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<b>let </b><font color="Maroon">R</font> be  <a href="group_1.html#V6">finite</a> <a href="vectsp_2.html#NM3">Skew-Field</a>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/>



<b>assume </b><a NAME="E1:51"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">s</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1">MultGroup</a> <font color="Maroon">R</font></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon">Vs</font> =  <a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font>;<br/>
<b>set </b><font color="Maroon">n</font> =  <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">ns</font> =  <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">q</font> =  <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span>;<br/>
<a NAME="E2:51"/><i><font color="Green">E36</font></i>: 
(  <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  &amp;  <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E3:51"/><i><font color="Green">E37</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;</a>  <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;</a>  <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="weddwitt.html#T2" target="_self">Th2</a>, </i>;<br/>
<a NAME="E4:51"/><i><font color="Green">E38</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;</a>  <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:51"/><b>then </b><i><font color="Green">E46</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a>  <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E6:51"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p2">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/>
<a NAME="E7:51"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E8:51"/><b>then </b><i><font color="Green">E50</font></i>: 
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p2">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E9:51"/>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p2">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/>
<a NAME="E10:51"/><b>then </b>
0 <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E11:51"/><b>then </b>
1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p2">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E12:51"/><b>then </b><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1
 
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E13:51"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1
 
<b>by </b><i><a class="txt" href="weddwitt.html#E8:51"><i><font color="Green">E50</font></i></a>, <a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E14:51"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="int_1.html#R2">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i>, </i>;<br/>
<a NAME="E15:51"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="nat_1.html#R1">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" target="_self">center</a> <font color="Maroon">R</font></span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">-'</a> 1
 
<b>by </b><i><a class="txt" href="weddwitt.html#E12:51"><i><font color="Green">E51</font></i></a>, <a class="txt" href="weddwitt.html#E13:51"><i><font color="Green">E52</font></i></a>, <a class="ref" href="prepower.html#T109">PREPOWER:109</a></i>;<br/>
<b>hence </b><a NAME="E16:51"/>
 <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K7" target="_self">VectSp_over_center</a> <font color="Maroon">s</font></span>)</span> <a href="nat_1.html#R1">divides</a>  <a href="vectsp_9.html#K1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K6" target="_self">VectSp_over_center</a> <font color="Maroon">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="weddwitt.html#E5:51"><i><font color="Green">E46</font></i></a>, , , </i>;<br/>


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