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

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

<b>assume </b><a NAME="E1:82"/>
(  <a href="real_1.html#K1">-</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 )
 ;<br/>

<a NAME="E2:82"/><b>then </b>
( 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>18</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="E3:82"/><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#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="sin_cos6.html#K6">arccos</a> <font color="Maroon">c<sub>18</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>18</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> <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="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>hence </b><a NAME="E4:82"/>
( 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>18</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>18</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="ref" href="xcmplx_1.html#T92">XCMPLX_1:92</a></i>;<br/>


</div>
