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<b>set </b><font color="Maroon">f</font> =  <a href="topalg_5.html#K5" target="_self">cLoop</a> <font color="Maroon">n</font>;<br/>
<a NAME="E1:36_1_1"/>
 <a href="topalg_5.html#K5" target="_self">cLoop</a> <font color="Maroon">n</font> <a href="funct_2.html#R2">=</a> <a href="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="topalg_5.html#K2" target="_self">ExtendInt</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:36_1_1"/>
 <a href="topalg_5.html#K5" target="_self">cLoop</a> <font color="Maroon">n</font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="tops_2.html#T58">TOPS_2:58</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D4">BORSUK_2:def 4</a><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="topalg_5.html#K5" target="_self">cLoop</a> <font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> 0 = 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K23">cos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">j0</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K20">sin</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">j0</font></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i/>
<br/>.= 
 <a href="toprealb.html#K9">c[10]</a> 
<b>by </b><i><a class="ref" href="toprealb.html#D8">TOPREALB:def 8</a>, <a class="ref" href="sin_cos.html#T34">SIN_COS:34</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="topalg_5.html#K5" target="_self">cLoop</a> <font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K23">cos</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">j1</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K20">sin</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">j1</font></span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K24">cos</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="sin_cos.html#K20">sin</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K35">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i><a class="ref" href="complex2.html#T10">COMPLEX2:10</a></i>
<br/>.= 
 <a href="toprealb.html#K9">c[10]</a> 
<b>by </b><i><a class="ref" href="toprealb.html#D8">TOPREALB:def 8</a>, <a class="ref" href="complex2.html#T9">COMPLEX2:9</a>, <a class="ref" href="sin_cos.html#T34">SIN_COS:34</a></i>
;<br/>


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