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

<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/>

<b>assume </b><a NAME="E1:94"/><i><font color="Green" title="E67">A1</font></i>: 
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ;<br/>

<a NAME="E2:94"/><b>then </b><i><font color="Green" title="E68">A2</font></i>: 
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</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#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 or  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 </span><b>by </b><i><a class="txt" href="polynom5.html#E2:94"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">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#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">z0</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> <b> such that </b><br/><a NAME="E3:94_1_1"/><i><font color="Green" title="E69">A3</font></i>: 
for <font color="Olive" title="b1">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  holds  <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<font color="Olive" title="b1">z</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">z0</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#T74" target="_self" title="POLYNOM5:th.74">Th74</a></i>;<br/><b>set </b><font color="Maroon" title="c3">q</font> =  <a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p1"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span>;<br/><i><font color="Green" title="E70">A4</font></i>:  <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">z0</font> = 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">z0</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
<br/>.= 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span>,<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T48" target="_self" title="POLYNOM5:th.48">Th48</a></i>
<br/>.= 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T54" target="_self" title="POLYNOM5:th.54">Th54</a></i>
;<br/><div><i><font color="Green" title="E71">A5</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" title="c4">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> ;<br/> <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span>,<font color="Maroon" title="c4">z</font> = 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<span class="p1">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span>,<font color="Maroon" title="c4">z</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T54" target="_self" title="POLYNOM5:th.54">Th54</a></i>
<br/>.= 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">z0</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">z</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T48" target="_self" title="POLYNOM5:th.48">Th48</a></i>
;<br/><a NAME="E2:94_1_1_2"/><b>then </b>
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span>,<font color="Maroon" title="c4">z</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">z0</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E3:94_1_1"><i><font color="Green" title="E69">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E3:94_1_1_2"/>
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span>,<font color="Maroon" title="c4">z</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E4:94_1_1"><i><font color="Green" title="E70">A4</font></i></a>, <a class="ref" href="polynom5.html#T32" target="_self" title="POLYNOM5:th.32">Th32</a></i>;<br/></div><b>end;</b></div><a NAME="E6:94_1_1"/>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21" title="VECTSP_1:def.21">VECTSP_1:def 21</a></i>;<br/><a NAME="E7:94_1_1"/><b>then </b>
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <b>by </b><i><a class="ref" href="polynom5.html#T41" target="_self" title="POLYNOM5:th.41">Th41</a></i>;<br/><b>then </b><i><font color="Green" title="E72">A6</font></i>:  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&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#K4" title="NAT_1:func.4">*</a> <span class="p4">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 2</span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> 2
<b>by </b><i><a class="txt" href="polynom5.html#E1:94"><i><font color="Green" title="E67">A1</font></i></a>, <a class="ref" href="polynom5.html#T53" target="_self" title="POLYNOM5:th.53">Th53</a></i>
<br/>.= 
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font>

;<br/><b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b>( $1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> $1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  );<br/><a NAME="E9:94_1_1"/><i><font color="Green" title="E73">A7</font></i>: 
 ex <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</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#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<b>by </b><i><a class="txt" href="polynom5.html#E1:94"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="polynom5.html#E8:94_1_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">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#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 
<b>by </b><i><a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">k</font> = <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c4">k</font>
;<br/>

<a NAME="E4:94_1_1_4"/>
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="txt" href="polynom5.html#E1:94"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="polynom5.html#E8:94_1_1"><i><font color="Green" title="E72">A6</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:94_1_1_4"/>
<font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/>

<a NAME="E6:94_1_1_4"/>
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
;<br/>
<b>hence </b><a NAME="E7:94_1_1_4"/>
<span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="algseq_1.html#T25" title="ALGSEQ_1:th.25">ALGSEQ_1:25</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon" title="c4">k</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E11:94_1_1"/><i><font color="Green" title="E74">A8</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">k</font>]
 <b>and </b><br/><a NAME="E12:94_1_1"/><i><font color="Green" title="E75">A9</font></i>: 
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font>
