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

<b>set </b><font color="Maroon">c<sub>5</sub></font> = the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font>;<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 ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> &amp; ex <font color="Olive">b<sub>3</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>3</sub></font> ) );<br/>
<a NAME="E1:20_1_1"/><i><font color="Green">E14</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] holds <br/><font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<a NAME="E2:20_1_1"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>] holds <br/><font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:20_1_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:20_1_1_1"/><i><font color="Green">E17</font></i>: 
<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>and </b><br/><a NAME="E3:20_1_1_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>]
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="projred1.html#E2:20_1_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projred1.html#E3:20_1_1_1"><i><font color="Green">E18</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="projred1.html#E1:20_1_1_1"><i><font color="Green">E16</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being    <a href="subset_1.html#M1">Element</a> of the <a href="incsp_1.html#U2">Lines</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E7:20_1_1_1"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E2:20_1_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E8:20_1_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:20"><i><font color="Green">E13</font></i></a>, <a class="txt" href="projred1.html#E3:20_1_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="projred1.html#E7:20_1_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E9:20_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:20"><i><font color="Green">E13</font></i></a>, <a class="txt" href="projred1.html#E2:20_1_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projred1.html#E3:20_1_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="projred1.html#E7:20_1_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="partfun1.html#NM1">PartFunc</a> of the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:20_1_1"/><i><font color="Green">E16</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> iff ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font> &amp; ex <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</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>] ) )
 <b>and </b><br/><a NAME="E5:20_1_1"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> holds <br/><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_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="partfun1.html#S2">PARTFUN1:sch 2</a>(<a class="txt" href="projred1.html#E1:20_1_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="projred1.html#E2:20_1_1"><i><font color="Green">E15</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E6:20_1_1"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>thus </b><a NAME="E7:20_1_1"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> iff <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>2</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E1:20_1_1_2"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> implies <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_2_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>

<a NAME="E2:20_1_1_2_1"/><b>then </b>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>]
 
<b>by </b><i><a class="txt" href="projred1.html#E5:20_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:20_1_1_2_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:20_1_1_2"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_2_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:20_1_1_2_2"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/>
<a NAME="E4:20_1_1_2_2"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="incproj.html#D14">INCPROJ:def 14</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1_2_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E4:20_1_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="projred1.html#E1:20_1_1_2_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="projred1.html#E3:20_1_1_2_2"><i><font color="Green">E21</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_1_1_2"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> iff <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E1:20_1_1_2"><i><font color="Green">E19</font></i></a></i>;<br/>


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

<b>let </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E8:20_1_1"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<b>thus </b><a NAME="E9:20_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> iff ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:20_1_1_3"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:20_1_1_3_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="projred1.html#E7:20_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="projred1.html#E8:20_1_1"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E3:20_1_1_3_1"/><b>then </b>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>]
 
<b>by </b><i><a class="txt" href="projred1.html#E5:20_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E1:20_1_1_3_1"><i><font color="Green">E21</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:20_1_1_3"/>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> ) implies <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1_3_2"/><i><font color="Green">E21</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>

<a NAME="E2:20_1_1_3_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="projred1.html#E7:20_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="projred1.html#E8:20_1_1"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E3:20_1_1_3_2"/><b>then </b>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>]
 
<b>by </b><i><a class="txt" href="projred1.html#E5:20_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:20_1_1_3_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:20_1_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="projred1.html#E8:20_1_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="projred1.html#E1:20_1_1_3_2"><i><font color="Green">E21</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:20_1_1_3"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> iff ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="projred1.html#E1:20_1_1_3"><i><font color="Green">E20</font></i></a></i>;<br/>


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


</div>
