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<b>set </b><font color="Maroon">c<sub>1</sub></font> =  <a href="complfld.html#K1">F_Complex</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="uniroots.html#K1" target="_self">MultGroup</a> <a href="complfld.html#K1">F_Complex</a> ;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span>;<br/>



<b>assume </b><a NAME="E1:38"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="uniroots.html#K2" target="_self">-roots_of_1</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> <b> such that </b><br/><a NAME="E3:38"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E4:38"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is    <a href="comptrig.html#M1">CRoot</a> of <font color="Maroon">c<sub>4</sub></font>, <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i><a class="txt" href="uniroots.html#E1:38"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E5:38"/><i><font color="Green">E37</font></i>: 
 <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> 
 
<b>by </b><i><a class="ref" href="uniroots.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E6:38"/>
<span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> 
 
<b>by </b><i><a class="txt" href="uniroots.html#E4:38"><i><font color="Green">E36</font></i></a>, <a class="ref" href="comptrig.html#D2">COMPTRIG:def 2</a></i>;<br/>
<a NAME="E7:38"/><b>then </b>
<span class="p1">(<span class="default"><a href="group_1.html#K5">power</a> <span class="p2">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="uniroots.html#E3:38"><i><font color="Green">E35</font></i></a>, <a class="txt" href="uniroots.html#E5:38"><i><font color="Green">E37</font></i></a>, <a class="ref" href="uniroots.html#T32" target="_self">Th32</a></i>;<br/>
<a NAME="E8:38"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#K6">|^</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <span class="p1">(<span class="default"><a href="uniroots.html#K1" target="_self">MultGroup</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E9:38"/>
<font color="Maroon">c<sub>5</sub></font> <a href="group_1.html#NR1" target="_self">is_not_of_order_0</a> 
 <b>by </b><i><a class="ref" href="group_1.html#D11">GROUP_1:def 11</a></i>;<br/>


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