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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="binarith.html#NM1">Tuple</a> of 1,<a href="margrel1.html#K6">BOOLEAN</a> ;<br/>

<b>assume </b><a NAME="E1:41"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><a href="margrel1.html#K8">TRUE</a> </span><a href="finseq_1.html#K12">*&gt;</a></span>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:41"/><i><font color="Green">E28</font></i>: 
 <a href="binarith.html#K8" target="_self">Binary</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="finseq_2.html#T117">FINSEQ_2:117</a></i>;<br/>
<a NAME="E4:41"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="margrel1.html#K7">FALSE</a> 
 
<b>by </b><i><a class="txt" href="binarith.html#E1:41"><i><font color="Green">E27</font></i></a>, <a class="ref" href="finseq_4.html#T25">FINSEQ_4:25</a></i>;<br/>
<a NAME="E5:41"/>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 1
 
;<br/>
<b>then </b><i><font color="Green">E30</font></i>: <span class="p1">(<span class="default"><a href="binarith.html#K8" target="_self">Binary</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 = 
 <a href="cqc_lang.html#K2">IFEQ</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="finseq_4.html#K4">/.</a> 1</span>)</span>,<a href="margrel1.html#K7">FALSE</a> ,0,<span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p2">(<span class="default">1 <a href="binarith.html#K5" target="_self">-'</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#D6" target="_self">Def6</a></i>
<br/>.= 
2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default">1 <a href="binarith.html#K5" target="_self">-'</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="binarith.html#E4:41"><i><font color="Green">E29</font></i></a>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>
;<br/>
<a NAME="E7:41"/><i><font color="Green">E31</font></i>: 
1 <a href="binop_2.html#K10">-</a> 1 <a href="hidden.html#R1">=</a> 0
 
;<br/>
<b>thus </b> <a href="binarith.html#K9" target="_self">Absval</a> <font color="Maroon">c<sub>1</sub></font> = 
<a href="binop_2.html#K47">addnat</a>  <a href="finsop_1.html#K2">$$</a> <span class="p1">(<span class="default"><a href="binarith.html#K8" target="_self">Binary</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<br/>.= 
<a href="binop_2.html#K47">addnat</a>  <a href="finsop_1.html#K2">$$</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <span class="p3">(<span class="default">1 <a href="binarith.html#K5" target="_self">-'</a> 1</span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span>
<b>by </b><i><a class="txt" href="binarith.html#E3:41"><i><font color="Green">E28</font></i></a>, <a class="txt" href="binarith.html#E6:41"><i><font color="Green">E30</font></i></a>, <a class="ref" href="finseq_4.html#T25">FINSEQ_4:25</a></i>
<br/>.= 
2 <a href="series_1.html#K3">to_power</a> <span class="p1">(<span class="default">1 <a href="binarith.html#K5" target="_self">-'</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="finsop_1.html#T12">FINSOP_1:12</a></i>
<br/>.= 
2 <a href="series_1.html#K3">to_power</a> 0
<b>by </b><i><a class="txt" href="binarith.html#E7:41"><i><font color="Green">E31</font></i></a>, <a class="ref" href="binarith.html#D3" target="_self">Def3</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="power.html#T29">POWER:29</a></i>
;<br/>


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