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

<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="vectsp_1.html#V5">left-distributive</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>;<br/>





<b>set </b><font color="Maroon">p</font> = <span class="p1"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span>;<br/>
<b>consider </b><font color="Maroon">r</font> being   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E2:52"/><i><font color="Green">E42</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> 0 <a href="binop_2.html#K23">+</a> 1
 <b>and </b><br/><a NAME="E3:52"/><i><font color="Green">E43</font></i>: 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="polynom3.html#K14">*'</a> <font color="Maroon">q</font></span>)</span> <a href="normsp_1.html#K2">.</a> 0 <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E4:52"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r</font> holds <br/><font color="Maroon">r</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Olive">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Olive">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom3.html#D11">POLYNOM3:def 11</a></i>;<br/>
<a NAME="E5:52"/><i><font color="Green">E45</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r</font>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">r1</font> = <font color="Maroon">r</font> <a href="funct_1.html#K1">.</a> 1 as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/>
<a NAME="E7:52"/>
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="binarith.html#K11">&lt;*</a><span class="default"><font color="Maroon">r1</font></span><a href="binarith.html#K11">*&gt;</a></span>
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T57">FINSEQ_1:57</a></i>;<br/>
<b>then </b> <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r</font> = 
<font color="Maroon">r1</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T61">RLVECT_1:61</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E2:52"><i><font color="Green">E42</font></i></a>, <a class="txt" href="uproots.html#E3:52"><i><font color="Green">E43</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/>
<b>hence </b><a NAME="E9:52"/>
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="polynom3.html#K14">*'</a> <font color="Maroon">q</font></span>)</span> <a href="normsp_1.html#K2">.</a> 0 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span>
 <b>by </b><i>, <a class="ref" href="polynom5.html#T39">POLYNOM5:39</a></i>;<br/>

<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>consider </b><font color="Maroon">r</font> being   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E11:52"/><i><font color="Green">E46</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1
 <b>and </b><br/><a NAME="E12:52"/><i><font color="Green">E47</font></i>: 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="polynom3.html#K14">*'</a> <font color="Maroon">q</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K9">Sum</a> <font color="Maroon">r</font>
 <b>and </b><br/><a NAME="E13:52"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r</font> holds <br/><font color="Maroon">r</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Olive">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Olive">k</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="polynom3.html#D11">POLYNOM3:def 11</a></i>;<br/>
<a NAME="E14:52"/><i><font color="Green">E51</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 2
 
<b>by </b><i><a class="txt" href="uproots.html#E4:52"><i><font color="Green">E44</font></i></a></i>;<br/>
<a NAME="E15:52"/><i><font color="Green">E52</font></i>: 
0 <a href="binop_2.html#K23">+</a> 2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font>
 
<b>by </b><i><a class="txt" href="uproots.html#E12:52"><i><font color="Green">E47</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E16:52"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">r</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/>
<a NAME="E17:52"/><b>then </b><i><font color="Green">E53</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r</font>
 
<b>by </b><i><a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<a NAME="E18:52"/><i><font color="Green">E54</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r</font>
 
<b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/>
<i><font color="Green">E55</font></i>: <font color="Maroon">r</font> <a href="finseq_4.html#K4">/.</a> 1 = 
<font color="Maroon">r</font> <a href="funct_1.html#K1">.</a> 1
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E11:52"><i><font color="Green">E46</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T51">BINARITH:51</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T39">POLYNOM5:39</a></i>
;<br/>
<i><font color="Green">E56</font></i>: <font color="Maroon">r</font> <a href="finseq_4.html#K4">/.</a> 2 = 
<font color="Maroon">r</font> <a href="funct_1.html#K1">.</a> 2
<b>by </b><i><a class="txt" href="uproots.html#E13:52"><i><font color="Green">E50</font></i></a>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E11:52"><i><font color="Green">E46</font></i></a>, <a class="txt" href="uproots.html#E13:52"><i><font color="Green">E50</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> <span class="p4">(<span class="default">1 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T39">POLYNOM5:39</a></i>
<br/>.= 
<font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:52_4"/><i><font color="Green">E57</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">k</font>
 <b>and </b><br/><a NAME="E2:52_4"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">r</font>
 ;<br/><a NAME="E3:52_4"/>
<font color="Maroon">k</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="uproots.html#E17:52"><i><font color="Green">E53</font></i></a></i>;<br/><b>then consider </b><font color="Maroon">k1</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:52_4"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k1</font> <a href="xcmplx_0.html#K2">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T22">NAT_1:22</a></i>;<br/><a NAME="E6:52_4"/><i><font color="Green">E60</font></i>: 
2 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k1</font>
 <b>by </b><i><a class="txt" href="uproots.html#E17:52"><i><font color="Green">E53</font></i></a>, <a class="txt" href="uproots.html#E19:52"><i><font color="Green">E55</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>reconsider </b><font color="Maroon">k1</font> = <font color="Maroon">k1</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/><b>thus </b><font color="Maroon">r</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">k</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E11:52"><i><font color="Green">E46</font></i></a>, <a class="txt" href="uproots.html#E18:52"><i><font color="Green">E54</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">k1</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E19:52"><i><font color="Green">E55</font></i></a>, <a class="ref" href="binarith.html#T39">BINARITH:39</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="uproots.html#E20:52"><i><font color="Green">E56</font></i></a>, <a class="ref" href="polynom5.html#T39">POLYNOM5:39</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E22:52"/>
<span class="p1">(<span class="default"><span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="polynom3.html#K14">*'</a> <font color="Maroon">q</font></span>)</span> <a href="normsp_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="group_1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="uproots.html#E5:52"><i><font color="Green">E45</font></i></a>, , <a class="txt" href="uproots.html#E14:52"><i><font color="Green">E51</font></i></a>, <a class="txt" href="uproots.html#E15:52"><i><font color="Green">E52</font></i></a>, </i>;<br/>


</div>
