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

<b>let </b><font color="Maroon" title="c1">th</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>

<b>thus </b><span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="sin_cos.html#K18" title="SIN_COS:func.18">exp</a> <span class="p3"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">th</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span> = 
<span class="p1"><a href="complex1.html#K17" title="COMPLEX1:func.17">|.</a><span class="default"><span class="p2">(<span class="default"><a href="comseq_3.html#K8" title="COMSEQ_3:func.8">Sum</a> <span class="p3">(<span class="default"><span class="p4"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c1">th</font></span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span> <a href="sin_cos.html#K6" title="SIN_COS:func.6">ExpSeq</a> </span>)</span></span>)</span></span><a href="complex1.html#K17" title="COMPLEX1:func.17">.|</a></span>
<b>by </b><i><a class="ref" href="sin_cos.html#D18" target="_self" title="SIN_COS:def.18">Def18</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="sin_cos.html#E57"><i><font color="Green" title="E43">Lm5</font></i></a></i>
;<br/>

<b>let </b><font color="Maroon" title="c2">th</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<a NAME="E2:61"/><i><font color="Green" title="E44">A1</font></i>: 
<font color="Maroon" title="c2">th</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 
<b>by </b><i><a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:61"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K20" title="SIN_COS:func.20">sin</a> <font color="Maroon" title="c2">th</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="sin_cos.html#E57"><i><font color="Green" title="E43">Lm5</font></i></a></i>;<br/>

<b>thus </b><a NAME="E4:61"/>
 <a href="complex1.html#K18" title="COMPLEX1:func.18">abs</a> <span class="p1">(<span class="default"><a href="sin_cos.html#K23" title="SIN_COS:func.23">cos</a> <font color="Maroon" title="c2">th</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="sin_cos.html#E2:61"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="sin_cos.html#E57"><i><font color="Green" title="E43">Lm5</font></i></a></i>;<br/>


</div>
