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<b>set </b><font color="Maroon">FC</font> =  <a href="complfld.html#K1">F_Complex</a> ;<br/>
<b>set </b><font color="Maroon">cMGFC</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">MGFC</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">n</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</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">E31</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">n</font> <a href="uniroots.html#K2" target="_self">-roots_of_1</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c</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">E38</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E4:38"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c</font> is    <a href="comptrig.html#M1">CRoot</a> of <font color="Maroon">n</font>, <a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> 
 <b>by </b><i/>;<br/>
<a NAME="E5:38"/><i><font color="Green">E40</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/>;<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</font>,<font color="Maroon">n</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="ref" href="complfld.html#D2">COMPLFLD: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">x</font>,<font color="Maroon">n</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#E2"><i><font color="Green">Lemma32</font></i></a></i>;<br/>
<a NAME="E8:38"/><b>then </b>
<font color="Maroon">x</font> <a href="group_1.html#K6">|^</a> <font color="Maroon">n</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">x</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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