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<b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">l</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:36"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">l</font> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span>
 ;<br/>

<i><font color="Green">E40</font></i>: <font color="Maroon">l</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">n</font></span>)</span> = 
<font color="Maroon">l</font> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3">to_power</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T101">NEWTON:101</a></i>
<br/>.= 
<font color="Maroon">m</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">n</font></span>)</span>
<b>by </b><i>, <a class="ref" href="newton.html#T101">NEWTON:101</a></i>
;<br/>
<a NAME="E3:36"/>
(  <a href="prepower.html#K1">abs</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> &amp;  <a href="prepower.html#K1">abs</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> )
 
<b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>
<a NAME="E4:36"/><b>then </b>
(  <a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">n</font>,<font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">l</font> &amp;  <a href="binari_4.html#K2" target="_self">2sComplement</a> <font color="Maroon">n</font>,<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">m</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:36"/>
<font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">l</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="binari_3.html#K1">-BinarySequence</a> <font color="Maroon">m</font>
 <b>by </b><i>, </i>;<br/>


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