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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:27"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="idea_1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E3:27"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E1:27"><i><font color="Green">E22</font></i></a>, <a class="ref" href="idea_1.html#D3" target="_self">Def3</a></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font> or  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></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">E25</font></i>: 
 <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><b>hence </b><font color="Maroon">c<sub>3</sub></font> = 
0
<b>by </b><i><a class="txt" href="idea_1.html#E1:27"><i><font color="Green">E22</font></i></a>, <a class="txt" href="idea_1.html#E3:27"><i><font color="Green">E24</font></i></a>, <a class="ref" href="idea_1.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E2:27"><i><font color="Green">E23</font></i></a>, <a class="txt" href="idea_1.html#E1:27_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="idea_1.html#D7" target="_self">Def7</a></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">E25</font></i>: 
 <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:27_1_2"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="ref" href="idea_1.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E3:27_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="idea_1.html#E1:27"><i><font color="Green">E22</font></i></a>, <a class="txt" href="idea_1.html#E1:27_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="idea_1.html#D7" target="_self">Def7</a></i>;<br/><b>hence </b><font color="Maroon">c<sub>3</sub></font> = 
 <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E1:27"><i><font color="Green">E22</font></i></a>, <a class="ref" href="idea_1.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="idea_1.html#E2:27_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="idea_1.html#D7" target="_self">Def7</a></i>
;<br/><br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
