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

<b>thus </b><a NAME="E1:1"/><i><font color="Green">E2</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1"><b>proof </b></a><div class="add">

<a NAME="E1:1_1"/>
 <a href="sin_cos.html#K33">PI</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_1.html#K2">].</a><span class="default">0,4</span><a href="rcomp_1.html#K2">.[</a></span>
 
<b>by </b><i><a class="ref" href="sin_cos.html#D30">SIN_COS:def 30</a></i>;<br/>
<a NAME="E2:1_1"/><b>then </b>
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="sin_cos.html#K33">PI</a>  &amp;  <a href="sin_cos.html#K33">PI</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 4 )
 
<b>by </b><i><a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>
<a NAME="E3:1_1"/><b>then </b>
0 <a href="binop_2.html#K12">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2
 
<b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>hence </b><a NAME="E4:1_1"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:1"/><i><font color="Green">E3</font></i>: 
<a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="sin_cos.html#K33">PI</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_2"><b>proof </b></a><div class="add">

<a NAME="E1:1_2"/>
0 <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="sin_cos2.html#E1:1"><i><font color="Green">E2</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<b>hence </b><a NAME="E2:1_2"/>
<a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="sin_cos.html#K33">PI</a> 
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:1"/><i><font color="Green">E4</font></i>: 
 <a href="sin_cos.html#K33">PI</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K33">PI</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_3"><b>proof </b></a><div class="add">

<a NAME="E1:1_3"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="sin_cos2.html#E2:1"><i><font color="Green">E3</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<b>hence </b><a NAME="E2:1_3"/>
 <a href="sin_cos.html#K33">PI</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K33">PI</a> 
 ;<br/>


</div><b>end;</b></div>

<a NAME="E4:1"/><i><font color="Green">E5</font></i>: 
<a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K33">PI</a> 
 
;<br/>
<a NAME="E5:1"/>
<span class="p1">(<span class="default"><a href="sin_cos.html#K33">PI</a>  <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="hidden.html#R1">=</a> 2 <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K33">PI</a> 
 
;<br/>
<b>hence </b><a NAME="E6:1"/>
<span class="p1">(<span class="default">3 <a href="binop_2.html#K12">/</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K33">PI</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 2 <a href="binop_2.html#K11">*</a> <a href="sin_cos.html#K33">PI</a> 
 <b>by </b><i><a class="txt" href="sin_cos2.html#E3:1"><i><font color="Green">E4</font></i></a>, <a class="txt" href="sin_cos2.html#E4:1"><i><font color="Green">E5</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>


</div>
