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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<a NAME="E1:13"/><i><font color="Green">E13</font></i>: 
 <a href="sin_cos.html#K29">exp_R</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="sin_cos.html#T60">SIN_COS:60</a></i>;<br/>
<b>thus </b> <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="sin_cos.html#K28">exp_R</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K3">*</a> 1</span>)</span>

<br/>.= 
<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">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="taylor_1.html#T8" target="_self">Th8</a></i>
;<br/>

<b>hence </b><a NAME="E3:13"/>
( <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">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">c<sub>1</sub></font> &amp; <a href="power.html#K8">number_e</a>  <a href="power.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">c<sub>1</sub></font> &amp; <a href="power.html#K8">number_e</a>  <a href="prepower.html#K12">#R</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="taylor_1.html#E1:13"><i><font color="Green">E13</font></i></a>, <a class="ref" href="irrat_1.html#D7">IRRAT_1:def 7</a>, <a class="ref" href="power.html#D2">POWER:def 2</a></i>;<br/>


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