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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">zero</a> <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><a NAME="E1:48"/><i><font color="Green">E34</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:48"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<b>thus </b><a NAME="E3:48"/>
(  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:48_1"/><i><font color="Green">E36</font></i>: 
 <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>assume </b><a NAME="E2:48_1"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>,  <a href="real_1.html#NM1">Real</a>] means ( <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a<sub>2</sub></font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">a<sub>2</sub></font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">a<sub>1</sub></font> );<br/>
<a NAME="E3:48_1"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:48_1_1_1"/>
( ( <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> ) or ( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> ) or <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_1"><b>suppose </b></a><a NAME="E1:48_1_1_1_1"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div class="add"><a NAME="E2:48_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="chain_1.html#E2:48"><i><font color="Green">E35</font></i></a></i>;<br/><b>then 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="E4:48_1_1_1_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="chain_1.html#T1" target="_self">Th1</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/><b>thus </b><a NAME="E5:48_1_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>]
 <b>by </b><i><a class="txt" href="chain_1.html#E1:48_1_1_1_1"><i><font color="Green">E39</font></i></a>, <a class="txt" href="chain_1.html#E4:48_1_1_1_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_2"><b>suppose </b></a><a NAME="E1:48_1_1_1_2"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div class="add"><b>take </b>
<font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>
;<br/><b>thus </b><a NAME="E2:48_1_1_1_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>]
 <b>by </b><i><a class="txt" href="chain_1.html#E1:48"><i><font color="Green">E34</font></i></a>, <a class="txt" href="chain_1.html#E2:48_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="chain_1.html#E1:48_1_1_1_2"><i><font color="Green">E39</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="48_1_1_1_3"><b>suppose </b></a><a NAME="E1:48_1_1_1_3"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><b>take </b>
<font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>
;<br/><b>thus </b><a NAME="E2:48_1_1_1_3"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>]
 <b>by </b><i><a class="txt" href="chain_1.html#E1:48"><i><font color="Green">E34</font></i></a>, <a class="txt" href="chain_1.html#E2:48_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="chain_1.html#E1:48_1_1_1_3"><i><font color="Green">E39</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K1">REAL</a> <b> such that </b><br/><a NAME="E5:48_1"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S3">FUNCT_2:sch 3</a>(<a class="txt" href="chain_1.html#E3:48_1"><i><font color="Green">E38</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="chain_1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E7:48_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="chain_1.html#E5:48_1"><i><font color="Green">E39</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E9:48_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="txt" href="chain_1.html#E2:48"><i><font color="Green">E35</font></i></a></i>;<br/>
<a NAME="E10:48_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> &amp; ( <font color="Maroon">c<sub>7</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<b>by </b><i><a class="txt" href="chain_1.html#E1:48_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="chain_1.html#E7:48_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="chain_1.html#T26" target="_self">Th26</a></i>;<br/>
<b>hence </b><a NAME="E11:48_1"/>
contradiction
 <b>by </b><i><a class="txt" href="chain_1.html#E5:48_1"><i><font color="Green">E39</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>given </b><font color="Maroon">c<sub>6</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E4:48"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E5:48"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="finseq_2.html#M2">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E7:48"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="chain_1.html#E1:48"><i><font color="Green">E34</font></i></a>, <a class="txt" href="chain_1.html#E5:48"><i><font color="Green">E37</font></i></a>, <a class="ref" href="chain_1.html#T25" target="_self">Th25</a></i>;<br/>
<a NAME="E8:48"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> &amp; ( <font color="Maroon">c<sub>8</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_2"><b>proof </b></a><div class="add">

<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E1:48_2"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( <font color="Maroon">c<sub>8</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>5</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> <a href="chain_1.html#K2" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> ) )
 <b>by </b><i><a class="txt" href="chain_1.html#E2:48"><i><font color="Green">E35</font></i></a>, <a class="txt" href="chain_1.html#E4:48"><i><font color="Green">E36</font></i></a>, <a class="txt" href="chain_1.html#E7:48"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:48"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="chain_1.html#K4" target="_self">cell</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>


</div>