 <b>from </b><i><a class="ref" href="nat_1.html#S5" title="NAT_1:sch.5">NAT_1:sch 5</a>(<a class="txt" href="polynom5.html#E9:94_1_1"><i><font color="Green" title="E73">A7</font></i></a>);<br/></i><a NAME="E13:94_1_1"/><i><font color="Green" title="E76">A10</font></i>: 
<font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E11:94_1_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">k1</font> = <font color="Maroon" title="c4">k</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <b>by </b><i><a class="txt" href="polynom5.html#E11:94_1_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/><a NAME="E15:94_1_1"/>
<font color="Maroon" title="c5">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E11:94_1_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="ref" href="algseq_1.html#T22" title="ALGSEQ_1:th.22">ALGSEQ_1:22</a></i>;<br/><a NAME="E16:94_1_1"/><b>then </b><i><font color="Green" title="E77">A11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">sq</font> being    <a href="complfld.html#M1" title="COMPLFLD:mode.1">CRoot</a> of <font color="Maroon" title="c5">k1</font>, <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>;<br/><b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">k1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> $1</span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">k1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> $1</span>)</span></span>)</span>;<br/><b>consider </b><font color="Maroon" title="c7">F2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> <b> such that </b><br/><a NAME="E19:94_1_1"/><i><font color="Green" title="E78">A12</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">k1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E20:94_1_1"/><i><font color="Green" title="E79">A13</font></i>: 
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">k1</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> holds <br/><font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">n</font>)
 <b>from </b><i><a class="ref" href="finseq_2.html#S1" title="FINSEQ_2:sch.1">FINSEQ_2:sch 1</a>();<br/></i><a NAME="E21:94_1_1"/>
<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="polynom5.html#E16:94_1_1"><i><font color="Green" title="E77">A11</font></i></a>, <a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><a NAME="E22:94_1_1"/><b>then </b><i><font color="Green" title="E80">A14</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E19:94_1_1"><i><font color="Green" title="E78">A12</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><div><i><font color="Green" title="E81">A15</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" title="c8">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:94_1_1_5"/>
<font color="Maroon" title="c8">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">F2</font>
 ;<br/><a NAME="E2:94_1_1_5"/><b>then </b>
<font color="Maroon" title="c8">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E19:94_1_1"><i><font color="Green" title="E78">A12</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E3:94_1_1_5"/>
<font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E20:94_1_1"><i><font color="Green" title="E79">A13</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" title="c8">c</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>assume </b><a NAME="E1:94_1_1_6"/><i><font color="Green" title="E82">A16</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c8">c</font> &amp; <font color="Maroon" title="c8">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 )
 ;<br/><b>set </b><font color="Maroon" title="c9">z1</font> = <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font>;<br/><b>consider </b><font color="Maroon" title="c10">F1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> <b> such that </b><br/><a NAME="E3:94_1_1_6"/><i><font color="Green" title="E83">A17</font></i>: 
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span>,<span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <font color="Maroon" title="c10">F1</font>
 <b>and </b><br/><a NAME="E4:94_1_1_6"/><i><font color="Green" title="E84">A18</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span>
 <b>and </b><br/><a NAME="E5:94_1_1_6"/><i><font color="Green" title="E85">A19</font></i>: 
for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c10">F1</font> holds <br/><font color="Maroon" title="c10">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">n</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom4.html#D2" title="POLYNOM4:def.2">POLYNOM4:def 2</a></i>;<br/><a NAME="E6:94_1_1_6"/>
<font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">F1</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E13:94_1_1"><i><font color="Green" title="E76">A10</font></i></a>, <a class="txt" href="polynom5.html#E16:94_1_1"><i><font color="Green" title="E77">A11</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green" title="E84">A18</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E7:94_1_1_6"/><b>then </b><i><font color="Green" title="E86">A20</font></i>: 
<font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c10">F1</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E8:94_1_1_6"/><b>then </b><i><font color="Green" title="E87">A21</font></i>: 
<font color="Maroon" title="c10">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">F1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/><a NAME="E9:94_1_1_6"/><i><font color="Green" title="E88">A22</font></i>: 
<font color="Maroon" title="c5">k1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">F1</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E11:94_1_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green" title="E84">A18</font></i></a>, <a class="ref" href="algseq_1.html#T22" title="ALGSEQ_1:th.22">ALGSEQ_1:22</a></i>;<br/><a NAME="E10:94_1_1_6"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c4">k</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E11:94_1_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E11:94_1_1_6"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E9:94_1_1_6"><i><font color="Green" title="E88">A22</font></i></a>, <a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a></i>;<br/><a NAME="E12:94_1_1_6"/><b>then </b><i><font color="Green" title="E89">A23</font></i>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E13:94_1_1_6"/><i><font color="Green" title="E90">A24</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c10">F1</font>
