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

<b>set </b><font color="Maroon">c<sub>57</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>56</sub></font></span>)</span>;<br/>
<b>set </b><font color="Maroon">c<sub>58</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>56</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span>;<br/>
<a NAME="E1:118_2_1"/><i><font color="Green">E104</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"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p4">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</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"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</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="E2:118_2_1"/><i><font color="Green">E105</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"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</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="toprealb.html#K5" target="_self">R^1</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</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="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E3:118_2_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">c<sub>56</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="E4:118_2_1"/><b>then </b><i><font color="Green">E106</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>56</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"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>5</sub></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</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="E5:118_2_1"/><i><font color="Green">E107</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">c<sub>56</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"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>5</sub></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"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K3">+</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/>
<b>then reconsider </b><font color="Maroon">c<sub>59</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>56</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span> as   <a href="struct_0.html#NM7">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"><span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>5</sub></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"><span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>5</sub></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#E1:118_2_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="toprealb.html#E2:118_2_1"><i><font color="Green">E105</font></i></a>, <a class="txt" href="toprealb.html#E4:118_2_1"><i><font color="Green">E106</font></i></a>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a></i>;<br/>
<a NAME="E7:118_2_1"/><i><font color="Green">E108</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"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</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> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>59</sub></font>
 
<b>by </b><i><a class="ref" href="toprealb.html#T42" target="_self">Th42</a></i>;<br/>
<a NAME="E8:118_2_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K6">/</a> 2 &amp; <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 
;<br/>
<a NAME="E9:118_2_1"/><b>then </b>
<span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="int_1.html#D4">INT_1:def 4</a></i>;<br/>
<a NAME="E10:118_2_1"/><b>then </b><i><font color="Green">E109</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1"><a href="int_1.html#K1">[\</a><span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span></span><a href="int_1.html#K1">/]</a></span> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K6">/</a> 2
 
;<br/>
 <a href="int_1.html#K4">frac</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span> = 
 <a href="int_1.html#K4">frac</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="topreala.html#T1">TOPREALA:1</a></i>
<br/>.= 
1 <a href="real_1.html#K6">/</a> 2
<b>by </b><i><a class="txt" href="toprealb.html#E10:118_2_1"><i><font color="Green">E109</font></i></a>, <a class="ref" href="int_1.html#D6">INT_1:def 6</a></i>
;<br/>
<b>then </b><i><font color="Green">E110</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> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span></span>)</span> = 
 <a href="toprealb.html#K10" target="_self">c[-10]</a> 
<b>by </b><i><a class="ref" href="toprealb.html#T35" target="_self">Th35</a></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> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K3">+</a> 0</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="toprealb.html#E66"><i><font color="Green">Lemma47</font></i></a></i>
;<br/>
<a NAME="E13:118_2_1"/><i><font color="Green">E111</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">c<sub>56</sub></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">c<sub>56</sub></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><a class="txt" href="toprealb.html#E27"><i><font color="Green">Lemma19</font></i></a></i>;<br/>
<a NAME="E14:118_2_1"/><i><font color="Green">E112</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">c<sub>56</sub></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">c<sub>56</sub></font></span>)</span>
 
;<br/>
<a NAME="E15:118_2_1"/>
<font color="Maroon">c<sub>59</sub></font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="txt" href="toprealb.html#E1:118_2_1"><i><font color="Green">E104</font></i></a>, <a class="txt" href="toprealb.html#E5:118_2_1"><i><font color="Green">E107</font></i></a>, <a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E16:118_2_1"/><b>then </b>
<font color="Maroon">c<sub>59</sub></font> is <a href="t_0topsp.html#V1">open</a>
 
<b>by </b><i><a class="txt" href="toprealb.html#E13:118_2_1"><i><font color="Green">E111</font></i></a>, <a class="txt" href="toprealb.html#E14:118_2_1"><i><font color="Green">E112</font></i></a>, <a class="ref" href="topreala.html#T31">TOPREALA:31</a></i>;<br/>
<b>hence </b><a NAME="E17:118_2_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> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>56</sub></font></span>)</span></span>)</span> is <a href="t_0topsp.html#V1">open</a>
 <b>by </b><i><a class="txt" href="toprealb.html#E7:118_2_1"><i><font color="Green">E108</font></i></a>, <a class="txt" href="toprealb.html#E12:118_2_1"><i><font color="Green">E110</font></i></a>, <a class="txt" href="toprealb.html#E168"><i><font color="Green">Lemma103</font></i></a>, <a class="ref" href="topreala.html#T32">TOPREALA:32</a></i>;<br/>


</div>
