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<span class="kw">let </span><font color="Maroon" title="c1">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 implies <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">-root</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<span class="kw">assume </span><a NAME="E1:9"/><span class="lab"><font color="Green" title="E6">A1</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">-root</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<span class="kw">thus </span><font color="Maroon" title="c1">n</font> <a href="power.html#K2" title="POWER:func.2">-root</a> 1 = 
<font color="Maroon" title="c1">n</font> <a href="prepower.html#K3" title="PREPOWER:func.3">-Root</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="power.html#D1" target="_self" title="POWER:def.1">Def1</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E6">A1</font></span></a>, <a class="ref" href="prepower.html#T29" title="PREPOWER:th.29">PREPOWER:29</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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