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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="E1:63"/><i><font color="Green" title="E39">A1</font></i>: 
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp; <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0 &amp; <font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c2">b</font> )
 <b>and </b><br/><a NAME="E2:63"/><i><font color="Green" title="E40">A2</font></i>: 
 <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>
 ;<br/>

<a NAME="E3:63"/><i><font color="Green" title="E41">A3</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="txt" href="power.html#E1:63"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="power.html#D3" target="_self" title="POWER:def.3">Def3</a></i>;<br/>
<a NAME="E4:63"/><i><font color="Green" title="E42">A4</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="power.html#K3" title="POWER:func.3">to_power</a> <span class="p1">(<span class="default"><a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font>
 
<b>by </b><i><a class="txt" href="power.html#E1:63"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="power.html#D3" target="_self" title="POWER:def.3">Def3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:63_1_1"/>
(  <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> or  <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> )
 </span><b>by </b><i><a class="txt" href="power.html#E2:63"><i><font color="Green" title="E40">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="63_1_1_1"><b>suppose </b></a><a NAME="E1:63_1_1_1"/>
 <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a>  <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:63_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="power.html#E1:63"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="power.html#E3:63"><i><font color="Green" title="E41">A3</font></i></a>, <a class="txt" href="power.html#E4:63"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="power.html#T44" target="_self" title="POWER:th.44">Th44</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="63_1_1_2"><b>suppose </b></a><a NAME="E1:63_1_1_2"/>
 <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="power.html#K5" title="POWER:func.5">log</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:63_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="power.html#E1:63"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="power.html#E4:63"><i><font color="Green" title="E42">A4</font></i></a>, <a class="ref" href="power.html#D3" target="_self" title="POWER:def.3">Def3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E6:63"/>
contradiction
 ;<br/>


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