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

<b>reconsider </b><font color="Maroon">c<sub>18</sub></font> =  <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> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <a href="topalg_2.html#K3">R^1</a>  ;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st <br/>( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="euclid.html#K23">]|</a></span> &amp; ( <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 implies <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> ) &amp; ( <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 implies <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> ) );<br/>
<a NAME="E2:94_1_1"/><i><font color="Green">E59</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,<span class="p4">(<span class="default">0 <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> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E3:94_1_1"/><i><font color="Green">E60</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>ex <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of 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,<span class="p4">(<span class="default">0 <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> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>19</sub></font> be    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>;<br/>

<a NAME="E1:94_1_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="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K8" target="_self">Tunit_circle</a> 2</span>)</span> <a href="subset_1.html#K6">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="toprealb.html#K9" target="_self">c[10]</a> </span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="toprealb.html#D10" target="_self">Def10</a></i>;<br/>
<a NAME="E2:94_1_1_1"/><b>then </b><i><font color="Green">E62</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K8" target="_self">Tunit_circle</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:94_1_1_1"/><i><font color="Green">E63</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K8" target="_self">Tunit_circle</a> 2</span>)</span> is   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>20</sub></font>, <font color="Maroon">c<sub>21</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E5:94_1_1_1"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="finseq_1.html#K10">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="toprealb.html#E2:94_1_1_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="euclid.html#T55">EUCLID:55</a></i>;<br/>
<a NAME="E6:94_1_1_1"/><i><font color="Green">E65</font></i>: 
not <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><a href="toprealb.html#K9" target="_self">c[10]</a> </span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="txt" href="toprealb.html#E1:94_1_1_1"><i><font color="Green">E61</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>22</sub></font> =  <a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>23</sub></font> = <font color="Maroon">c<sub>19</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="toprealb.html#E2:94_1_1_1"><i><font color="Green">E62</font></i></a>, <a class="txt" href="toprealb.html#E3:94_1_1_1"><i><font color="Green">E63</font></i></a></i>;<br/>
<a NAME="E8:94_1_1_1"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="euclid.html#K23">]|</a></span>
 
<b>by </b><i><a class="txt" href="toprealb.html#E5:94_1_1_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="euclid.html#D16">EUCLID:def 16</a></i>;<br/>
<a NAME="E9:94_1_1_1"/><b>then </b><i><font color="Green">E67</font></i>: 
( <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font> <a href="euclid.html#K21">`1</a>  &amp; <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>23</sub></font> <a href="euclid.html#K22">`2</a>  )
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E10:94_1_1_1"/><b>then </b><i><font color="Green">E68</font></i>: 
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>20</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 
<b>by </b><i><a class="ref" href="toprealb.html#T27" target="_self">Th27</a></i>;<br/>
<a NAME="E11:94_1_1_1"/><b>then </b><i><font color="Green">E69</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font> &amp;  <a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="sin_cos.html#K33">PI</a>  )
 
<b>by </b><i><a class="ref" href="sin_cos6.html#T101">SIN_COS6:101</a></i>;<br/>
<a NAME="E12:94_1_1_1"/><i><font color="Green">E70</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K6">/</a> 2 )
 
