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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="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:28_1"/>
<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/><a NAME="E2:28_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">z</font> where <font color="Olive">z</font> is   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a>  : <font color="Olive">z</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>  </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">y</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="E4:28_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E5:28_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">y</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> 
 ;<br/><b>thus </b><a NAME="E6:28_1"/>
<font color="Maroon">x</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>, </i>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:28"/>
( <font color="Maroon">x</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>  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>  )
 ;<br/>


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