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<div class="add">

<b>let </b><font color="Maroon">a1</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>, <font color="Maroon">a2</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_1_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">a1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> <font color="Maroon">p</font>
 <b>and </b><br/><a NAME="E2:1_1_2"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">a2</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="seq_1.html#K2">.</a> <font color="Olive">n</font></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> <font color="Maroon">p</font>
 ;<br/>

<a NAME="E3:1_1_2"/>
for <font color="Olive">s</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">s</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">a1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> <a href="seq_1.html#K2">.</a> <font color="Olive">s</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:1_1_2_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/>

<font color="Maroon">a1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">s</font> = 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">s</font></span>)</span></span>)</span> <a href="power.html#K4">to_power</a> <font color="Maroon">p</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">a2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">s</font>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E3:1_1_2_1"/>
<font color="Maroon">a1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">s</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:1_1_2"/>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font>
 <b>by </b><i><a class="ref" href="seq_1.html#T8">SEQ_1:8</a></i>;<br/>


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