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<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>consider </b><font color="Maroon">s</font> being  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <a href="complfld.html#K1">F_Complex</a> <b> such that </b><br/><a NAME="E2:61"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">y</font> where <font color="Olive">y</font> is    <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> :  <a href="group_1.html#K7">ord</a> <font color="Olive">y</font> <a href="hidden.html#R1">=</a> 1 </span>}</span> 
 <b>and </b><br/><a NAME="E3:61"/><i><font color="Green">E38</font></i>: 
 <a href="uniroots.html#K6" target="_self">cyclotomic_poly</a> 1 <a href="funct_2.html#R2">=</a>  <a href="uproots.html#K10">poly_with_roots</a> <span class="p1">(<span class="default"><font color="Maroon">s</font>,1 <a href="uproots.html#K2">-bag</a> </span>)</span>
 <b>by </b><i/>;<br/>
<a NAME="E4:61"/><i><font color="Green">E39</font></i>: 
1 <a href="uniroots.html#K2" target="_self">-roots_of_1</a>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <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> :  <a href="group_1.html#K7">ord</a> <font color="Olive">x</font> <a href="nat_1.html#R1">divides</a> 1 </span>}</span> 
 
<b>by </b><i/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:61_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">s</font>
 ;<br/><b>then consider </b><font color="Maroon">x1</font> being    <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><b> such that </b><br/><a NAME="E3:61_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font>
 <b>and </b><br/><a NAME="E4:61_1_1"/><i><font color="Green">E41</font></i>: 
 <a href="group_1.html#K7">ord</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="uniroots.html#E5:61_1"><i><font color="Green">E53</font></i></a></i>;<br/><b>thus </b><a NAME="E5:61_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> 1 <a href="uniroots.html#K2" target="_self">-roots_of_1</a> 
 <b>by </b><i>, , </i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:61_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> 1 <a href="uniroots.html#K2" target="_self">-roots_of_1</a> 
 ;<br/><b>then consider </b><font color="Maroon">x1</font> being    <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><b> such that </b><br/><a NAME="E4:61_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font>
 <b>and </b><br/><a NAME="E5:61_1"/><i><font color="Green">E53</font></i>: 
 <a href="group_1.html#K7">ord</a> <font color="Maroon">x1</font> <a href="nat_1.html#R1">divides</a> 1
 <b>by </b><i/>;<br/><a NAME="E6:61_1"/>
 <a href="group_1.html#K7">ord</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i>, <a class="ref" href="wsierp_1.html#T20">WSIERP_1:20</a></i>;<br/><b>hence </b><a NAME="E7:61_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="txt" href="uniroots.html#E5:61_1"><i><font color="Green">E53</font></i></a>, </i>;<br/></div><b>end;</b></div>
<a NAME="E6:61"/><b>then </b>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> 1 <a href="uniroots.html#K2" target="_self">-roots_of_1</a> 
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<b>hence </b><a NAME="E7:61"/>
 <a href="uniroots.html#K6" target="_self">cyclotomic_poly</a> 1 <a href="funct_2.html#R2">=</a> <span class="p1"><a href="polynom5.html#K4">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <a href="complfld.html#K1">F_Complex</a> </span>)</span></span><a href="polynom5.html#K4">%&gt;</a></span>
 <b>by </b><i>, , </i>;<br/>


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