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

<b>let </b><font color="Maroon">th1</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">th2</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:125_1_2"/><i><font color="Green">E57</font></i>: 
( <a href="sin_cos.html#K32" target="_self">tan</a>  <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">th1</font> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">th1</font> <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>and </b><br/><a NAME="E2:125_1_2"/><i><font color="Green">E59</font></i>: 
( <a href="sin_cos.html#K32" target="_self">tan</a>  <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">th2</font> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">th2</font> <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> )
 ;<br/>

<a NAME="E3:125_1_2"/>
( <font color="Maroon">th1</font> <a href="xcmplx_0.html#K7">/</a> 4 <a href="hidden.html#R2">in</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> &amp; <font color="Maroon">th2</font> <a href="xcmplx_0.html#K7">/</a> 4 <a href="hidden.html#R2">in</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> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="125_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:125_1_2_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">th1</font> &amp; <font color="Maroon">th1</font> <a href="xxreal_0.html#R1">&lt;</a> 4 )
 
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>
<a NAME="E2:125_1_2_1"/><b>then </b>
( 0 <a href="real_1.html#K6">/</a> 4 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">th1</font> <a href="xcmplx_0.html#K7">/</a> 4 &amp; <font color="Maroon">th1</font> <a href="xcmplx_0.html#K7">/</a> 4 <a href="xxreal_0.html#R1">&lt;</a> 4 <a href="real_1.html#K6">/</a> 4 )
 
<b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>hence </b><a NAME="E3:125_1_2_1"/>
<font color="Maroon">th1</font> <a href="xcmplx_0.html#K7">/</a> 4 <a href="hidden.html#R2">in</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="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>

<a NAME="E4:125_1_2_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">th2</font> &amp; <font color="Maroon">th2</font> <a href="xxreal_0.html#R1">&lt;</a> 4 )
 
<b>by </b><i>, <a class="ref" href="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>
<a NAME="E5:125_1_2_1"/><b>then </b>
( 0 <a href="real_1.html#K6">/</a> 4 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">th2</font> <a href="xcmplx_0.html#K7">/</a> 4 &amp; <font color="Maroon">th2</font> <a href="xcmplx_0.html#K7">/</a> 4 <a href="xxreal_0.html#R1">&lt;</a> 4 <a href="real_1.html#K6">/</a> 4 )
 
<b>by </b><i><a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/>
<b>hence </b><a NAME="E6:125_1_2_1"/>
<font color="Maroon">th2</font> <a href="xcmplx_0.html#K7">/</a> 4 <a href="hidden.html#R2">in</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="rcomp_1.html#T47">RCOMP_1:47</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:125_1_2"/><b>then </b>
<font color="Maroon">th1</font> <a href="xcmplx_0.html#K7">/</a> 4 <a href="hidden.html#R1">=</a> <font color="Maroon">th2</font> <a href="xcmplx_0.html#K7">/</a> 4
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:125_1_2"/>
<font color="Maroon">th1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">th2</font>
 ;<br/>


</div>
