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



<b>assume </b><a NAME="E1:26"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:26"/><i><font color="Green">E22</font></i>: 
2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="power.html#T39">POWER:39</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:26_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_1"><b>suppose </b></a><a NAME="E1:26_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:26_1_1"/>
(  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="idea_1.html#E2:26"><i><font color="Green">E22</font></i></a>, <a class="ref" href="idea_1.html#D7" target="_self">Def7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="26_1_2"><b>suppose </b></a><a NAME="E1:26_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:26_1_2"/><b>then </b>
 <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="idea_1.html#D7" target="_self">Def7</a></i>;<br/><b>hence </b><a NAME="E3:26_1_2"/>
(  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="idea_1.html#K7" target="_self">ChangeVal_1</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="idea_1.html#E1:26"><i><font color="Green">E21</font></i></a>, <a class="txt" href="idea_1.html#E1:26_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="idea_1.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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