 <b>by </b><i><a class="ref" href="finseq_5.html#T20" title="FINSEQ_5:th.20">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" title="c11">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:94_1_1_6_1"/><i><font color="Green" title="E91">A25</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">k</font></span>)</span>
 <b>and </b><br/><a NAME="E2:94_1_1_6_1"/><i><font color="Green" title="E92">A26</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 ;<br/><a NAME="E3:94_1_1_6_1"/><i><font color="Green" title="E93">A27</font></i>: 
( <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c11">i</font> &amp; <font color="Maroon" title="c11">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">k</font></span>)</span> )
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6_1"><i><font color="Green" title="E91">A25</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E4:94_1_1_6_1"/><b>then </b><i><font color="Green" title="E94">A28</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><a NAME="E5:94_1_1_6_1"/>
<font color="Maroon" title="c11">i</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E2:94_1_1_6_1"><i><font color="Green" title="E92">A26</font></i></a>, <a class="txt" href="polynom5.html#E3:94_1_1_6_1"><i><font color="Green" title="E93">A27</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><a NAME="E6:94_1_1_6_1"/><b>then </b>
<font color="Maroon" title="c11">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E7:94_1_1_6_1"/><b>then </b>
<font color="Maroon" title="c11">i</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E8:94_1_1_6_1"/><b>then </b><i><font color="Green" title="E95">A29</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E9:94_1_1_6_1"/>
<font color="Maroon" title="c11">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">k</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E9:94_1_1_6"><i><font color="Green" title="E88">A22</font></i></a>, <a class="txt" href="polynom5.html#E3:94_1_1_6_1"><i><font color="Green" title="E93">A27</font></i></a>, <a class="ref" href="finseq_1.html#T80" title="FINSEQ_1:th.80">FINSEQ_1:80</a></i>;<br/><a NAME="E10:94_1_1_6_1"/><b>then </b>
<font color="Maroon" title="c11">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E11:94_1_1_6_1"/><b>then </b>
<font color="Maroon" title="c11">i</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">k</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><a NAME="E12:94_1_1_6_1"/><b>then </b><i><font color="Green" title="E96">A30</font></i>: 
<font color="Maroon" title="c11">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">k</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E4:94_1_1_6_1"><i><font color="Green" title="E94">A28</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c5">k1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">i</font> = 
<font color="Maroon" title="c10">F1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c11">i</font>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6_1"><i><font color="Green" title="E91">A25</font></i></a>, <a class="ref" href="finseq_4.html#T85" title="FINSEQ_4:th.85">FINSEQ_4:85</a></i>
<br/>.= 
<font color="Maroon" title="c10">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">i</font>
<b>by </b><i><a class="txt" href="polynom5.html#E13:94_1_1_6"><i><font color="Green" title="E90">A24</font></i></a>, <a class="txt" href="polynom5.html#E1:94_1_1_6_1"><i><font color="Green" title="E91">A25</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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" title="E85">A19</font></i></a>, <a class="txt" href="polynom5.html#E13:94_1_1_6"><i><font color="Green" title="E90">A24</font></i></a>, <a class="txt" href="polynom5.html#E1:94_1_1_6_1"><i><font color="Green" title="E91">A25</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c11">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1"><i><font color="Green" title="E75">A9</font></i></a>, <a class="txt" href="polynom5.html#E8:94_1_1_6_1"><i><font color="Green" title="E95">A29</font></i></a>, <a class="txt" href="polynom5.html#E12:94_1_1_6_1"><i><font color="Green" title="E96">A30</font></i></a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
<b>by </b><i><a class="ref" href="vectsp_1.html#T39" title="VECTSP_1:th.39">VECTSP_1:39</a></i>
;<br/></div><b>end;</b></div><b>then </b><i><font color="Green" title="E91">A31</font></i>:  <a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">k</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c5">k1</font></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1_6"><i><font color="Green" title="E89">A23</font></i></a>, <a class="ref" href="polynom2.html#T5" title="POLYNOM2:th.5">POLYNOM2:5</a></i>
<br/>.= 
<font color="Maroon" title="c10">F1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1_6"><i><font color="Green" title="E89">A23</font></i></a>, <a class="ref" href="finseq_4.html#T85" title="FINSEQ_4:th.85">FINSEQ_4:85</a></i>
<br/>.= 
<font color="Maroon" title="c10">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="polynom5.html#E12:94_1_1_6"><i><font color="Green" title="E89">A23</font></i></a>, <a class="txt" href="polynom5.html#E13:94_1_1_6"><i><font color="Green" title="E90">A24</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<span class="p2">(<span class="default">1 <a href="binarith.html#K3" title="BINARITH:func.3">-'</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" title="E85">A19</font></i></a>, <a class="txt" href="polynom5.html#E12:94_1_1_6"><i><font color="Green" title="E89">A23</font></i></a>, <a class="txt" href="polynom5.html#E13:94_1_1_6"><i><font color="Green" title="E90">A24</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<span class="p2">(<span class="default">1 <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51" title="BINARITH:th.51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D8" title="GROUP_1:def.8">GROUP_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<b>by </b><i><a class="ref" href="group_1.html#D5" title="GROUP_1:def.5">GROUP_1:def 5</a></i>
