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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="incproj.html#V10">Desarguesian</a> <a href="incproj.html#NM2">IncProjSp</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>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font>, <font color="Maroon">c<sub>20</sub></font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>14</sub></font> <a href="incproj.html#R1">are_mutually_different</a>  &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<a NAME="E2:12"/><b>then </b><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <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>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> )
 
<b>by </b><i><a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<a NAME="E3:12"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<a NAME="E4:12"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>20</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<a NAME="E5:12"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a></i>;<br/>
<a NAME="E6:12"/><b>then </b><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>20</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<div><i><font color="Green">E15</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div><i><font color="Green">E19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:12_1_1_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_1_1_1"/>
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_1_1_1"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="projred1.html#E2:12_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_1_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_1_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_1_1_1"/>
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_1_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="projred1.html#E4:12_1_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="projred1.html#E5:12_1_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>21</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="E9:12_1_1_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>21</sub></font>;<br/><b>thus </b><a NAME="E10:12_1_1_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E7:12_1_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="projred1.html#E9:12_1_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:12_1_1_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_1_1_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="projred1.html#E1:12_1_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_1_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_1_1_2"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_1_1_2"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="projred1.html#E4:12_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>13</sub></font>;<br/><b>thus </b><a NAME="E7:12_1_1_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E2:12_1_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="projred1.html#E3:12_1_1_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="projred1.html#E6:12_1_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_1_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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12_1_1"><i><font color="Green">E19</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1"><b>now </b></a><div class="add"><div><i><font color="Green">E19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_2_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:12_1_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_1_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_1_2_1_1"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E6:12"><i><font color="Green">E14</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_1_2_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_1_2_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_1_2_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_1_2_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="txt" href="projred1.html#E3:12_1_2_1_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="projred1.html#E4:12_1_2_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>19</sub></font>;<br/><b>thus </b><a NAME="E7:12_1_2_1_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E6:12_1_2_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_2_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:12_1_2_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_1_2_1_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_1_2_1_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_1_2_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_1_2_1_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E2:12_1_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="projred1.html#E4:12_1_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_1_2_1_2"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E3:12_1_2_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="projred1.html#E5:12_1_2_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>17</sub></font>;<br/><b>thus </b><a NAME="E8:12_1_2_1_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E7:12_1_2_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:12_1_2_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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12_1_2_1"><i><font color="Green">E19</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:12_1_2"/>
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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12_1"><i><font color="Green">E17</font></i></a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:12_2_1"/><b>then </b><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_2_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_2_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_2_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E3:12_2_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="projred1.html#E4:12_2_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_2_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E2:12_2_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="projred1.html#E5:12_2_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>21</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="E9:12_2_1"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>21</sub></font>;<br/><b>thus </b><a NAME="E10:12_2_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E7:12_2_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="projred1.html#E9:12_2_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2_2"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2_2_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:12_2_2_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>18</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_2_2_1_1"/>
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_2_2_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<b>hence </b><a NAME="E2:12_2_2_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:12_2_2_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_2_2_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projred1.html#E1:12_2_2_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_2_2_1"/><b>then </b>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E3:12_2_2_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_2_2_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_2_2_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="projred1.html#E2:12_2_2_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>21</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="E8:12_2_2_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>21</sub></font>;<br/><b>thus </b><a NAME="E9:12_2_2_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E6:12_2_2_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="projred1.html#E8:12_2_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2_2_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:12_2_2_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projred1.html#E1:12_2_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_2_2_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_2_2_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_2_2_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_2_2_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E2:12_2_2_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="projred1.html#E4:12_2_2_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_2_2_2"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E3:12_2_2_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="projred1.html#E5:12_2_2_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>18</sub></font>;<br/><b>thus </b><a NAME="E8:12_2_2_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E7:12_2_2_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_2_2"/>
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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12_2_2"><i><font color="Green">E20</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_2"/>
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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12_2"><i><font color="Green">E18</font></i></a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><div><i><font color="Green">E19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_1_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:12_3_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>20</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_3_1_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>20</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<b>hence </b><a NAME="E2:12_3_1_1_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/>


</div><b>end;</b></div><a NAME="E3:12_3_1_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>18</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:12_3_1_1_2"/>
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<b>hence </b><a NAME="E2:12_3_1_1_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:12_3_1_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="projred1.html#E2:12_3_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_3_1_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="projred1.html#E3:12_3_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>19</sub></font>;<br/><b>thus </b><a NAME="E6:12_3_1_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E5:12_3_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_1_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:12_3_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_3_1_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_3_1_2_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <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>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<b>hence </b><a NAME="E2:12_3_1_2_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:12_3_1_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_3_1_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="projred1.html#E3:12_3_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_3_1_2"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="projred1.html#E2:12_3_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="projred1.html#E4:12_3_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>21</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="E8:12_3_1_2"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>21</sub></font>;<br/><b>thus </b><a NAME="E9:12_3_1_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E6:12_3_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="projred1.html#E8:12_3_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12_3_1"><i><font color="Green">E21</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><div><i><font color="Green">E21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_2_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:12_3_2_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_3_2_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_3_2_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <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>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_2"><i><font color="Green">E20</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_2_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<b>hence </b><a NAME="E2:12_3_2_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/>


