<?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="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a> <a href="vectsp_1.html#V9">Field-like</a> non <a href="vectsp_1.html#V10">degenerated</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>;<br/>



<div><i><font color="Green">E29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">z</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E1:41_1"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> &amp; <font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">x</font> <a href="polynom5.html#K3">*</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<font color="Maroon">z</font></span>)</span> )
 ;<br/><b>thus </b> <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p</font> = 
 <a href="hurwitz.html#NK3" target="_self">deg</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T26">POLYNOM5:26</a>, </i>
<br/>.= 
1
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:41_2"/><i><font color="Green">E31</font></i>: 
 <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><a NAME="E2:41_2"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 1 <a href="nat_1.html#K1">+</a> 1
 ;<br/><b>set </b><font color="Maroon">x</font> = <font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1;<br/><b>set </b><font color="Maroon">z</font> = <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span>;<br/><b>set </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="polynom5.html#K3">*</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span>;<br/><a NAME="E3:41_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="algseq_1.html#T25">ALGSEQ_1:25</a></i>;<br/><b>then </b><i><font color="Green">E37</font></i>:  <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="polynom5.html#K3">*</a> <span class="p2">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="hurwitz.html#NK3" target="_self">deg</a> <span class="p2">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
<b>by </b><i><a class="ref" href="polynom5.html#T26">POLYNOM5:26</a></i>
<br/>.= 
1 <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="hurwitz.html#E3:41_2"><i><font color="Green">E36</font></i></a></i>
<br/>.= 
 <a href="algseq_1.html#K3">len</a> <font color="Maroon">p</font>
<b>by </b><i/>
;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2_2"><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><a NAME="E1:41_2_2"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p</font>
 ;<br/><a NAME="E2:41_2_2"/><b>then </b>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i/>;<br/><a NAME="E3:41_2_2"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:41_2_2_1"/>
( <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 </span><b>by </b><i>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_2_2_1_1"><b>suppose </b></a><a NAME="E1:41_2_2_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="polynom5.html#K3">*</a> <span class="p2">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#D3">POLYNOM5:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="txt" href="hurwitz.html#E2:41_2"><i><font color="Green">E34</font></i></a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="vectsp_1.html#D13">VECTSP_1:def 13</a></i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="41_2_2_1_2"><b>suppose </b></a><a NAME="E1:41_2_2_1_2"/>
<font color="Maroon">k</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1
 ;<br/><div class="add"><a NAME="E2:41_2_2_1_2"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="nat_1.html#T39">NAT_1:39</a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="polynom5.html#K3">*</a> <span class="p2">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#D3">POLYNOM5:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">L</font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default">1 <a href="nat_1.html#K1">+</a> 0</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="hurwitz.html#E2:41_2"><i><font color="Green">E34</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="group_1.html#K5">power</a> <font color="Maroon">L</font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p0">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span>,0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D8">GROUP_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D8">GROUP_1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T41">VECTSP_1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="group_1.html#K10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="group_1.html#D4">GROUP_1:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="hurwitz.html#E2:41_2_2_1_2"><i><font color="Green">E41</font></i></a>, <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">k</font>
<b>by </b><i>, <a class="ref" href="vectsp_1.html#D19">VECTSP_1:def 19</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><a NAME="E6:41_2"/><b>then </b>
<font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="polynom5.html#K3">*</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span>)</span> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 1</span>)</span> <a href="vectsp_1.html#K4">"</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="algseq_1.html#T28">ALGSEQ_1:28</a></i>;<br/><b>hence </b><a NAME="E7:41_2"/>
 ex <font color="Olive">x</font>, <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> &amp; <font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <font color="Olive">x</font> <a href="polynom5.html#K3">*</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<font color="Olive">z</font></span>)</span> )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:41"/>
(  <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 1 iff  ex <font color="Olive">x</font>, <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> &amp; <font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <font color="Olive">x</font> <a href="polynom5.html#K3">*</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" target="_self">rpoly</a> 1,<font color="Olive">z</font></span>)</span> ) )
 <b>by </b><i/>;<br/>


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