;<br/><i><font color="Green" title="E92">A32</font></i>: <font color="Maroon" title="c10">F1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<font color="Maroon" title="c10">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E7:94_1_1_6"><i><font color="Green" title="E86">A20</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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" title="E85">A19</font></i></a>, <a class="txt" href="polynom5.html#E7:94_1_1_6"><i><font color="Green" title="E86">A20</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">k1</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<font color="Maroon" title="c5">k1</font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39" title="BINARITH:th.39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">k1</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</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" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<font color="Maroon" title="c5">k1</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<font color="Maroon" title="c5">k1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#T100" title="GROUP_1:th.100">GROUP_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</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" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<font color="Maroon" title="c5">k1</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="complfld.html#D2" title="COMPLFLD:def.2">COMPLFLD: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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">k1</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">k1</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<font color="Maroon" title="c5">k1</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">k1</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">k1</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<font color="Maroon" title="c5">k1</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E11:94_1_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="ref" href="complfld.html#T78" title="COMPLFLD:th.78">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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">k1</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c5">k1</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<font color="Maroon" title="c5">k1</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E11:94_1_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="ref" href="complfld.html#T64" title="COMPLFLD:th.64">COMPLFLD:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<font color="Maroon" title="c5">k1</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E11:94_1_1"><i><font color="Green" title="E74">A8</font></i></a>, <a class="ref" href="complfld.html#T66" title="COMPLFLD:th.66">COMPLFLD:66</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="hahnban1.html#T37" title="HAHNBAN1:th.37">HAHNBAN1:37</a></i>
;<br/><b>set </b><font color="Maroon" title="c11">gc</font> = <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>;<br/><a NAME="E17:94_1_1_6"/><i><font color="Green" title="E93">A33</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></i>;<br/><a NAME="E18:94_1_1_6"/><i><font color="Green" title="E94">A34</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></i>;<br/><a NAME="E19:94_1_1_6"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c5">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="tbsp_1.html#T2" title="TBSP_1:th.2">TBSP_1:2</a></i>;<br/><a NAME="E20:94_1_1_6"/><b>then </b><i><font color="Green" title="E95">A35</font></i>: 
1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><i><font color="Green" title="E96">A36</font></i>:  <a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6"><i><font color="Green" title="E93">A33</font></i></a>, <a class="ref" href="complfld.html#T9" title="COMPLFLD:th.9">COMPLFLD:9</a>, <a class="ref" href="complfld.html#T66" title="COMPLFLD:th.66">COMPLFLD:66</a></i>
<br/>.= 
<span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6"><i><font color="Green" title="E93">A33</font></i></a>, <a class="ref" href="complfld.html#T9" title="COMPLFLD:th.9">COMPLFLD:9</a>, <a class="ref" href="complfld.html#T64" title="COMPLFLD:th.64">COMPLFLD:64</a></i>
;<br/><a NAME="E22:94_1_1_6"/>
<font color="Maroon" title="c10">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E13:94_1_1"><i><font color="Green" title="E76">A10</font></i></a>, <a class="txt" href="polynom5.html#E16:94_1_1"><i><font color="Green" title="E77">A11</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green" title="E84">A18</font></i></a>, <a class="ref" href="polynom4.html#T3" title="POLYNOM4:th.3">POLYNOM4:3</a></i>;<br/><b>then </b> <a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <font color="Maroon" title="c10">F1</font> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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" title="E87">A21</font></i></a>, <a class="ref" href="rlvect_1.html#T58" title="RLVECT_1:th.58">RLVECT_1:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p3"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T58" title="RLVECT_1:th.58">RLVECT_1:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p3"><a href="binarith.html#K11" title="BINARITH:func.11">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span><a href="binarith.html#K11" title="BINARITH:func.11">*&gt;</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39" title="BINARITH:th.39">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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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" title="E91">A31</font></i></a>, <a class="txt" href="polynom5.html#E16:94_1_1_6"><i><font color="Green" title="E92">A32</font></i></a>, <a class="ref" href="rlvect_1.html#T61" title="RLVECT_1:th.61">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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T41" title="VECTSP_1:th.41">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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D13" title="VECTSP_1:def.13">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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E21:94_1_1_6"><i><font color="Green" title="E96">A36</font></i></a>, <a class="ref" href="vectsp_1.html#T43" title="VECTSP_1:th.43">VECTSP_1:43</a></i>
