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<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="hidden.html#M1">set</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/>
<a NAME="E1:44"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">n</font> <a href="uniroots.html#K2" target="_self">-roots_of_1</a>  <a href="tarski.html#R1">c=</a> 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>
 
<b>by </b><i/>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:44_1"/><i><font color="Green">E38</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>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</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> <b>by </b><i/>;<br/><a NAME="E3:44_1"/>
 <a href="group_1.html#K7">ord</a> <font color="Maroon">a</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:44_1"/>
 ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</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> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> &amp;  <a href="group_1.html#K7">ord</a> <font color="Olive">y</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> )
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E3:44"/>
(  ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</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> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> &amp;  <a href="group_1.html#K7">ord</a> <font color="Olive">y</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> ) implies <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>  )
 <b>by </b><i/>;<br/>


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