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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</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>assume </b><b>that </b><br/><a NAME="E1:16"/><i><font color="Green" title="E11">A1</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">a</font>
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green" title="E12">A2</font></i>: 
<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">b</font>
 <b>and </b><br/><a NAME="E3:16"/><i><font color="Green" title="E13">A3</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_1"/>
( <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span><b>by </b><i><a class="txt" href="asympt_1.html#E3:16"><i><font color="Green" title="E13">A3</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1"><b>suppose </b></a><a NAME="E1:16_1_1"/>
<font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:16_1_1"/><b>then </b>
( <font color="Maroon" title="c1">a</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="ref" href="power.html#T29" title="POWER:th.29">POWER:29</a></i>;<br/><b>hence </b><a NAME="E3:16_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_2"><b>suppose </b></a><a NAME="E1:16_1_2"/><i><font color="Green" title="E14">A4</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_1_2_1"/>
( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> or <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">b</font> )
 </span><b>by </b><i><a class="txt" href="asympt_1.html#E2:16"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="real_1.html#D5" title="REAL_1:def.5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_2_1_1"><b>suppose </b></a><a NAME="E1:16_1_2_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:16_1_2_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_2_1_2"><b>suppose </b></a><a NAME="E1:16_1_2_1_2"/>
<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">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:16_1_2_1_2"/>
<font color="Maroon" title="c1">a</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <font color="Maroon" title="c3">c</font>
 <b>by </b><i><a class="txt" href="asympt_1.html#E1:16"><i><font color="Green" title="E11">A1</font></i></a>, <a class="txt" href="asympt_1.html#E1:16_1_2"><i><font color="Green" title="E14">A4</font></i></a>, <a class="ref" href="power.html#T42" title="POWER:th.42">POWER:42</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>

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