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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:20"/>
<font color="Maroon" title="c1">i</font> <a href="idea_1.html#R1" title="IDEA_1:pred.1">is_expressible_by</a> <font color="Maroon" title="c2">n</font>
 ;<br/>

<b>then </b><i><font color="Green" title="E16">A1</font></i>: <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="idea_1.html#K5" title="IDEA_1:func.5">NEG_N</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">n</font></span>)</span> = 
<font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">i</font></span>)</span>
<b>by </b><i><a class="ref" href="idea_1.html#D5" target="_self" title="IDEA_1:def.5">Def5</a></i>
<br/>.= 
0 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c2">n</font></span>)</span>

;<br/>
<b>thus </b> <a href="idea_1.html#K4" title="IDEA_1:func.4">ADD_MOD</a> <font color="Maroon" title="c1">i</font>,<span class="p1">(<span class="default"><a href="idea_1.html#K6" title="IDEA_1:func.6">NEG_MOD</a> <font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">n</font></span>)</span>,<font color="Maroon" title="c2">n</font> = 
<span class="p1">(<span class="default">2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c2">n</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default">2 <a href="series_1.html#K3" title="SERIES_1:func.3">to_power</a> <font color="Maroon" title="c2">n</font></span>)</span>
<b>by </b><i><a class="txt" href="idea_1.html#E2:20"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="nat_d.html#T23" title="NAT_D:th.23">NAT_D:23</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="nat_d.html#T25" title="NAT_D:th.25">NAT_D:25</a></i>
;<br/>


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