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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>let </b><font color="Maroon">c<sub>3</sub></font> be   <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">c<sub>1</sub></font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:43"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="weddwitt.html#K1" target="_self">Centralizer</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="weddwitt.html#K5" target="_self">centralizer</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K1" target="_self">Centralizer</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = 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>;<br/>
<a NAME="E2:43"/>
the <a href="struct_0.html#U1">carrier</a> of <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> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="uniroots.html#D1">UNIROOTS:def 1</a></i>;<br/>
<a NAME="E3:43"/><b>then </b>
not  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1">MultGroup</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T64">ZFMISC_1:64</a></i>;<br/>
<a NAME="E4:43"/><b>then </b>
not  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a>  <a href="uniroots.html#K1">MultGroup</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E5:43"/><b>then </b>
not  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> <a href="rlvect_1.html#R1">in</a>  <a href="weddwitt.html#K1" target="_self">Centralizer</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="weddwitt.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E6:43"/><b>then </b><i><font color="Green">E38</font></i>: 
not  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K1" target="_self">Centralizer</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D1">RLVECT_1:def 1</a></i>;<br/>
<a NAME="E7:43"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="weddwitt.html#K1" target="_self">Centralizer</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</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>
 
<b>by </b><i><a class="txt" href="weddwitt.html#E1:43"><i><font color="Green">E37</font></i></a>, <a class="ref" href="weddwitt.html#T30" target="_self">Th30</a></i>;<br/>
<a NAME="E8:43"/><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> <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#K1" target="_self">Centralizer</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="weddwitt.html#E6:43"><i><font color="Green">E38</font></i></a>, <a class="ref" href="card_2.html#T54">CARD_2:54</a></i>;<br/>
<b>hence </b><a NAME="E9:43"/>
 <a href="group_1.html#K9">ord</a> <span class="p1">(<span class="default"><a href="weddwitt.html#K1" target="_self">Centralizer</a> <font color="Maroon">c<sub>3</sub></font></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#K5" target="_self">centralizer</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="ref" href="group_1.html#D15">GROUP_1:def 15</a></i>;<br/>


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