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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="group_1.html#V6">finite</a> <a href="vectsp_2.html#NM3">Skew-Field</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="uniroots.html#K1">MultGroup</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E1:46"/>
 <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="wsierp_1.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">c<sub>1</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="weddwitt.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E2:46"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1">MultGroup</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="wsierp_1.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">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 
<b>by </b><i><a class="ref" href="uniroots.html#T21">UNIROOTS:21</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:46_1"/><i><font color="Green">E41</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">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:46_1"/>
<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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="wsierp_1.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">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</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">c<sub>1</sub></font></span>)</span></span>)</span> <a href="prepower.html#K7">#Z</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">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="prepower.html#T46">PREPOWER:46</a></i>;<br/><a NAME="E3:46_1"/><b>then </b>
 <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1">MultGroup</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="weddwitt.html#E2:46"><i><font color="Green">E40</font></i></a>, <a class="txt" href="weddwitt.html#E1:46_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="prepower.html#T44">PREPOWER:44</a></i>;<br/><b>hence </b><a NAME="E4:46_1"/>
contradiction
 <b>by </b><i><a class="ref" href="group_1.html#T90">GROUP_1:90</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:46"/>
0 <a href="xxreal_0.html#NR3" target="_self">&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">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T19">NAT_1:19</a></i>;<br/>


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