94_1_1_6"><i><font color="Green">E106</font></i></a>, <a class="txt" href="polynom5.html#E2:94_1_1_6_10"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E11:94_1_1_6_10"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E23:94_1_1"><i><font color="Green">E81</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green">E85</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E12:94_1_1_6_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E13:94_1_1_6_10"/><b>then </b><i><font color="Green">E115</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E9:94_1_1_6_10"><i><font color="Green">E114</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E14:94_1_1_6_10"/>
<font color="Maroon">c<sub>12</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="txt" href="polynom5.html#E2:94_1_1_6_10"><i><font color="Green">E108</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E15:94_1_1_6_10"/><b>then </b><i><font color="Green">E116</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E16:94_1_1_6_10"/>
<font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="tbsp_1.html#T2">TBSP_1:2</a></i>;<br/><a NAME="E17:94_1_1_6_10"/><b>then </b><i><font color="Green">E117</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E15:94_1_1_6_10"><i><font color="Green">E116</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><a NAME="E18:94_1_1_6_10"/><i><font color="Green">E118</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="power.html#T39">POWER:39</a></i>;<br/><a NAME="E19:94_1_1_6_10"/><i><font color="Green">E119</font></i>: 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="ref" href="complex1.html#T132">COMPLEX1:132</a></i>;<br/><i><font color="Green">E120</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> = 
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="polynom5.html#E24:94_1_1"><i><font color="Green">E82</font></i></a>, <a class="txt" href="polynom5.html#E8:94_1_1_6_10"><i><font color="Green">E113</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="polynom5.html#E8:94_1_1_6_10"><i><font color="Green">E113</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
;<br/><i><font color="Green">E121</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="polynom5.html#E45:94_1_1_6"><i><font color="Green">E105</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6_10"><i><font color="Green">E109</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1"><i><font color="Green">E78</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green">E85</font></i></a>, <a class="txt" href="polynom5.html#E45:94_1_1_6"><i><font color="Green">E105</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6_10"><i><font color="Green">E109</font></i></a>, <a class="ref" href="rfinseq.html#D2">RFINSEQ:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="group_1.html#K10">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E5:94_1_1_6"><i><font color="Green">E86</font></i></a>, <a class="txt" href="polynom5.html#E13:94_1_1_6_10"><i><font color="Green">E115</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p3"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E5:94_1_1_6_10"><i><font color="Green">E110</font></i></a>, <a class="ref" href="comptrig.html#T15">COMPTRIG:15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p2"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
;<br/><a NAME="E22:94_1_1_6_10"/><i><font color="Green">E122</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K5">-</a> 1
 ;<br/><span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6_10"><i><font color="Green">E107</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E4:94_1_1_6_10"><i><font color="Green">E109</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E45:94_1_1_6"><i><font color="Green">E105</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6_10"><i><font color="Green">E109</font></i></a>, <a class="ref" href="polynom1.html#D3">POLYNOM1:def 3</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span><a href="complfld.html#K3">.|</a></span>
<b>by </b><i><a class="ref" href="complfld.html#T109">COMPLFLD:109</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E24:94_1_1_6"><i><font color="Green">E99</font></i></a>, <a class="ref" href="complfld.html#T110">COMPLFLD:110</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><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="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E21:94_1_1_6_10"><i><font color="Green">E121</font></i></a>, <a class="ref" href="hahnban1.html#T13">HAHNBAN1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,0</span><a href="hahnban1.html#K1">**]</a></span>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="complfld.html#T109">COMPLFLD:109</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span><a href="complfld.html#K3">.|</a></span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="comptrig.html#T16">COMPTRIG:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="hahnban1.html#T13">HAHNBAN1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E18:94_1_1_6_10"><i><font color="Green">E118</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p0"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6"><i><font color="Green">E94</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p0">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>12</sub></font> <a href="real_1.html#K5">-</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="txt" href="polynom5.html#E22:94_1_1_6_10"><i><font color="Green">E122</font></i></a>, <a class="ref" href="power.html#T34">POWER:34</a></i>
;<br/><a NAME="E24:94_1_1_6_10"/><b>then </b>
<span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6_10"><i><font color="Green">E117</font></i></a>, <a class="txt" href="polynom5.html#E19:94_1_1_6_10"><i><font color="Green">E119</font></i></a>, <a class="txt" href="polynom5.html#E20:94_1_1_6_10"><i><font color="Green">E120</font></i></a>, <a class="ref" href="real_2.html#T147">REAL_2:147</a></i>;<br/><a NAME="E25:94_1_1_6_10"/><b>then </b>
<span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E8:94_1_1_6_10"><i><font color="Green">E113</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self">Def1</a></i>;<br/><b>hence </b><a NAME="E26:94_1_1_6_10"/>
<span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E7:94_1_1_6_10"><i><font color="Green">E112</font></i></a>, <a class="txt" href="polynom5.html#E8:94_1_1_6_10"><i><font color="Green">E113</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/></div><b>end;</b></div><a NAME="E48:94_1_1_6"/><b>then </b>
 <a href="rvsum_1.html#K15">Sum</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" target="_self">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E46:94_1_1_6"><i><font color="Green">E106</font></i></a>, <a class="ref" href="integra5.html#T3">INTEGRA5:3</a></i>;<br/><a NAME="E49:94_1_1_6"/><b>then </b>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rvsum_1.html#K15">Sum</a> <span class="p1"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E44:94_1_1_6"><i><font color="Green">E104</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E50:94_1_1_6"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K9">Sum</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="rfinseq.html#K1">/^</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K5">/</a> <span class="p3"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="power.html#K4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,0</span><a href="hahnban1.html#K1">**]</a></span></span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green">E83</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><b>hence </b><a NAME="E51:94_1_1_6"/>
