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

<b>let </b><font color="Maroon" title="c1">y1</font>, <font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>





<b>assume </b><a NAME="E1:4"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c1">y1</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>  &amp; <font color="Maroon" title="c2">x1</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>  &amp; <font color="Maroon" title="c3">x2</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="4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:4_1"/>
( ( <font color="Maroon" title="c2">x1</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>  &amp; <font color="Maroon" title="c3">x2</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>  ) or ( <font color="Maroon" title="c2">x1</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>  &amp; <font color="Maroon" title="c3">x2</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="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">x2</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>  ) or ( <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )
 </span><b>by </b><i><a class="txt" href="lp_space.html#E1:4"><i><font color="Green" title="E5">A1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_1"><b>suppose </b></a><a NAME="E1:4_1_1"/>
( <font color="Maroon" title="c2">x1</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>  &amp; <font color="Maroon" title="c3">x2</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"><b>hence </b><a NAME="E2:4_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font></span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T35" title="POWER:th.35">POWER:35</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_2"><b>suppose </b></a><a NAME="E1:4_1_2"/><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c2">x1</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>  &amp; <font color="Maroon" title="c3">x2</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="E2:4_1_2"/><b>then </b>
<font color="Maroon" title="c3">x2</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="lp_space.html#E1:4"><i><font color="Green" title="E5">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="E3:4_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font></span>)</span>
 <b>by </b><i><a class="txt" href="lp_space.html#E1:4_1_2"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_3"><b>suppose </b></a><a NAME="E1:4_1_3"/><i><font color="Green" title="E6">A3</font></i>: 
( <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">x2</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"><a NAME="E2:4_1_3"/><b>then </b>
<font color="Maroon" title="c2">x1</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="lp_space.html#E1:4"><i><font color="Green" title="E5">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="E3:4_1_3"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font></span>)</span>
 <b>by </b><i><a class="txt" href="lp_space.html#E1:4_1_3"><i><font color="Green" title="E6">A3</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_4"><b>suppose </b></a><a NAME="E1:4_1_4"/><i><font color="Green" title="E6">A4</font></i>: 
( <font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c3">x2</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="E2:4_1_4"/><b>then </b>
<font color="Maroon" title="c3">x2</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="lp_space.html#E1:4"><i><font color="Green" title="E5">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="E3:4_1_4"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <font color="Maroon" title="c3">x2</font></span>)</span> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x2</font> <a href="power.html#K4" title="POWER:func.4">to_power</a> <font color="Maroon" title="c1">y1</font></span>)</span>
 <b>by </b><i><a class="txt" href="lp_space.html#E1:4_1_4"><i><font color="Green" title="E6">A4</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
