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<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be  <a href="integra1.html#V1" target="_self">closed-interval</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:20_1_2_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E2:20_1_2_1"/><i><font color="Green">E14</font></i>: 
(  <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E3:20_1_2_1"/><i><font color="Green">E15</font></i>: 
(  <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E5:20_1_2_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E6:20_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K3">inf</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font></span><a href="rcomp_1.html#K1">.]</a></span>
 <b>by </b><i><a class="txt" href="integra1.html#E2:20_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="integra1.html#E5:20_1_2_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="integra1.html#T5" target="_self">Th5</a></i>;<br/><b>hence </b><a NAME="E7:20_1_2_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="integra1.html#E3:20_1_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="integra1.html#E5:20_1_2_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="integra1.html#T5" target="_self">Th5</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><b>that </b><br/><a NAME="E2:20_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E3:20_1_2"/><i><font color="Green">E14</font></i>: 
(  <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> 1</span>)</span> &amp;  <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E4:20_1_2"/><i><font color="Green">E15</font></i>: 
(  <a href="pscomp_1.html#K3">inf</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> 1</span>)</span> &amp;  <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E6:20_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K10">-</a> 1</span>)</span>
 <b>and </b><br/><a NAME="E7:20_1_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="goboard1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>
<a NAME="E8:20_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="rcomp_1.html#K1">.]</a></span>
 
<b>by </b><i><a class="txt" href="integra1.html#E3:20_1_2"><i><font color="Green">E14</font></i></a>, <a class="txt" href="integra1.html#E6:20_1_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="integra1.html#E7:20_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="integra1.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E9:20_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="integra1.html#E4:20_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="integra1.html#E6:20_1_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="integra1.html#E7:20_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="integra1.html#T5" target="_self">Th5</a></i>;<br/>


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