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

<b>let </b><font color="Maroon">A</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="supinf_1.html#K3">REAL</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:42_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">A</font> is   <a href="measure5.html#NM1">Interval</a>
 ;<br/><a NAME="E2:42_1"/><b>then </b>
( <font color="Maroon">A</font> is <a href="measure5.html#V1">open_interval</a> or <font color="Maroon">A</font> is <a href="measure5.html#V2">closed_interval</a> or <font color="Maroon">A</font> is <a href="measure5.html#V3">right_open_interval</a> or <font color="Maroon">A</font> is <a href="measure5.html#V4">left_open_interval</a> )
 <b>by </b><i><a class="ref" href="measure5.html#D9">MEASURE5:def 9</a></i>;<br/><a NAME="E3:42_1"/><b>then </b>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="measure5.html#K2">.[</a></span> ) or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1">[.</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="measure5.html#K1">.]</a></span> ) or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4">[.</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="measure5.html#K4">.[</a></span> ) or  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="supinf_1.html#NM3">R_eal</a> st <br/>( <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3">].</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="measure5.html#K3">.]</a></span> ) )
 <b>by </b><i><a class="ref" href="measure5.html#D5">MEASURE5:def 5</a>, <a class="ref" href="measure5.html#D6">MEASURE5:def 6</a>, <a class="ref" href="measure5.html#D7">MEASURE5:def 7</a>, <a class="ref" href="measure5.html#D8">MEASURE5:def 8</a></i>;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="supinf_1.html#NM3">R_eal</a>, <font color="Maroon">b</font> being   <a href="supinf_1.html#NM3">R_eal</a><b> such that </b><br/><a NAME="E5:42_1"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K2">.[</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K1">.]</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K4">.[</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K3">.]</a></span> )
 ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">G</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E6:42_1"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">F</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">G</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><b>let </b><font color="Maroon">c</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E7:42_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">F</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">G</font> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_1_1_1"/>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K2">.[</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K1">.]</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K3">.]</a></span> or <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K4">.[</a></span> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_1"><b>case </b></a><a NAME="E1:42_1_1_1_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K2">.[</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:42_1_1_1_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="measure6.html#T10" target="_self">Th10</a>, , <a class="txt" href="measure6.html#E3:42"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_2"><b>case </b></a><a NAME="E1:42_1_1_1_2"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K1">.]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:42_1_1_1_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="measure6.html#T10" target="_self">Th10</a>, , <a class="txt" href="measure6.html#E3:42"><i><font color="Green">E33</font></i></a>, <a class="txt" href="measure6.html#E6:42_1"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_3"><b>case </b></a><a NAME="E1:42_1_1_1_3"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3">].</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K3">.]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:42_1_1_1_3"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="measure6.html#T10" target="_self">Th10</a>, , <a class="txt" href="measure6.html#E3:42"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_1_1_1_4"><b>case </b></a><a NAME="E1:42_1_1_1_4"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="measure5.html#K4">.[</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:42_1_1_1_4"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="measure6.html#T10" target="_self">Th10</a>, , <a class="txt" href="measure6.html#E3:42"><i><font color="Green">E33</font></i></a>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E9:42_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:42"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/>for <font color="Olive">c</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">c</font> &amp; <font color="Olive">c</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b</font> holds <br/><font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>assume </b><a NAME="E3:42"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">A</font> is  not   <a href="measure5.html#NM1">Interval</a>
 ;<br/>

<a NAME="E4:42"/><b>then </b><i><font color="Green">E34</font></i>: 
( not <font color="Maroon">A</font> is <a href="measure5.html#V1">open_interval</a> &amp; not <font color="Maroon">A</font> is <a href="measure5.html#V2">closed_interval</a> &amp; not <font color="Maroon">A</font> is <a href="measure5.html#V3">right_open_interval</a> &amp; not <font color="Maroon">A</font> is <a href="measure5.html#V4">left_open_interval</a> )
 
