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<b>let </b><font color="Maroon" title="c1">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="radix_1.html#K2" title="RADIX_1:func.2">-SD</a>  iff <font color="Maroon" title="c1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<a NAME="E1:11"/><i><font color="Green" title="E8">A1</font></i>: 
 <a href="radix_1.html#K1" title="RADIX_1:func.1">Radix</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <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/>
<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="radix_1.html#K2" title="RADIX_1:func.2">-SD</a>  )</span>
<div class="add"><b>assume </b><a NAME="E1:11_1"/>
<font color="Maroon" title="c1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="radix_1.html#K2" title="RADIX_1:func.2">-SD</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><b>then consider </b><font color="Maroon" title="c2">b</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> <b> such that </b><br/><a NAME="E3:11_1"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 <b>and </b><br/><a NAME="E4:11_1"/><i><font color="Green" title="E10">A3</font></i>: 
( <font color="Maroon" title="c2">b</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">b</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>  )
 <b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E8">A1</font></i></a></i>;<br/><b>thus </b><a NAME="E5:11_1"/>
<font color="Maroon" title="c1">e</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="#E3:11_1"><i><font color="Green" title="E9">A2</font></i></a>, <a class="txt" href="#E4:11_1"><i><font color="Green" title="E10">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:11"/><i><font color="Green" title="E9">A4</font></i>: 
<font color="Maroon" title="c1">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="radix_1.html#K2" title="RADIX_1:func.2">-SD</a> </span><br/>

<a NAME="E4:11"/><b>then </b>
<font color="Maroon" title="c1">e</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="mesfunc1.html#K2" title="MESFUNC1:func.2">INT</a> 
 
<b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:11"/>
<font color="Maroon" title="c1">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="radix_1.html#K2" title="RADIX_1:func.2">-SD</a> 
 <b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="#E3:11"><i><font color="Green" title="E9">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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