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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>set </b><font color="Maroon">x</font> = <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="binop_2.html#K11">*</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="binop_2.html#K11">*</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <font color="Maroon">n</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span>;<br/>
<a NAME="E1:41"/><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/>
<a NAME="E2:41"/>
<span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="binop_2.html#K11">*</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="binop_2.html#K11">*</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <font color="Maroon">n</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span> <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/>
<b>then reconsider </b><font color="Maroon">y</font> = <span class="p1"><a href="hahnban1.html#K1">[**</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="binop_2.html#K11">*</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <font color="Maroon">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K21">sin</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="binop_2.html#K11">*</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <font color="Maroon">n</font></span>)</span></span>)</span></span><a href="hahnban1.html#K1">**]</a></span> 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="E4:41"/><i><font color="Green">E38</font></i>: 
 <a href="group_1.html#K7">ord</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="int_1.html#K5">div</a> <span class="p1">(<span class="default">1 <a href="int_2.html#K3">gcd</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:41"/>
1 <a href="int_2.html#K3">gcd</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="wsierp_1.html#T13">WSIERP_1:13</a></i>;<br/>
<a NAME="E6:41"/><b>then </b>
 <a href="group_1.html#K7">ord</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="nat_1.html#K5">div</a> 1
 
<b>by </b><i>, <a class="ref" href="newton.html#T101">NEWTON:101</a></i>;<br/>
<a NAME="E7:41"/><b>then </b>
 <a href="group_1.html#K7">ord</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="nat_2.html#T6">NAT_2:6</a></i>;<br/>
<b>hence </b><a NAME="E8:41"/>
 ex <font color="Olive">x</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  <a href="group_1.html#K7">ord</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 ;<br/>


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