;<br/><a NAME="E24:94_1_1_6"/><b>then </b><i><font color="Green" title="E97">A37</font></i>: 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E5:94_1_1"><i><font color="Green" title="E71">A5</font></i></a>, <a class="txt" href="polynom5.html#E3:94_1_1_6"><i><font color="Green" title="E83">A17</font></i></a></i>;<br/><i><font color="Green" title="E98">A38</font></i>: <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> = 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="ref" href="complex1.html#D7" title="COMPLEX1:def.7">COMPLEX1:def 7</a>, <a class="ref" href="complfld.html#T10" title="COMPLFLD:th.10">COMPLFLD:10</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c5">k1</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="ref" href="polynom5.html#T6" target="_self" title="POLYNOM5:th.6">Th6</a></i>
<br/>.= 
1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E20:94_1_1_6"><i><font color="Green" title="E95">A35</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>
;<br/><a NAME="E26:94_1_1_6"/>
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p0">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="complfld.html#T100" title="COMPLFLD:th.100">COMPLFLD:100</a></i>;<br/><a NAME="E27:94_1_1_6"/><b>then </b>
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E24:94_1_1_6"><i><font color="Green" title="E97">A37</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E28:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="complfld.html#T109" title="COMPLFLD:th.109">COMPLFLD:109</a></i>;<br/><a NAME="E29:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="complfld.html#T109" title="COMPLFLD:th.109">COMPLFLD:109</a></i>;<br/><a NAME="E30:94_1_1_6"/><b>then </b>
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E25:94_1_1_6"><i><font color="Green" title="E98">A38</font></i></a>, <a class="ref" href="xreal_1.html#T22" title="XREAL_1:th.22">XREAL_1:22</a></i>;<br/><a NAME="E31:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6"><i><font color="Green" title="E93">A33</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>;<br/><a NAME="E32:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E18:94_1_1_6"><i><font color="Green" title="E94">A34</font></i></a>, <a class="ref" href="real_1.html#T73" title="REAL_1:th.73">REAL_1:73</a></i>;<br/><a NAME="E33:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p5">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E18:94_1_1_6"><i><font color="Green" title="E94">A34</font></i></a>, <a class="ref" href="xcmplx_1.html#T90" title="XCMPLX_1:th.90">XCMPLX_1:90</a></i>;<br/><a NAME="E34:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T75" title="XCMPLX_1:th.75">XCMPLX_1:75</a></i>;<br/><a NAME="E35:94_1_1_6"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <font color="Maroon" title="c4">k</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="power.html#T34" title="POWER:th.34">POWER:34</a></i>;<br/><a NAME="E36:94_1_1_6"/><b>then </b><i><font color="Green" title="E99">A39</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="ref" href="power.html#T30" title="POWER:th.30">POWER:30</a></i>;<br/><span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p1"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> = 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D23" title="VECTSP_1:def.23">VECTSP_1:def 23</a></i>
<br/>.= 
 <a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#T29" title="POLYNOM1:th.29">POLYNOM1:29</a></i>
;<br/><a NAME="E38:94_1_1_6"/><b>then </b><i><font color="Green" title="E100">A40</font></i>: 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#T15" target="_self" title="POLYNOM5:th.15">Th15</a></i>;<br/><a NAME="E39:94_1_1_6"/><i><font color="Green" title="E101">A41</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></i>;<br/><i><font color="Green" title="E102">A42</font></i>:  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E39:94_1_1_6"><i><font color="Green" title="E101">A41</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">F1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E16:94_1_1"><i><font color="Green" title="E77">A11</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green" title="E84">A18</font></i></a>, <a class="ref" href="rfinseq.html#D2" title="RFINSEQ:def.2">RFINSEQ:def 2</a></i>
<br/>.= 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E22:94_1_1"><i><font color="Green" title="E80">A14</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green" title="E84">A18</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_6_9"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c12">i</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>assume </b><a NAME="E1:94_1_1_6_9"/><i><font color="Green" title="E103">A43</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 ;<br/><a NAME="E2:94_1_1_6_9"/><b>then </b><i><font color="Green" title="E104">A44</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E3:94_1_1_6_9"/><b>then </b>
<font color="Maroon" title="c12">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>;<br/><a NAME="E4:94_1_1_6_9"/><b>then </b><i><font color="Green" title="E105">A45</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><i><font color="Green" title="E106">A46</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">i</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
<b>by </b><i><a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>
<br/>.= 
<font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font>

;<br/><a NAME="E6:94_1_1_6_9"/><i><font color="Green" title="E107">A47</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>;<br/><a NAME="E7:94_1_1_6_9"/><b>then </b><i><font color="Green" title="E108">A48</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><a NAME="E8:94_1_1_6_9"/><i><font color="Green" title="E109">A49</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">F2</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E40:94_1_1_6"><i><font color="Green" title="E102">A42</font></i></a>, <a class="txt" href="polynom5.html#E2:94_1_1_6_9"><i><font color="Green" title="E104">A44</font></i></a>, <a class="txt" href="polynom5.html#E6:94_1_1_6_9"><i><font color="Green" title="E107">A47</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E9:94_1_1_6_9"/><i><font color="Green" title="E110">A50</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E10:94_1_1_6_9"/>
<font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E40:94_1_1_6"><i><font color="Green" title="E102">A42</font></i></a>, <a class="txt" href="polynom5.html#E2:94_1_1_6_9"><i><font color="Green" title="E104">A44</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E11:94_1_1_6_9"/><b>then </b>
