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<b>let </b><font color="Maroon" title="c1">a</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E29">A1</font></i>: 
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 &amp; <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 )
 ;<br/>

<a NAME="E2:35"/><b>then </b>
<font color="Maroon" title="c2">n</font> <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">n</font> <a href="prepower.html#K3" title="PREPOWER:func.3">-Root</a> 1
 
<b>by </b><i><a class="ref" href="prepower.html#T36" target="_self" title="PREPOWER:th.36">Th36</a></i>;<br/>
<b>hence </b><a NAME="E3:35"/>
<font color="Maroon" title="c2">n</font> <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1
 <b>by </b><i><a class="txt" href="prepower.html#E1:35"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="prepower.html#T29" target="_self" title="PREPOWER:th.29">Th29</a></i>;<br/>

<a NAME="E4:35"/>
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="txt" href="prepower.html#E1:35"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="prepower.html#T20" target="_self" title="PREPOWER:th.20">Th20</a></i>;<br/>
<a NAME="E5:35"/><b>then </b>
<font color="Maroon" title="c2">n</font> <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> <font color="Maroon" title="c2">n</font></span>)</span>
 
<b>by </b><i><a class="txt" href="prepower.html#E1:35"><i><font color="Green" title="E29">A1</font></i></a>, <a class="ref" href="prepower.html#T36" target="_self" title="PREPOWER:th.36">Th36</a></i>;<br/>
<b>hence </b><a NAME="E6:35"/>
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <font color="Maroon" title="c2">n</font> <a href="prepower.html#K2" title="PREPOWER:func.2">-Root</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="prepower.html#E1:35"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="prepower.html#E31"><i><font color="Green" title="E18">Lm2</font></i></a></i>;<br/>


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