</div><b>end;</b></div><a NAME="E4:12_3_2_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_3_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_3_2_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="projred1.html#E3:12_3_2_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_3_2_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E2:12_3_2_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="projred1.html#E4:12_3_2_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>21</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="E8:12_3_2_1"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>21</sub></font>;<br/><b>thus </b><a NAME="E9:12_3_2_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E6:12_3_2_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="projred1.html#E8:12_3_2_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_2_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:12_3_2_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_3_2_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E1:12_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_3_2_2"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>20</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_3_2_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E5:12"><i><font color="Green">E13</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_3_2_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E2:12_3_2_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="projred1.html#E4:12_3_2_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_3_2_2"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E3:12_3_2_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="projred1.html#E5:12_3_2_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>19</sub></font>;<br/><b>thus </b><a NAME="E8:12_3_2_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E7:12_3_2_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_3_2"/>
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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12_3_2"><i><font color="Green">E21</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12_3"><i><font color="Green">E19</font></i></a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_4"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/><div><i><font color="Green">E20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_4_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:12_4_1"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/><a NAME="E3:12_4_1"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E4:12_4_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>20</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_4"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/><a NAME="E5:12_4_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E6:12_4_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_4_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="projred1.html#E3:12_4_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_4_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_4"><i><font color="Green">E19</font></i></a>, <a class="txt" href="projred1.html#E5:12_4_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon">c<sub>21</sub></font> = <font color="Maroon">c<sub>19</sub></font>;<br/><b>thus </b><a NAME="E8:12_4_1"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>21</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E7:12_4_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_4_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:12_4_2"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>20</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>17</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_4"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/><a NAME="E3:12_4_2"/><b>then </b>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>20</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E4:12_4_2"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_4"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_4_2"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_4"><i><font color="Green">E19</font></i></a>, <a class="txt" href="projred1.html#E1:12_4_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/><a NAME="E6:12_4_2"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E7:12_4_2"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_4"><i><font color="Green">E19</font></i></a>, <a class="txt" href="projred1.html#E4:12_4_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>21</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="E9:12_4_2"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>21</sub></font>;<br/><b>thus </b><a NAME="E10:12_4_2"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E7:12_4_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="projred1.html#E9:12_4_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_4"/>
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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12_4"><i><font color="Green">E20</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_5"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/><a NAME="E2:12_5"/><b>then </b><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>16</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>19</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/><a NAME="E3:12_5"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>18</sub></font> )
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E1:12_5"><i><font color="Green">E19</font></i></a>, <a class="ref" href="incproj.html#D5">INCPROJ:def 5</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/><a NAME="E4:12_5"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>19</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E2:12"><i><font color="Green">E10</font></i></a>, <a class="txt" href="projred1.html#E2:12_5"><i><font color="Green">E20</font></i></a>, <a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E5:12_5"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>18</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12_5"><i><font color="Green">E21</font></i></a>, <a class="ref" href="projred1.html#T12" target="_self">Th12</a></i>;<br/><a NAME="E6:12_5"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12"><i><font color="Green">E11</font></i></a>, <a class="txt" href="projred1.html#E4:12"><i><font color="Green">E12</font></i></a>, <a class="txt" href="projred1.html#E1:12_5"><i><font color="Green">E19</font></i></a>, <a class="txt" href="projred1.html#E4:12_5"><i><font color="Green">E22</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_5"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E3:12_5"><i><font color="Green">E21</font></i></a>, <a class="txt" href="projred1.html#E5:12_5"><i><font color="Green">E23</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>21</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="E9:12_5"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon">c<sub>22</sub></font> = <font color="Maroon">c<sub>21</sub></font>;<br/><b>thus </b><a NAME="E10:12_5"/>
<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>22</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E7:12_5"><i><font color="Green">E24</font></i></a>, <a class="txt" href="projred1.html#E9:12_5"><i><font color="Green">E25</font></i></a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:12"/>
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 <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="incproj.html#R4">on</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="projred1.html#E1:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="projred1.html#E7:12"><i><font color="Green">E15</font></i></a>, <a class="txt" href="projred1.html#E8:12"><i><font color="Green">E16</font></i></a>, <a class="txt" href="projred1.html#E9:12"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projred1.html#E10:12"><i><font color="Green">E18</font></i></a>, <a class="ref" href="incproj.html#D19">INCPROJ:def 19</a></i>;<br/>


</div>
