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<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>assume </b><a NAME="E1:34"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>assume </b><a NAME="E2:34"/><i><font color="Green">E25</font></i>: 
 <a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1
 ;<br/>

<font color="Maroon">x</font> = 
 <a href="power.html#K5">log</a> <a href="power.html#K8">number_e</a> ,<span class="p1">(<span class="default"><a href="sin_cos.html#K28">exp_R</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="taylor_1.html#T12">TAYLOR_1:12</a></i>
<br/>.= 
0
<b>by </b><i>, <a class="txt" href="sin_cos7.html#E21"><i><font color="Green">Lemma42</font></i></a>, <a class="ref" href="power.html#T59">POWER:59</a></i>
;<br/>
<b>hence </b><a NAME="E4:34"/>
contradiction
 <b>by </b><i><a class="ref" href="sin_cos7.html#T14" target="_self">Th14</a></i>;<br/>


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