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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>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>3</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>4</sub></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">c<sub>2</sub></font></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:49_1"/><i><font color="Green">E43</font></i>: 
 <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">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:49_1"/>
<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#K7" target="_self">VectSp_over_center</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <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="prepower.html#K7">#Z</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">c<sub>2</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="prepower.html#T46">PREPOWER:46</a></i>;<br/><a NAME="E3:49_1"/><b>then </b>
<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#K7" target="_self">VectSp_over_center</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="weddwitt.html#E1:49_1"><i><font color="Green">E43</font></i></a>, <a class="ref" href="prepower.html#T44">PREPOWER:44</a></i>;<br/><a NAME="E4:49_1"/><b>then </b>
 <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#K5" target="_self">centralizer</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="weddwitt.html#T34" target="_self">Th34</a></i>;<br/><b>hence </b><a NAME="E5:49_1"/>
contradiction
 <b>by </b><i><a class="ref" href="weddwitt.html#T29" target="_self">Th29</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:49"/>
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#K7" target="_self">VectSp_over_center</a> <font color="Maroon">c<sub>2</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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