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<div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of  <a href="toprealb.html#K4">R^1</a> 0, <a href="toprealb.html#K4">R^1</a> <font color="Maroon">c<sub>8</sub></font>;<br/>



<b>set </b><font color="Maroon">c<sub>10</sub></font> = <a href="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font>;<br/>
<a NAME="E1:44"/>
<a href="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font> is   <a href="topalg_1.html#NM1">Loop</a> of  <a href="toprealb.html#K9">c[10]</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:44_1"/>
<a href="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></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="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 0 = 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="toprealb.html#K4">R^1</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="borsuk_2.html#D4">BORSUK_2:def 4</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> 0
<b>by </b><i><a class="ref" href="toprealb.html#D2">TOPREALB:def 2</a></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> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K4">*</a> 0</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">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K4">*</a> 0</span>)</span></span>)</span></span><a href="euclid.html#K23">]|</a></span>
<b>by </b><i><a class="ref" href="toprealb.html#D11">TOPREALB:def 11</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="sin_cos.html#T34">SIN_COS:34</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 = 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="toprealb.html#K4">R^1</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_2.html#D4">BORSUK_2:def 4</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="toprealb.html#D2">TOPREALB:def 2</a></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#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#K33">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0</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#K33">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></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="toprealb.html#D11">TOPREALB:def 11</a></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#K33">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></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/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <a href="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font> as   <a href="topalg_1.html#NM1">Loop</a> of  <a href="toprealb.html#K9">c[10]</a>  ;<br/>
<a NAME="E3:44"/><i><font color="Green">E42</font></i>: 
 <a href="topalg_5.html#K6" target="_self">cLoop</a> <font color="Maroon">c<sub>8</sub></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">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="topalg_5.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E4:44"/><i><font color="Green">E43</font></i>: 
 <a href="topalg_5.html#K6" target="_self">cLoop</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="borsuk_2.html#R4">are_homotopic</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_2"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> =  <a href="topalg_2.html#K3">R^1</a>  as  non <a href="struct_0.html#V3">empty</a> <a href="topalg_2.html#V3">convex</a>  <a href="pre_topc.html#M1">SubSpace</a> of  <a href="topalg_2.html#K3">R^1</a>  ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> =  <a href="toprealb.html#K4">R^1</a> 0, <font color="Maroon">c<sub>14</sub></font> =  <a href="toprealb.html#K4">R^1</a> <font color="Maroon">c<sub>8</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>12</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>15</sub></font> =  <a href="topalg_5.html#K2" target="_self">ExtendInt</a> <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>9</sub></font> as    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</sub></font> =  <a href="topalg_2.html#K5">R1Homotopy</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>16</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><a href="topmetr.html#K5">I[01]</a> ,<a href="topmetr.html#K5">I[01]</a> </span><a href="borsuk_1.html#K5">:]</a></span>,<a href="topalg_2.html#K3">R^1</a>  ;<br/>
<b>take </b><font color="Maroon">c<sub>18</sub></font> = <a href="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>17</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="borsuk_2.html#D7">BORSUK_2:def 7</a><br/>

<b>thus </b><a NAME="E5:44_2"/>
<font color="Maroon">c<sub>18</sub></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>;<br/>

<b>let </b><font color="Maroon">c<sub>19</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/>

<b>thus </b><font color="Maroon">c<sub>18</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,0 = 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="topalg_5.html#E5"><i><font color="Green">Lemma5</font></i></a>, <a class="ref" href="binop_1.html#T30">BINOP_1:30</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="topalg_5.html#K2" target="_self">ExtendInt</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_2.html#D5">TOPALG_2:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="topalg_5.html#K6" target="_self">cLoop</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="txt" href="topalg_5.html#E3:44"><i><font color="Green">E42</font></i></a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>18</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,1 = 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="topalg_5.html#E5"><i><font color="Green">Lemma5</font></i></a>, <a class="ref" href="binop_1.html#T30">BINOP_1:30</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="topalg_5.html#K2" target="_self">ExtendInt</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_2.html#D5">TOPALG_2:def 5</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>19</sub></font>
<b>by </b><i><a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
;<br/>

<b>let </b><font color="Maroon">c<sub>20</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <a href="topmetr.html#K5">I[01]</a> ;<br/>

<b>thus </b><font color="Maroon">c<sub>18</sub></font> <a href="binop_1.html#K1">.</a> 0,<font color="Maroon">c<sub>20</sub></font> = 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="topalg_5.html#E5"><i><font color="Green">Lemma5</font></i></a>, <a class="ref" href="binop_1.html#T30">BINOP_1:30</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="topalg_5.html#K2" target="_self">ExtendInt</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_2.html#D5">TOPALG_2:def 5</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4">R^1</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_2.html#D4">BORSUK_2:def 4</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4">R^1</a> 0</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4">R^1</a> 0</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_2.html#D4">BORSUK_2:def 4</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="xcmplx_0.html#K3">*</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="toprealb.html#D2">TOPREALB:def 2</a></i>
<br/>.= 
 <a href="toprealb.html#K9">c[10]</a> 
<b>by </b><i><a class="ref" href="toprealb.html#T33">TOPREALB:33</a></i>
;<br/>

<b>thus </b><font color="Maroon">c<sub>18</sub></font> <a href="binop_1.html#K1">.</a> 1,<font color="Maroon">c<sub>20</sub></font> = 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>20</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="topalg_5.html#E5"><i><font color="Green">Lemma5</font></i></a>, <a class="ref" href="binop_1.html#T30">BINOP_1:30</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="topalg_5.html#K2" target="_self">ExtendInt</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_2.html#D5">TOPALG_2:def 5</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4">R^1</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_2.html#D4">BORSUK_2:def 4</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4">R^1</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4">R^1</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="borsuk_2.html#D4">BORSUK_2:def 4</a></i>
<br/>.= 
<a href="toprealb.html#K12">CircleMap</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="toprealb.html#D2">TOPREALB:def 2</a></i>
<br/>.= 
 <a href="toprealb.html#K9">c[10]</a> 
<b>by </b><i><a class="ref" href="toprealb.html#T33">TOPREALB:33</a></i>
;<br/>


</div><b>end;</b></div>
<b>thus </b><a href="topalg_5.html#K7" target="_self">Ciso</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> = 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <span class="p2">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> </span>)</span>,<span class="p1">(<span class="default"><a href="topalg_5.html#K6" target="_self">cLoop</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="topalg_5.html#D5" target="_self">Def5</a></i>
<br/>.= 
 <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="topalg_1.html#K2">EqRel</a> <span class="p2">(<span class="default"><a href="toprealb.html#K8">Tunit_circle</a> 2</span>)</span>,<a href="toprealb.html#K9">c[10]</a> </span>)</span>,<span class="p1">(<span class="default"><a href="toprealb.html#K12">CircleMap</a>  <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="topalg_5.html#E4:44"><i><font color="Green">E43</font></i></a>, <a class="ref" href="topalg_1.html#T47">TOPALG_1:47</a></i>
;<br/>


</div>
