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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="prepower.html#K4" title="PREPOWER:func.4">#Z</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
<b>by </b><i><a class="ref" href="power.html#D2" title="POWER:def.2">POWER:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="prepower.html#K4" title="PREPOWER:func.4">#Z</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
<b>by </b><i><a class="ref" href="prepower.html#T51" title="PREPOWER:th.51">PREPOWER:51</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="prepower.html#K4" title="PREPOWER:func.4">#Z</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> 2
<b>by </b><i><a class="ref" href="power.html#T53" title="POWER:th.53">POWER:53</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="prepower.html#K4" title="PREPOWER:func.4">#Z</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 2
<b>by </b><i><a class="ref" href="power.html#T46" title="POWER:th.46">POWER:46</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="prepower.html#K4" title="PREPOWER:func.4">#Z</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T14" title="PREPOWER:th.14">PREPOWER:14</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="prepower.html#K4" title="PREPOWER:func.4">#Z</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="prepower.html#K4" title="PREPOWER:func.4">#Z</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T46" title="PREPOWER:th.46">PREPOWER:46</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="prepower.html#K4" title="PREPOWER:func.4">#Z</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="nat_1.html#K3" title="NAT_1:func.3">*</a> 2</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T55" title="PREPOWER:th.55">PREPOWER:55</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prepower.html#T46" title="PREPOWER:th.46">PREPOWER:46</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">1 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="wsierp_1.html#T3" title="WSIERP_1:th.3">WSIERP_1:3</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2</span>)</span> <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T14" title="NEWTON:th.14">NEWTON:14</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">1 <a href="newton.html#K3" title="NEWTON:func.3">|^</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T15" title="NEWTON:th.15">NEWTON:15</a></i>
<br/>.= 
1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 1
<b>by </b><i><a class="ref" href="newton.html#T15" title="NEWTON:th.15">NEWTON:15</a></i>
;<br/>
<b>hence </b><a NAME="E2:9"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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