<font color="Maroon">c<sub>8</sub></font> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K15">Sum</a> <span class="p2"><a href="polynom5.html#K1" target="_self">|.</a><span class="default"><font color="Maroon">c<sub>7</sub></font></span><a href="polynom5.html#K1" target="_self">.|</a></span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E42:94_1_1_6"><i><font color="Green">E103</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><a NAME="E26:94_1_1"/><b>then </b>
<span class="p1"><a href="complfld.html#K3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p4"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p5">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="complfld.html#K3">.|</a></span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i><a class="txt" href="polynom5.html#E4"><i><font color="Green">Lemma4</font></i></a></i>;<br/><a NAME="E27:94_1_1"/><b>then </b><i><font color="Green">E83</font></i>: 
<span class="p1">(<span class="default"><a href="polynom5.html#K5" target="_self">Subst</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span></span>)</span> <a href="normsp_1.html#K2">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="complfld.html#T96">COMPLFLD:96</a></i>;<br/><a NAME="E28:94_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a>  st <font color="Olive">b<sub>1</sub></font> <a href="polynom5.html#R1" target="_self">is_a_root_of</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_7"><b>proof </b></a><div class="add">

<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<a NAME="E1:94_1_1_7"/>
 <a href="polynom4.html#K2">eval</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 
<b>by </b><i><a class="txt" href="polynom5.html#E4:94_1_1"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polynom5.html#E27:94_1_1"><i><font color="Green">E83</font></i></a>, <a class="ref" href="polynom5.html#T32" target="_self">Th32</a></i>;<br/>
<b>hence </b><a NAME="E2:94_1_1_7"/>
<font color="Maroon">c<sub>2</sub></font> <a href="polynom5.html#R1" target="_self">is_a_root_of</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="polynom5.html#D6" target="_self">Def6</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E29:94_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="polynom5.html#V1" target="_self">with_roots</a>
 <b>by </b><i><a class="ref" href="polynom5.html#D7" target="_self">Def7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_2"><b>suppose </b></a><a NAME="E1:94_1_2"/><i><font color="Green">E69</font></i>: 
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E2:94_1_2"/><i><font color="Green">E70</font></i>: 
 <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="polynom5.html#T58" target="_self">Th58</a></i>;<br/><a NAME="E3:94_1_2"/>
 <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21">VECTSP_1:def 21</a></i>;<br/><a NAME="E4:94_1_2"/><b>then </b><i><font color="Green">E71</font></i>: 
 <a href="algseq_1.html#K3">len</a> <span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i><a class="ref" href="polynom5.html#T41" target="_self">Th41</a></i>;<br/><a NAME="E5:94_1_2"/><i><font color="Green">E72</font></i>: 
<span class="p1">(<span class="default"><a href="algseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> 2 <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:94_1_2_1"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:94_1_2_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1 )
 </span><b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="polynom5.html#E2:94_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polynom5.html#E1:94_1_2_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="nat_1.html#T71">NAT_1:71</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:94_1_2_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:94_1_2_1_1_1"/>
<span class="p1">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="polynom5.html#T39" target="_self">Th39</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:94_1_2_1_1_2"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> = 
 <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="polynom5.html#E5:94_1_2"><i><font color="Green">E72</font></i></a>, <a class="ref" href="polynom5.html#T57" target="_self">Th57</a></i>
<br/>.= 
<span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2_1_1_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="polynom5.html#T39" target="_self">Th39</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E7:94_1_2"/><b>then </b><i><font color="Green">E73</font></i>: 
 <a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="polynom5.html#K4" target="_self">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" target="_self">%&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green">E69</font></i></a>, <a class="txt" href="polynom5.html#E2:94_1_2"><i><font color="Green">E70</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_2"><i><font color="Green">E71</font></i></a>, <a class="ref" href="algseq_1.html#T28">ALGSEQ_1:28</a></i>;<br/><a NAME="E8:94_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a>  st <font color="Olive">b<sub>1</sub></font> <a href="polynom5.html#R1" target="_self">is_a_root_of</a>  <a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_2_2"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon">c<sub>3</sub></font> =  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span>;<br/>

 <a href="polynom4.html#K2">eval</a> <span class="p1">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="polynom5.html#E7:94_1_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="polynom5.html#T48" target="_self">Th48</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <a href="complfld.html#K1">F_Complex</a> 
<b>by </b><i><a class="ref" href="rlvect_1.html#T16">RLVECT_1:16</a></i>
;<br/>
<b>hence </b><a NAME="E2:94_1_2_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="polynom5.html#R1" target="_self">is_a_root_of</a>  <a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="polynom5.html#D6" target="_self">Def6</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:94_1_2"/><b>then </b>
 <a href="polynom5.html#K7" target="_self">NormPolynomial</a> <font color="Maroon">c<sub>1</sub></font> is <a href="polynom5.html#V1" target="_self">with_roots</a>
 <b>by </b><i><a class="ref" href="polynom5.html#D7" target="_self">Def7</a></i>;<br/><b>hence </b><a NAME="E10:94_1_2"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="polynom5.html#V1" target="_self">with_roots</a>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green">E69</font></i></a>, <a class="ref" href="polynom5.html#T61" target="_self">Th61</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
