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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:104"/><i><font color="Green">E84</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] means ( <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> );<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>3</sub></font>[   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font>,   <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font>) <b>-&gt; </b>  <a href="real_1.html#NM1">Real</a> = <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font>) <b>-&gt; </b>  <a href="real_1.html#NM1">Real</a> = <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>) where B is    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span>  as   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  <b>from </b><i><a class="ref" href="complsp1.html#S1" target="_self">COMPLSP1:sch 1</a>();<br/></i>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>) where B is    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">S<sub>3</sub></font>[<font color="Olive">b<sub>1</sub></font>] </span>}</span>  as   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  <b>from </b><i><a class="ref" href="complsp1.html#S1" target="_self">COMPLSP1:sch 1</a>();<br/></i>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">{<span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) where B is    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font>, B is    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font> : <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] </span>}</span>  as   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a>  <b>from </b><i><a class="ref" href="complsp1.html#S2" target="_self">COMPLSP1:sch 2</a>();<br/></i>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:104"/><i><font color="Green">E85</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="complsp1.html#E1:104"><i><font color="Green">E84</font></i></a>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E8:104"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="complsp1.html#E1:104"><i><font color="Green">E84</font></i></a>, <a class="ref" href="subset_1.html#T10">SUBSET_1:10</a></i>;<br/>
<a NAME="E9:104"/>
( <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="complsp1.html#E6:104"><i><font color="Green">E85</font></i></a>, <a class="txt" href="complsp1.html#E8:104"><i><font color="Green">E86</font></i></a></i>;<br/>
<a NAME="E10:104"/><b>then </b><i><font color="Green">E87</font></i>: 
<span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="binop_2.html#K9">+</a> <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="complsp1.html#K21" target="_self">+</a> <font color="Maroon">c<sub>6</sub></font>
 
;<br/>
<a NAME="E11:104"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="seq_4.html#V2">bounded_below</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_1"><b>proof </b></a><div class="add">

<b>take </b>
0
; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_4.html#D2">SEQ_4:def 2</a><br/>

<b>let </b><font color="Maroon">c<sub>10</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:104_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<a NAME="E2:104_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Olive">b<sub>2</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E3:104_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="complsp1.html#T65" target="_self">Th65</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E12:104"/><i><font color="Green">E89</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="seq_4.html#V2">bounded_below</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_2"><b>proof </b></a><div class="add">

<a NAME="E1:104_2"/>
<span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="complsp1.html#E6:104"><i><font color="Green">E85</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:104_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>take </b>
0
; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_4.html#D2">SEQ_4:def 2</a><br/>

<b>let </b><font color="Maroon">c<sub>10</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E3:104_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E4:104_2"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E5:104_2"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="complsp1.html#T65" target="_self">Th65</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E13:104"/><i><font color="Green">E90</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="seq_4.html#V2">bounded_below</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_3"><b>proof </b></a><div class="add">

<a NAME="E1:104_3"/>
<span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="complsp1.html#E8:104"><i><font color="Green">E86</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:104_3"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>take </b>
0
; <i><font color="Red">:: according to </font></i><a class="ref" href="seq_4.html#D2">SEQ_4:def 2</a><br/>

<b>let </b><font color="Maroon">c<sub>10</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E3:104_3"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E4:104_3"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Olive">b<sub>1</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E5:104_3"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="ref" href="complsp1.html#T65" target="_self">Th65</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="104_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E1:104_4"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> <a href="complsp1.html#K21" target="_self">+</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:104_4"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="binop_2.html#K9">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> where B is   <a href="real_1.html#NM1">Real</a>, B is   <a href="real_1.html#NM1">Real</a> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:104_4"/><i><font color="Green">E91</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="binop_2.html#K9">+</a> <font color="Maroon">c<sub>12</sub></font>
 <b>and </b><br/><a NAME="E5:104_4"/><i><font color="Green">E92</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><b>consider </b><font color="Maroon">c<sub>13</sub></font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:104_4"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>13</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span>
 <b>and </b><br/><a NAME="E8:104_4"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="complsp1.html#E5:104_4"><i><font color="Green">E92</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>14</sub></font> being    <a href="finseq_2.html#M2">Element</a> of  <a href="complsp1.html#K8" target="_self">COMPLEX</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E10:104_4"/><i><font color="Green">E95</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="complsp1.html#E5:104_4"><i><font color="Green">E92</font></i></a></i>;<br/><b>take </b><font color="Maroon">c<sub>15</sub></font> = <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>14</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span>;<br/><a NAME="E11:104_4"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complsp1.html#K16" target="_self">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="complsp1.html#K13" target="_self">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="complsp1.html#K16" target="_self">.|</a></span>
 <b>by </b><i><a class="txt" href="complsp1.html#E7:104_4"><i><font color="Green">E93</font></i></a>, <a class="ref" href="complsp1.html#T74" target="_self">Th74</a></i>;<br/><b>hence </b><a NAME="E12:104_4"/>
( <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="complsp1.html#E4:104_4"><i><font color="Green">E91</font></i></a>, <a class="txt" href="complsp1.html#E8:104_4"><i><font color="Green">E94</font></i></a>, <a class="txt" href="complsp1.html#E10:104_4"><i><font color="Green">E95</font></i></a>, <a class="ref" href="complsp1.html#T75" target="_self">Th75</a></i>;<br/></div><b>end;</b></div>
<a NAME="E15:104"/><b>then </b><i><font color="Green">E91</font></i>: 
 <a href="seq_4.html#K5">lower_bound</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="complsp1.html#K21" target="_self">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="seq_4.html#K5">lower_bound</a> <font color="Maroon">c<sub>7</sub></font>
 
<b>by </b><i><a class="txt" href="complsp1.html#E10:104"><i><font color="Green">E87</font></i></a>, <a class="txt" href="complsp1.html#E11:104"><i><font color="Green">E88</font></i></a>, <a class="ref" href="complsp1.html#T97" target="_self">Th97</a></i>;<br/>
<a NAME="E16:104"/>
(  <a href="seq_4.html#K5">lower_bound</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K18" target="_self">dist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="seq_4.html#K5">lower_bound</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K18" target="_self">dist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="seq_4.html#K5">lower_bound</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="complsp1.html#K20" target="_self">dist</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="complsp1.html#D18" target="_self">Def18</a>, <a class="ref" href="complsp1.html#D20" target="_self">Def20</a></i>;<br/>
<b>hence </b><a NAME="E17:104"/>
<span class="p1">(<span class="default"><a href="complsp1.html#K18" target="_self">dist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="complsp1.html#K18" target="_self">dist</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="complsp1.html#K20" target="_self">dist</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="complsp1.html#E12:104"><i><font color="Green">E89</font></i></a>, <a class="txt" href="complsp1.html#E13:104"><i><font color="Green">E90</font></i></a>, <a class="txt" href="complsp1.html#E15:104"><i><font color="Green">E91</font></i></a>, <a class="ref" href="complsp1.html#T96" target="_self">Th96</a></i>;<br/>


</div>