<font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">F1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E22:94_1_1"><i><font color="Green" title="E80">A14</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green" title="E84">A18</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>;<br/><a NAME="E12:94_1_1_6_9"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c10">F1</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><a NAME="E13:94_1_1_6_9"/><b>then </b><i><font color="Green" title="E111">A51</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c10">F1</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E9:94_1_1_6_9"><i><font color="Green" title="E110">A50</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E14:94_1_1_6_9"/>
<font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E2:94_1_1_6_9"><i><font color="Green" title="E104">A44</font></i></a>, <a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><a NAME="E15:94_1_1_6_9"/><b>then </b><i><font color="Green" title="E112">A52</font></i>: 
<font color="Maroon" title="c12">i</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="xreal_1.html#T21" title="XREAL_1:th.21">XREAL_1:21</a></i>;<br/><a NAME="E16:94_1_1_6_9"/>
<font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="tbsp_1.html#T2" title="TBSP_1:th.2">TBSP_1:2</a></i>;<br/><a NAME="E17:94_1_1_6_9"/><b>then </b><i><font color="Green" title="E113">A53</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E15:94_1_1_6_9"><i><font color="Green" title="E112">A52</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/><a NAME="E18:94_1_1_6_9"/><i><font color="Green" title="E114">A54</font></i>: 
<font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="power.html#T39" title="POWER:th.39">POWER:39</a></i>;<br/><a NAME="E19:94_1_1_6_9"/><i><font color="Green" title="E115">A55</font></i>: 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="complex1.html#T132" title="COMPLEX1:th.132">COMPLEX1:132</a></i>;<br/><i><font color="Green" title="E116">A56</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c7">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i</font>
<b>by </b><i><a class="txt" href="polynom5.html#E23:94_1_1"><i><font color="Green" title="E81">A15</font></i></a>, <a class="txt" href="polynom5.html#E8:94_1_1_6_9"><i><font color="Green" title="E109">A49</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c7">F2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font>
<b>by </b><i><a class="txt" href="polynom5.html#E8:94_1_1_6_9"><i><font color="Green" title="E109">A49</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
;<br/><i><font color="Green" title="E117">A57</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c12">i</font>
<b>by </b><i><a class="txt" href="polynom5.html#E39:94_1_1_6"><i><font color="Green" title="E101">A41</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6_9"><i><font color="Green" title="E105">A45</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<font color="Maroon" title="c10">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">i</font></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E16:94_1_1"><i><font color="Green" title="E77">A11</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6"><i><font color="Green" title="E84">A18</font></i></a>, <a class="txt" href="polynom5.html#E39:94_1_1_6"><i><font color="Green" title="E101">A41</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6_9"><i><font color="Green" title="E105">A45</font></i></a>, <a class="ref" href="rfinseq.html#D2" title="RFINSEQ:def.2">RFINSEQ:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">i</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c6">sq</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c12">i</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</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" title="E85">A19</font></i></a>, <a class="txt" href="polynom5.html#E13:94_1_1_6_9"><i><font color="Green" title="E111">A51</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p3"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p4">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</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" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E5:94_1_1_6_9"><i><font color="Green" title="E106">A46</font></i></a>, <a class="ref" href="group_1.html#T100" title="GROUP_1:th.100">GROUP_1:100</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p2"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span>

;<br/><a NAME="E22:94_1_1_6_9"/><i><font color="Green" title="E118">A58</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">i</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 ;<br/><span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c12">i</font> = 
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6_9"><i><font color="Green" title="E103">A43</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p4">(<span class="default"><span class="p5"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E4:94_1_1_6_9"><i><font color="Green" title="E105">A45</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="txt" href="polynom5.html#E39:94_1_1_6"><i><font color="Green" title="E101">A41</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_1_6_9"><i><font color="Green" title="E105">A45</font></i></a>, <a class="ref" href="polynom1.html#D3" title="POLYNOM1:def.3">POLYNOM1:def 3</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
<b>by </b><i><a class="ref" href="complfld.html#T109" title="COMPLFLD:th.109">COMPLFLD:109</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6"><i><font color="Green" title="E93">A33</font></i></a>, <a class="txt" href="polynom5.html#E21:94_1_1_6_9"><i><font color="Green" title="E117">A57</font></i></a>, <a class="ref" href="complfld.html#T9" title="COMPLFLD:th.9">COMPLFLD:9</a>, <a class="ref" href="complfld.html#T110" title="COMPLFLD:th.110">COMPLFLD:110</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><font color="Maroon" title="c8">c</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="complfld.html#T109" title="COMPLFLD:th.109">COMPLFLD:109</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="hahnban1.html#T37" title="HAHNBAN1:th.37">HAHNBAN1:37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E18:94_1_1_6_9"><i><font color="Green" title="E114">A54</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p0"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6"><i><font color="Green" title="E93">A33</font></i></a>, <a class="ref" href="absvalue.html#D1" title="ABSVALUE:def.1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K2" title="REAL_1:func.2">"</a> </span>)</span></span>)</span>