<b>by </b><i><a class="txt" href="toprealb.html#E10:94_1_1_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="toprealb.html#E74"><i><font color="Green">Lemma52</font></i></a></i>;<br/>
<i><font color="Green">E71</font></i>: 1 <a href="square_1.html#K5">^2</a>  = 
<span class="p1"><a href="toprns_1.html#K5">|.</a><span class="default"><font color="Maroon">c<sub>23</sub></font></span><a href="toprns_1.html#K5">.|</a></span> <a href="square_1.html#K5">^2</a> 
<b>by </b><i><a class="txt" href="toprealb.html#E2:94_1_1_1"><i><font color="Green">E62</font></i></a>, <a class="ref" href="toprealb.html#T12" target="_self">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>20</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>21</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="toprealb.html#E9:94_1_1_1"><i><font color="Green">E67</font></i></a>, <a class="ref" href="jgraph_3.html#T10">JGRAPH_3:10</a></i>
;<br/>
<div><i><font color="Green">E72</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="94_1_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:94_1_1_1_2"/><i><font color="Green">E73</font></i>: 
 <a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><a NAME="E2:94_1_1_1_2"/><b>then </b><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="txt" href="toprealb.html#E10:94_1_1_1"><i><font color="Green">E68</font></i></a>, <a class="ref" href="sin_cos6.html#T98">SIN_COS6:98</a></i>;<br/><a NAME="E3:94_1_1_1_2"/>
1 <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>21</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1
 <b>by </b><i><a class="txt" href="toprealb.html#E10:94_1_1_1"><i><font color="Green">E68</font></i></a>, <a class="txt" href="toprealb.html#E13:94_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="toprealb.html#E1:94_1_1_1_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="sin_cos6.html#T98">SIN_COS6:98</a></i>;<br/><a NAME="E4:94_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/><a NAME="E5:94_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a>  <a href="toprealb.html#K9" target="_self">c[10]</a> 
 <b>by </b><i><a class="txt" href="toprealb.html#E5:94_1_1_1"><i><font color="Green">E64</font></i></a>, <a class="txt" href="toprealb.html#E2:94_1_1_1_2"><i><font color="Green">E74</font></i></a>, <a class="ref" href="euclid.html#D16">EUCLID:def 16</a></i>;<br/><b>hence </b><a NAME="E6:94_1_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="toprealb.html#E6:94_1_1_1"><i><font color="Green">E65</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_1_1_3"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:94_1_1_1_3"/>
( <font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_1_1_3_1"><b>suppose </b></a><a NAME="E1:94_1_1_1_3_1"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:94_1_1_1_3_1"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>by </b><i><a class="txt" href="toprealb.html#E6:94_1_1_1"><i><font color="Green">E65</font></i></a>, <a class="txt" href="toprealb.html#E8:94_1_1_1"><i><font color="Green">E66</font></i></a>, <a class="txt" href="toprealb.html#E1:94_1_1_1_3_1"><i><font color="Green">E73</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>set </b><font color="Maroon">c<sub>24</sub></font> = <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span>;<br/><a NAME="E3:94_1_1_1_3_1"/>
<span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="toprealb.html#E14:94_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xcmplx_1.html#T50">XCMPLX_1:50</a></i>;<br/><a NAME="E4:94_1_1_1_3_1"/><b>then </b>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i><a class="txt" href="toprealb.html#E12:94_1_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>25</sub></font> = <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> as    <a href="subset_1.html#M1">Element</a> of 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,<span class="p4">(<span class="default">0 <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#E2:94_1_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>25</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>20</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>21</sub></font>
;<br/><b>thus </b><a NAME="E6:94_1_1_1_3_1"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="euclid.html#K23">]|</a></span>
 <b>by </b><i><a class="txt" href="toprealb.html#E5:94_1_1_1"><i><font color="Green">E64</font></i></a>, <a class="ref" href="euclid.html#D16">EUCLID:def 16</a></i>;<br/><b>thus </b><a NAME="E7:94_1_1_1_3_1"/>
( <font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 implies <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> )
 ;<br/><b>assume </b><a NAME="E8:94_1_1_1_3_1"/>
<font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><b>thus </b><font color="Maroon">c<sub>25</sub></font> = 
<span class="p1">(<span class="default">1 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span>
<b>by </b><i><a class="txt" href="toprealb.html#E13:94_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="toprealb.html#E1:94_1_1_1_3_1"><i><font color="Green">E73</font></i></a>, <a class="txt" href="toprealb.html#E2:94_1_1_1_3_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="sin_cos6.html#T95">SIN_COS6:95</a>, <a class="ref" href="square_1.html#T110">SQUARE_1:110</a></i>
<br/>.= 
1 <a href="real_1.html#K5">-</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="xcmplx_1.html#T92">XCMPLX_1:92</a></i>
<br/>.= 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T92">XCMPLX_1:92</a></i>
<br/>.= 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="toprealb.html#E13:94_1_1_1"><i><font color="Green">E71</font></i></a>, <a class="txt" href="toprealb.html#E1:94_1_1_1_3_1"><i><font color="Green">E73</font></i></a>, <a class="txt" href="toprealb.html#E2:94_1_1_1_3_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="sin_cos6.html#T95">SIN_COS6:95</a>, <a class="ref" href="square_1.html#T110">SQUARE_1:110</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_1_1_3_2"><b>suppose </b></a><a NAME="E1:94_1_1_1_3_2"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>24</sub></font> = <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span>;<br/><a NAME="E2:94_1_1_1_3_2"/>