<b>by </b><i><a class="ref" href="measure5.html#D9">MEASURE5:def 9</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_2"/>
( <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="measure5.html#K6">{}</a>  or <font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="measure5.html#K6">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_1"><b>suppose </b></a><a NAME="E1:42_2_1"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="measure5.html#K6">{}</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:42_2_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_2"><b>suppose </b></a><a NAME="E1:42_2_2"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="measure5.html#K6">{}</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a>  <b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>set </b><font color="Maroon">m</font> =  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font>;<br/><b>set </b><font color="Maroon">M</font> =  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font>;<br/><b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:42_2_2"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="supinf_1.html#NM3">R_eal</a> <b>by </b><i><a class="txt" href="measure6.html#E3:42"><i><font color="Green">E33</font></i></a></i>;<br/><a NAME="E6:42_2_2"/>
(  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="txt" href="measure6.html#E3:42"><i><font color="Green">E33</font></i></a>, <a class="ref" href="supinf_1.html#T76">SUPINF_1:76</a>, <a class="ref" href="supinf_1.html#T79">SUPINF_1:79</a></i>;<br/><a NAME="E7:42_2_2"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="supinf_1.html#T29">SUPINF_1:29</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:42_2_2_1_1"/>
( (  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp;  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> ) or (  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> ) or ( not  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp;  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> ) or ( not  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_2_1_1_1"><b>case </b></a><a NAME="E1:42_2_2_1_1_1"/>
(  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp;  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><div class="add"><a NAME="E2:42_2_2_1_1_1"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font></span>)</span></span><a href="measure5.html#K1">.]</a></span>
 <b>by </b><i><a class="ref" href="measure6.html#T10" target="_self">Th10</a>, <a class="txt" href="measure6.html#E2:42"><i><font color="Green">E26</font></i></a></i>;<br/><b>hence </b><a NAME="E3:42_2_2_1_1_1"/>
contradiction
 <b>by </b><i>, <a class="txt" href="measure6.html#E4:42"><i><font color="Green">E34</font></i></a>, <a class="ref" href="measure5.html#D6">MEASURE5:def 6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_2_1_1_2"><b>case </b></a><a NAME="E1:42_2_2_1_1_2"/>
(  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><div class="add"><a NAME="E2:42_2_2_1_1_2"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4">[.</a><span class="default"><span class="p2">(<span class="default"><a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font></span>)</span></span><a href="measure5.html#K4">.[</a></span>
 <b>by </b><i><a class="ref" href="measure6.html#T10" target="_self">Th10</a>, <a class="ref" href="measure6.html#T8" target="_self">Th8</a></i>;<br/><b>hence </b><a NAME="E3:42_2_2_1_1_2"/>
contradiction
 <b>by </b><i>, <a class="txt" href="measure6.html#E4:42"><i><font color="Green">E34</font></i></a>, <a class="ref" href="measure5.html#D7">MEASURE5:def 7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_2_1_1_3"><b>case </b></a><a NAME="E1:42_2_2_1_1_3"/>
( not  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp;  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><div class="add"><a NAME="E2:42_2_2_1_1_3"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3">].</a><span class="default"><span class="p2">(<span class="default"><a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font></span>)</span></span><a href="measure5.html#K3">.]</a></span>
 <b>by </b><i><a class="ref" href="measure6.html#T10" target="_self">Th10</a>, </i>;<br/><b>hence </b><a NAME="E3:42_2_2_1_1_3"/>
contradiction
 <b>by </b><i>, <a class="txt" href="measure6.html#E4:42"><i><font color="Green">E34</font></i></a>, <a class="ref" href="measure5.html#D8">MEASURE5:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="42_2_2_1_1_4"><b>case </b></a><a NAME="E1:42_2_2_1_1_4"/>
( not  <a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; not  <a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> )
 ;<br/><div class="add"><a NAME="E2:42_2_2_1_1_4"/><b>then </b>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2">].</a><span class="default"><span class="p2">(<span class="default"><a href="supinf_1.html#K7">inf</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="supinf_1.html#K6">sup</a> <font color="Maroon">A</font></span>)</span></span><a href="measure5.html#K2">.[</a></span>
 <b>by </b><i><a class="ref" href="measure6.html#T10" target="_self">Th10</a>, </i>;<br/><b>hence </b><a NAME="E3:42_2_2_1_1_4"/>
contradiction
 <b>by </b><i>, <a class="txt" href="measure6.html#E4:42"><i><font color="Green">E34</font></i></a>, <a class="ref" href="measure5.html#D5">MEASURE5:def 5</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E9:42_2_2"/>
contradiction
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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