<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9" title="XCMPLX_0:def.9">XCMPLX_0:def 9</a></i>
<br/>.= 
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</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" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p5"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p0">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5" title="GROUP_1:func.5">power</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c6">sq</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c12">i</font></span>)</span></span>)</span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p2">(<span class="default"><font color="Maroon" title="c12">i</font> <a href="real_1.html#K9" title="REAL_1:func.9">-</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" title="E82">A16</font></i></a>, <a class="txt" href="polynom5.html#E22:94_1_1_6_9"><i><font color="Green" title="E118">A58</font></i></a>, <a class="ref" href="power.html#T34" title="POWER:th.34">POWER:34</a></i>
;<br/><a NAME="E24:94_1_1_6_9"/><b>then </b>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">F2</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E17:94_1_1_6_9"><i><font color="Green" title="E113">A53</font></i></a>, <a class="txt" href="polynom5.html#E19:94_1_1_6_9"><i><font color="Green" title="E115">A55</font></i></a>, <a class="txt" href="polynom5.html#E20:94_1_1_6_9"><i><font color="Green" title="E116">A56</font></i></a>, <a class="ref" href="real_2.html#T147" title="REAL_2:th.147">REAL_2:147</a></i>;<br/><a NAME="E25:94_1_1_6_9"/><b>then </b>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c12">i</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E8:94_1_1_6_9"><i><font color="Green" title="E109">A49</font></i></a>, <a class="ref" href="polynom5.html#D1" target="_self" title="POLYNOM5:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E26:94_1_1_6_9"/>
<span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c12">i</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c12">i</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E7:94_1_1_6_9"><i><font color="Green" title="E108">A48</font></i></a>, <a class="txt" href="polynom5.html#E8:94_1_1_6_9"><i><font color="Green" title="E109">A49</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/></div><b>end;</b></div><a NAME="E42:94_1_1_6"/><b>then </b>
 <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="polynom1.html#K7" title="POLYNOM1:func.7">*</a> <span class="p3">(<span class="default"><span class="p4"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p0">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">"</a> </span>)</span></span>)</span></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E40:94_1_1_6"><i><font color="Green" title="E102">A42</font></i></a>, <a class="ref" href="integra5.html#T3" title="INTEGRA5:th.3">INTEGRA5:3</a></i>;<br/><a NAME="E43:94_1_1_6"/><b>then </b>
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E38:94_1_1_6"><i><font color="Green" title="E100">A40</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E44:94_1_1_6"/><b>then </b>
<font color="Maroon" title="c8">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K8" title="RLVECT_1:func.8">Sum</a> <span class="p4">(<span class="default"><font color="Maroon" title="c10">F1</font> <a href="rfinseq.html#K2" title="RFINSEQ:func.2">/^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">/</a> <span class="p3"><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">[**</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c8">c</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="hahnban1.html#K1" title="HAHNBAN1:func.1">**]</a></span></span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_1_6"><i><font color="Green" title="E82">A16</font></i></a>, <a class="ref" href="xreal_1.html#T66" title="XREAL_1:th.66">XREAL_1:66</a></i>;<br/><b>hence </b><a NAME="E45:94_1_1_6"/>
<font color="Maroon" title="c8">c</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p2"><a href="polynom5.html#K1" title="POLYNOM5:func.1">|.</a><span class="default"><font color="Maroon" title="c7">F2</font></span><a href="polynom5.html#K1" title="POLYNOM5:func.1">.|</a></span></span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E36:94_1_1_6"><i><font color="Green" title="E99">A39</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><a NAME="E25:94_1_1"/><b>then </b>
<span class="p1"><a href="complfld.html#K3" title="COMPLFLD:func.3">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p4"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p5">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span><a href="complfld.html#K3" title="COMPLFLD:func.3">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="polynom5.html#E4"><i><font color="Green" title="E4">Lm1</font></i></a></i>;<br/><a NAME="E26:94_1_1"/><b>then </b><i><font color="Green" title="E82">A59</font></i>: 
<span class="p1">(<span class="default"><a href="polynom5.html#K5" title="POLYNOM5:func.5">Subst</a> <font color="Maroon" title="c1">p</font>,<span class="p2"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><font color="Maroon" title="c2">z0</font>,<span class="p3">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="complfld.html#T96" title="COMPLFLD:th.96">COMPLFLD:96</a></i>;<br/><a NAME="E27:94_1_1"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  st <font color="Olive" title="b1">x</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a> <font color="Maroon" title="c1">p</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" title="c2">z0</font>
;<br/>

<a NAME="E1:94_1_1_7"/>
 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <font color="Maroon" title="c1">p</font>,<font color="Maroon" title="c2">z0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 
<b>by </b><i><a class="txt" href="polynom5.html#E4:94_1_1"><i><font color="Green" title="E70">A4</font></i></a>, <a class="txt" href="polynom5.html#E26:94_1_1"><i><font color="Green" title="E82">A59</font></i></a>, <a class="ref" href="polynom5.html#T32" target="_self" title="POLYNOM5:th.32">Th32</a></i>;<br/>