<span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="toprealb.html#E14:94_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="xcmplx_1.html#T50">XCMPLX_1:50</a></i>;<br/><a NAME="E3:94_1_1_1_3_2"/><b>then </b>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i><a class="txt" href="toprealb.html#E12:94_1_1_1"><i><font color="Green">E70</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>25</sub></font> = <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> as    <a href="subset_1.html#M1">Element</a> of 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,<span class="p4">(<span class="default">0 <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#E2:94_1_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>25</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>20</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>21</sub></font>
;<br/><b>thus </b><a NAME="E5:94_1_1_1_3_2"/>
( <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="euclid.html#K23">]|</a></span> &amp; ( <font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 implies <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> ) &amp; ( <font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 implies <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="toprealb.html#E5:94_1_1_1"><i><font color="Green">E64</font></i></a>, <a class="txt" href="toprealb.html#E1:94_1_1_1_3_2"><i><font color="Green">E73</font></i></a>, <a class="ref" href="euclid.html#D16">EUCLID:def 16</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="94_1_1_1_3_3"><b>suppose </b></a><a NAME="E1:94_1_1_1_3_3"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><b>set </b><font color="Maroon">c<sub>24</sub></font> = 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span>;<br/><i><font color="Green">E74</font></i>: <span class="p1">(<span class="default"><span class="p2">(<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#K5">-</a> <span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<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#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T121">XCMPLX_1:121</a></i>
<br/>.= 
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>
;<br/><a NAME="E3:94_1_1_1_3_3"/>
1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> 
 <b>by </b><i><a class="txt" href="toprealb.html#E11:94_1_1_1"><i><font color="Green">E69</font></i></a>, <a class="ref" href="real_2.html#T199">REAL_2:199</a></i>;<br/><a NAME="E4:94_1_1_1_3_3"/><b>then </b>
( <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<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#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> &amp; <span class="p1">(<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#K5">-</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<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#K5">-</a> 0 )
 <b>by </b><i><a class="txt" href="toprealb.html#E11:94_1_1_1"><i><font color="Green">E69</font></i></a>, <a class="txt" href="toprealb.html#E14:94_1_1_1"><i><font color="Green">E72</font></i></a>, <a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><a NAME="E5:94_1_1_1_3_3"/><b>then </b>
( 0 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> &amp; 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<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#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> )
 <b>by </b><i><a class="txt" href="toprealb.html#E2:94_1_1_1_3_3"><i><font color="Green">E74</font></i></a>, <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E6:94_1_1_1_3_3"/><b>then </b>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> &amp; 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T60">XCMPLX_1:60</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>25</sub></font> = 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> as    <a href="subset_1.html#M1">Element</a> of 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,<span class="p4">(<span class="default">0 <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#E2:94_1_1"><i><font color="Green">E59</font></i></a>, <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>25</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>20</sub></font>
;<br/><b>take </b>
<font color="Maroon">c<sub>21</sub></font>
;<br/><b>thus </b><a NAME="E8:94_1_1_1_3_3"/>
( <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Maroon">c<sub>20</sub></font>,<font color="Maroon">c<sub>21</sub></font></span><a href="euclid.html#K23">]|</a></span> &amp; ( <font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 implies <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> ) &amp; ( <font color="Maroon">c<sub>21</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 implies <font color="Maroon">c<sub>25</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> ) )
 <b>by </b><i><a class="txt" href="toprealb.html#E5:94_1_1_1"><i><font color="Green">E64</font></i></a>, <a class="txt" href="toprealb.html#E1:94_1_1_1_3_3"><i><font color="Green">E73</font></i></a>, <a class="ref" href="euclid.html#D16">EUCLID:def 16</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E4:94_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </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">c<sub>5</sub></font></span>)</span></span><a href="rcomp_1.html#K2">.[</a></span></span>)</span></span>)</span> st <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font>]
 
<b>from </b><i><a class="ref" href="funct_2.html#S3">FUNCT_2:sch 3</a>(<a class="txt" href="toprealb.html#E3:94_1_1"><i><font color="Green">E60</font></i></a>);<br/></i>
<b>hence </b><a NAME="E5:94_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </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">0,1</span><a href="rcomp_1.html#K2">.[</a></span></span>)</span></span>)</span> st <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>ex <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid.html#K23">|[</a><span class="default"><font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="euclid.html#K23">]|</a></span> &amp; ( <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 implies <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> ) &amp; ( <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 implies <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span> ) )
 ;<br/>


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