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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">a1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">a2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">a1</font> <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> &amp; <font color="Maroon">a2</font> <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> &amp;  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">a1</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">a2</font>,<font color="Maroon">n</font> )
 ;<br/>

<a NAME="E2:27"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:27"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">a2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font>
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:27_1"/>
(  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">a1</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font> or  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">a1</font>,<font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_1"><b>suppose </b></a><a NAME="E1:27_1_1"/><i><font color="Green">E39</font></i>: 
 <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">a1</font>,<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">a2</font> = 
0
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">a1</font>
<b>by </b><i>, , </i>
;<br/><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="27_1_2"><b>suppose </b></a><a NAME="E1:27_1_2"/><i><font color="Green">E40</font></i>: 
 <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">a1</font>,<font color="Maroon">n</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font>
 ;<br/><div class="add"><a NAME="E2:27_1_2"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i/>;<br/><a NAME="E3:27_1_2"/>
<font color="Maroon">a2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i>, , </i>;<br/><b>hence </b><font color="Maroon">a2</font> = 
 <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">a1</font>,<font color="Maroon">n</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">a1</font>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

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