<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">p</font>, <font color="Maroon" title="c2">q</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>

<b>assume </b><a NAME="E1:3"/><i><font color="Green" title="E1">A1</font></i>: 
( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">p</font> &amp; 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c2">q</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c3">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>

<b>assume </b><a NAME="E2:3"/><i><font color="Green" title="E2">A2</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">a</font>
 ;<br/>

<a NAME="E3:3"/><i><font color="Green" title="E3">A3</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">p</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c2">q</font>
 
<b>by </b><i><a class="txt" href="holder_1.html#E1:3"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="real_2.html#T122" title="REAL_2:th.122">REAL_2:122</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:3_1_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1"><b>case </b></a><a NAME="E1:3_1_1_1"/><i><font color="Green" title="E4">A4</font></i>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">q</font> = 
0 <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">q</font>
<b>by </b><i><a class="txt" href="holder_1.html#E1:3"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="power.html#D2" title="POWER:def.2">POWER:def 2</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="holder_1.html#E1:3"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="power.html#D2" title="POWER:def.2">POWER:def 2</a></i>
;<br/><b>hence </b><a NAME="E3:3_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c2">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E3:3"><i><font color="Green" title="E3">A3</font></i></a>, <a class="txt" href="holder_1.html#E1:3_1_1_1"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="power.html#D2" title="POWER:def.2">POWER:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_2"><b>case </b></a><a NAME="E1:3_1_1_2"/>
<font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:3_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c2">q</font></span>)</span>
 <b>by </b><i><a class="txt" href="holder_1.html#E2:3"><i><font color="Green" title="E2">A2</font></i></a>, <a class="ref" href="power.html#T38" title="POWER:th.38">POWER:38</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E5:3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c2">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">p</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c2">q</font></span>)</span>
 ;<br/>


</div>
