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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <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="E1:37"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<i><font color="Green">E27</font></i>: <font color="Maroon">c<sub>2</sub></font> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T101">NEWTON:101</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font> <a href="int_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="binari_4.html#E1:37"><i><font color="Green">E26</font></i></a>, <a class="ref" href="newton.html#T101">NEWTON:101</a></i>
;<br/>
<a NAME="E3:37"/>
(  <a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="prepower.html#K1">abs</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<a NAME="E4:37"/><b>then </b>
(  <a href="binari_4.html#K2" target="_self">2sComplement</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> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="binari_4.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E5:37"/>
<font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="binari_4.html#E2:37"><i><font color="Green">E27</font></i></a>, <a class="txt" href="binari_4.html#E34"><i><font color="Green">Lemma23</font></i></a></i>;<br/>


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