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<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> <a href="vectsp_2.html#NM3" title="VECTSP_2:NM.3">Skew-Field</a>;<br/><b>let </b><font color="Maroon" title="c2">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>;<br/>



<b>assume </b><a NAME="E1:49"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c2">s</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" title="UNIROOTS:func.1">MultGroup</a> <font color="Maroon" title="c1">R</font></span>)</span>
 ;<br/>

<b>set </b><font color="Maroon" title="c3">n</font> =  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c4">ns</font> =  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">q</font> =  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>;<br/>
<a NAME="E2:49"/><i><font color="Green" title="E43">A2</font></i>: 
(  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E3:49"/><i><font color="Green" title="E44">A3</font></i>: 
(  <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="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</span> &amp;  <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="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="weddwitt.html#T33" target="_self" title="WEDDWITT:th.33">Th33</a>, <a class="ref" href="weddwitt.html#T35" target="_self" title="WEDDWITT:th.35">Th35</a></i>;<br/>
<a NAME="E4:49"/><i><font color="Green" title="E45">A4</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 
<b>by </b><i><a class="ref" href="weddwitt.html#T21" target="_self" title="WEDDWITT:th.21">Th21</a></i>;<br/>
<a NAME="E5:49"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p1">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p2">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#T13" title="PREPOWER:th.13">PREPOWER:13</a></i>;<br/>
<a NAME="E6:49"/><b>then </b>
<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E7:49"/><b>then </b><i><font color="Green" title="E46">A5</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p1">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p2">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</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/>
<a NAME="E8:49"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p1">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p2">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="prepower.html#T13" title="PREPOWER:th.13">PREPOWER:13</a></i>;<br/>
<a NAME="E9:49"/><b>then </b>
<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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/>
<a NAME="E10:49"/><b>then </b>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p1">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p2">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</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/>
<a NAME="E11:49"/><b>then </b><i><font color="Green" title="E47">A6</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</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"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</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#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/>
<a NAME="E12:49"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</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"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p3">(<span class="default"><a href="weddwitt.html#K4" title="WEDDWITT:func.4">center</a> <font color="Maroon" title="c1">R</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p2">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p3">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 
<b>by </b><i><a class="txt" href="weddwitt.html#E7:49"><i><font color="Green" title="E46">A5</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/>
<b>hence </b><a NAME="E13:49"/>
 <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K7" title="WEDDWITT:func.7">VectSp_over_center</a> <font color="Maroon" title="c2">s</font></span>)</span> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K6" title="WEDDWITT:func.6">VectSp_over_center</a> <font color="Maroon" title="c1">R</font></span>)</span>
 <b>by </b><i><a class="txt" href="weddwitt.html#E1:49"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="weddwitt.html#E2:49"><i><font color="Green" title="E43">A2</font></i></a>, <a class="txt" href="weddwitt.html#E3:49"><i><font color="Green" title="E44">A3</font></i></a>, <a class="txt" href="weddwitt.html#E4:49"><i><font color="Green" title="E45">A4</font></i></a>, <a class="txt" href="weddwitt.html#E11:49"><i><font color="Green" title="E47">A6</font></i></a>, <a class="ref" href="weddwitt.html#T3" target="_self" title="WEDDWITT:th.3">Th3</a>, <a class="ref" href="weddwitt.html#T36" target="_self" title="WEDDWITT:th.36">Th36</a></i>;<br/>


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