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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  implies <font color="Maroon" title="c1">n</font> <a href="power.html#K1" title="POWER:func.1">-root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 )</span><br/>

<span class="kw">assume </span><a NAME="E1:9"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
<font color="Maroon" title="c1">n</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">n</font> <a href="power.html#K1" title="POWER:func.1">-root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span><br/>

<a NAME="E2:9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E8">A2</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#T12" onmouseover="rs('abian/T12')" onmouseout="rh()">ABIAN:12</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c1">n</font> <a href="power.html#K1" title="POWER:func.1">-root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> = 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E7">A1</font></span></a>, <a class="ref" href="power.html#D1" target="_self" onmouseover="rs('power/D1')" onmouseout="rh()">Def1</a></span>
<br/>.= 
 <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="ref" href="prepower.html#T20" onmouseover="rs('prepower/T20')" onmouseout="rh()">PREPOWER:20</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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