<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>18</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">c<sub>19</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>set </b><font color="Maroon">c<sub>20</sub></font> = <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>21</sub></font> = <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> =  <a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p1">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>23</sub></font> =  <a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p1">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>24</sub></font> =  <a href="jordan16.html#K1">AffineMap</a> 1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>25</sub></font> = <span class="p1">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>;<br/>
<a NAME="E1:92"/><i><font color="Green">E59</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="txt" href="toprealb.html#E62"><i><font color="Green">Lemma43</font></i></a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<a NAME="E2:92"/><i><font color="Green">E60</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="txt" href="toprealb.html#E62"><i><font color="Green">Lemma43</font></i></a>, <a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<a NAME="E3:92"/>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E4:92"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<a NAME="E5:92"/>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="txt" href="toprealb.html#E80"><i><font color="Green">Lemma57</font></i></a></i>;<br/>
<a NAME="E6:92"/><b>then </b><i><font color="Green">E62</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="toprealb.html#E2:92"><i><font color="Green">E60</font></i></a>, <a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>;<br/>
<a NAME="E7:92"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> holds <br/><span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>26</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:92_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">c<sub>26</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>27</sub></font> = <font color="Maroon">c<sub>26</sub></font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="txt" href="toprealb.html#E1:92"><i><font color="Green">E59</font></i></a>, <a class="txt" href="toprealb.html#E1:92_1"><i><font color="Green">E63</font></i></a></i>;<br/>
<a NAME="E3:92_1"/>
( <font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>27</sub></font> &amp; <font color="Maroon">c<sub>27</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1 )
 
<b>by </b><i><a class="txt" href="toprealb.html#E1:92"><i><font color="Green">E59</font></i></a>, <a class="txt" href="toprealb.html#E1:92_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>
<a NAME="E4:92_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>27</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>27</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E5:92_1"/><b>then </b><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>27</sub></font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">c<sub>19</sub></font>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p3">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font> = 
<span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <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"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="toprealb.html#E1:92"><i><font color="Green">E59</font></i></a>, <a class="txt" href="toprealb.html#E4:92"><i><font color="Green">E61</font></i></a>, <a class="txt" href="toprealb.html#E1:92_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>26</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="toprealb.html#E1:92"><i><font color="Green">E59</font></i></a>, <a class="txt" href="toprealb.html#E1:92_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>27</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="jordan16.html#D3">JORDAN16:def 3</a></i>
<br/>.= 
<a href="toprealb.html#K12" target="_self">CircleMap</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>27</sub></font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="toprealb.html#E5:92_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<a href="toprealb.html#K12" target="_self">CircleMap</a>  <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>27</sub></font>
<b>by </b><i><a class="ref" href="toprealb.html#T32" target="_self">Th32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>26</sub></font>
<b>by </b><i><a class="txt" href="toprealb.html#E1:92"><i><font color="Green">E59</font></i></a>, <a class="txt" href="toprealb.html#E1:92_1"><i><font color="Green">E63</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:92"/>
 <a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p1">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="toprealb.html#K13" target="_self">CircleMap</a> <span class="p2">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan16.html#K1">AffineMap</a> 1,<span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>18</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>19</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>18</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="toprealb.html#E1:92"><i><font color="Green">E59</font></i></a>, <a class="txt" href="toprealb.html#E4:92"><i><font color="Green">E61</font></i></a>, <a class="txt" href="toprealb.html#E6:92"><i><font color="Green">E62</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
