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

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

<b>thus </b><span class="p1">(<span class="default"><a href="sin_cos.html#K27">exp_R</a>  <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="prepower.html#K12">#R</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="sin_cos.html#K29">exp_R</a> 1</span>)</span> <a href="prepower.html#K12">#R</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="sin_cos.html#D27">SIN_COS:def 27</a></i>
<br/>.= 
 <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<a href="sin_cos.html#K27">exp_R</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="sin_cos.html#D27">SIN_COS:def 27</a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="sin_cos.html#K27">exp_R</a>  <a href="seq_1.html#K2">.</a> 1</span>)</span> <a href="power.html#K3">to_power</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><a href="sin_cos.html#K29">exp_R</a> 1</span>)</span> <a href="power.html#K3">to_power</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="sin_cos.html#D27">SIN_COS:def 27</a></i>
<br/>.= 
 <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<a href="sin_cos.html#K27">exp_R</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="sin_cos.html#D27">SIN_COS:def 27</a></i>
;<br/>

<b>thus </b><a href="power.html#K8">number_e</a>  <a href="power.html#K3">to_power</a> <font color="Maroon">x</font> = 
 <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<a href="sin_cos.html#K27">exp_R</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="sin_cos.html#D27">SIN_COS:def 27</a></i>
;<br/>

<b>thus </b><a href="power.html#K8">number_e</a>  <a href="prepower.html#K12">#R</a> <font color="Maroon">x</font> = 
 <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">x</font>
<b>by </b><i/>
<br/>.= 
<a href="sin_cos.html#K27">exp_R</a>  <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="sin_cos.html#D27">SIN_COS:def 27</a></i>
;<br/>


</div>
