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

<b>let </b><font color="Maroon" title="c1">r</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="E4">A1</font></i>: 
<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 ;<br/>

<a NAME="E2:3"/><b>then </b>
<font color="Maroon" title="c1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">g</font> where <font color="Olive" title="b1">g</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> : 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Olive" title="b1">g</font> </span>}</span> 
 
;<br/>
<a NAME="E3:3"/><b>then </b>
<font color="Maroon" title="c1">r</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="limfunc1.html#K4" title="LIMFUNC1:func.4">right_open_halfline</a> 0
 
<b>by </b><i><a class="ref" href="limfunc1.html#T152" title="LIMFUNC1:th.152">LIMFUNC1:152</a></i>;<br/>
<a NAME="E4:3"/><b>then </b>
 <a href="power.html#K6" title="POWER:func.6">log</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> ,<font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="taylor_1.html#K2" title="TAYLOR_1:func.2">log_</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> </span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c1">r</font>
 
<b>by </b><i><a class="ref" href="taylor_1.html#D2" title="TAYLOR_1:def.2">TAYLOR_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:3"/>
(  <a href="power.html#K6" title="POWER:func.6">log</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> ,<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">r</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 &amp; ( <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies  <a href="power.html#K6" title="POWER:func.6">log</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> ,<font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 ) &amp; (  <a href="power.html#K6" title="POWER:func.6">log</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> ,<font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">r</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 implies <font color="Maroon" title="c1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) &amp; ( <font color="Maroon" title="c1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 implies  <a href="power.html#K6" title="POWER:func.6">log</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> ,<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">r</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 ) &amp; (  <a href="power.html#K6" title="POWER:func.6">log</a> <a href="power.html#K8" title="POWER:func.8">number_e</a> ,<font color="Maroon" title="c1">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;</a> <font color="Maroon" title="c1">r</font> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 implies <font color="Maroon" title="c1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 ) )
 <b>by </b><i><a class="txt" href="entropy1.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="entropy1.html#T2" target="_self" title="ENTROPY1:th.2">Th2</a></i>;<br/>


</div>