<b>hence </b><a NAME="E2:94_1_1_7"/>
<font color="Maroon" title="c2">z0</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="polynom5.html#D6" target="_self" title="POLYNOM5:def.6">Def6</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E28:94_1_1"/>
<font color="Maroon" title="c1">p</font> is <a href="polynom5.html#V1" title="POLYNOM5:attr.1">with_roots</a>
 <b>by </b><i><a class="ref" href="polynom5.html#D7" target="_self" title="POLYNOM5:def.7">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" title="E69">A60</font></i>: 
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c2">np</font> =  <a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font>;<br/><a NAME="E2:94_1_2"/><i><font color="Green" title="E70">A61</font></i>: 
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green" title="E69">A60</font></i></a>, <a class="ref" href="polynom5.html#T58" target="_self" title="POLYNOM5:th.58">Th58</a></i>;<br/><a NAME="E3:94_1_2"/>
 <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
 <b>by </b><i><a class="ref" href="vectsp_1.html#D21" title="VECTSP_1:def.21">VECTSP_1:def 21</a></i>;<br/><a NAME="E4:94_1_2"/><b>then </b><i><font color="Green" title="E71">A62</font></i>: 
 <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <b>by </b><i><a class="ref" href="polynom5.html#T41" target="_self" title="POLYNOM5:th.41">Th41</a></i>;<br/><a NAME="E5:94_1_2"/><i><font color="Green" title="E72">A63</font></i>: 
<span class="p1">(<span class="default"><a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green" title="E69">A60</font></i></a>, <a class="ref" href="binarith.html#D3" title="BINARITH:def.3">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" title="c3">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:94_1_2_1"/><i><font color="Green" title="E73">A64</font></i>: 
<font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="algseq_1.html#K1" title="ALGSEQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</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" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 </span><b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green" title="E69">A60</font></i></a>, <a class="txt" href="polynom5.html#E2:94_1_2"><i><font color="Green" title="E70">A61</font></i></a>, <a class="txt" href="polynom5.html#E1:94_1_2_1"><i><font color="Green" title="E73">A64</font></i></a>, <a class="ref" href="nat_1.html#T23" title="NAT_1:th.23">NAT_1:23</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" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<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" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="ref" href="polynom5.html#T39" target="_self" title="POLYNOM5:th.39">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" title="E74">A65</font></i>: 
<font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">k</font> = 
 <a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green" title="E69">A60</font></i></a>, <a class="txt" href="polynom5.html#E5:94_1_2"><i><font color="Green" title="E72">A63</font></i></a>, <a class="ref" href="polynom5.html#T57" target="_self" title="POLYNOM5:th.57">Th57</a></i>
<br/>.= 
<span class="p1"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <font color="Maroon" title="c3">k</font>
<b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2_1_1_2"><i><font color="Green" title="E74">A65</font></i></a>, <a class="ref" href="polynom5.html#T39" target="_self" title="POLYNOM5:th.39">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" title="E73">A66</font></i>: 
 <a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1"><a href="polynom5.html#K4" title="POLYNOM5:func.4">&lt;%</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4" title="POLYNOM5:func.4">%&gt;</a></span>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green" title="E69">A60</font></i></a>, <a class="txt" href="polynom5.html#E2:94_1_2"><i><font color="Green" title="E70">A61</font></i></a>, <a class="txt" href="polynom5.html#E4:94_1_2"><i><font color="Green" title="E71">A62</font></i></a>, <a class="ref" href="algseq_1.html#T28" title="ALGSEQ_1:th.28">ALGSEQ_1:28</a></i>;<br/><a NAME="E8:94_1_2"/>
 ex <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  st <font color="Olive" title="b1">x</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a>  <a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</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" title="c3">z0</font> =  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>;<br/>

 <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> <span class="p1">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span>,<font color="Maroon" title="c3">z0</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="seq_1.html#K23" title="SEQ_1:func.23">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c3">z0</font>
<b>by </b><i><a class="txt" href="polynom5.html#E7:94_1_2"><i><font color="Green" title="E73">A66</font></i></a>, <a class="ref" href="polynom5.html#T48" target="_self" title="POLYNOM5:th.48">Th48</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a> 
<b>by </b><i><a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></i>
;<br/>
<b>hence </b><a NAME="E2:94_1_2_2"/>
<font color="Maroon" title="c3">z0</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a>  <a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="ref" href="polynom5.html#D6" target="_self" title="POLYNOM5:def.6">Def6</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:94_1_2"/><b>then </b>
 <a href="polynom5.html#K7" title="POLYNOM5:func.7">NormPolynomial</a> <font color="Maroon" title="c1">p</font> is <a href="polynom5.html#V1" title="POLYNOM5:attr.1">with_roots</a>
 <b>by </b><i><a class="ref" href="polynom5.html#D7" target="_self" title="POLYNOM5:def.7">Def7</a></i>;<br/><b>hence </b><a NAME="E10:94_1_2"/>
<font color="Maroon" title="c1">p</font> is <a href="polynom5.html#V1" title="POLYNOM5:attr.1">with_roots</a>
 <b>by </b><i><a class="txt" href="polynom5.html#E1:94_1_2"><i><font color="Green" title="E69">A60</font></i></a>, <a class="ref" href="polynom5.html#T61" target="_self" title="POLYNOM5:th.61">Th61</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
