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

<b>set </b><font color="Maroon">F</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">i</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">f</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">i</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">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">p1</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>;<br/>
<a NAME="E1:114_1_1"/><i><font color="Green">E61</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default">0,1</span><a href="rcomp_1.html#K2">.[</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="toprealb.html#K5" target="_self">R^1</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default">0,1</span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E2:114_1_1"/><i><font color="Green">E66</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">i</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <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="toprealb.html#K5" target="_self">R^1</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">i</font>,<span class="p2">(<span class="default"><font color="Maroon">i</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="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E3:114_1_1"/>
 <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">i</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="E4:114_1_1"/><b>then </b><i><font color="Green">E68</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">i</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">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">p1</font></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">i</font>,<span class="p2">(<span class="default"><font color="Maroon">i</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="relat_1.html#T91">RELAT_1:91</a></i>;<br/>
<a NAME="E5:114_1_1"/><i><font color="Green">E69</font></i>: 
 <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">i</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">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">p1</font></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">0,<span class="p2">(<span class="default">0 <a href="real_1.html#K3">+</a> 1</span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">f</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">i</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">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">p1</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> as   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default"><font color="Maroon">i</font>,<span class="p4">(<span class="default"><font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">p1</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p3"><a href="rcomp_1.html#K2">].</a><span class="default">0,<span class="p4">(<span class="default">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">p1</font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span></span>)</span> <b>by </b><i><a class="txt" href="toprealb.html#E34"><i><font color="Green">Lemma104</font></i></a>, <a class="ref" href="toprealb.html#T12" target="_self">Th12</a>, , <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>
<a NAME="E7:114_1_1"/><i><font color="Green">E71</font></i>: 
 <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">0 <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">i</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> 0</span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<i><font color="Green">E72</font></i>: <a href="toprealb.html#K12" target="_self">CircleMap</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="toprealb.html#K9" target="_self">c[10]</a> 
<b>by </b><i/>
<br/>.= 
<a href="toprealb.html#K12" target="_self">CircleMap</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="toprealb.html#K4" target="_self">R^1</a> 0</span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E9:114_1_1"/><i><font color="Green">E73</font></i>: 
( <a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p2">(<span class="default"><a href="relset_1.html#K4">dom</a> <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">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="topalg_2.html#K3">R^1</a>  &amp; <a href="topalg_2.html#K3">R^1</a>  <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><a href="toprealb.html#K5" target="_self">R^1</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <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">i</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="topalg_2.html#K3">R^1</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E10:114_1_1"/><i><font color="Green">E74</font></i>: 
 <a href="toprealb.html#K6" target="_self">R^1</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">i</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="jordan16.html#K1">AffineMap</a> 1,<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">i</font></span>)</span>
 
;<br/>
<a NAME="E11:114_1_1"/>
<font color="Maroon">f</font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="txt" href="toprealb.html#E34"><i><font color="Green">Lemma104</font></i></a>, <a class="ref" href="toprealb.html#T13" target="_self">Th13</a>, <a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E12:114_1_1"/><b>then </b>
<font color="Maroon">f</font> is <a href="t_0topsp.html#V1">open</a>
 
<b>by </b><i>, <a class="ref" href="toprealb.html#T19" target="_self">Th19</a>, <a class="ref" href="topreala.html#T31">TOPREALA:31</a></i>;<br/>
<b>hence </b><a NAME="E13:114_1_1"/>
 <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">i</font></span>)</span> is <a href="t_0topsp.html#V1">open</a>
 <b>by </b><i><a class="ref" href="toprealb.html#T14" target="_self">Th14</a>, <a class="ref" href="toprealb.html#T15" target="_self">Th15</a>, , <a class="ref" href="topreala.html#T32">TOPREALA:32</a></i>;<br/>


</div>
