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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="prepower.html#K6">#Z</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="power.html#D2">POWER:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="prepower.html#K6">#Z</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="prepower.html#K6">#Z</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T55">PREPOWER:55</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="prepower.html#K6">#Z</a> 1</span>)</span></span>)</span> <a href="prepower.html#K6">#Z</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T51">PREPOWER:51</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span></span>)</span> <a href="prepower.html#K6">#Z</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T45">PREPOWER:45</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T46">PREPOWER:46</a></i>
<br/>.= 
1 <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span>
<b>by </b><i><a class="ref" href="wsierp_1.html#T3">WSIERP_1:3</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="wsierp_1.html#K2">|^</a> 2</span>)</span> <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="newton.html#T14">NEWTON:14</a></i>
<br/>.= 
1 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="newton.html#T15">NEWTON:15</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="newton.html#T15">NEWTON:15</a></i>
;<br/>
<b>hence </b><a NAME="E2:11"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> 1</span>)</span> <a href="power.html#K3">to_power</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/>


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