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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="incproj.html#V9">Fanoian</a> <a href="incproj.html#NM2">IncProjSp</a>;<br/>

<b>consider </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> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</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>, <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> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>17</sub></font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:17"/>
( not <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; not <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>13</sub></font> &amp; not <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; not <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>12</sub></font> &amp; not <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; not <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; not <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>15</sub></font> )
 <b>and </b><br/><a NAME="E3:17"/><i><font color="Green">E12</font></i>: 
( <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</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>6</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>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>14</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="incproj.html#R4">on</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font> <a href="incproj.html#R3">on</a> <font color="Maroon">c<sub>11</sub></font> )
 <b>and </b><br/><a NAME="E4:17"/>
not <font color="Maroon">c<sub>8</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>11</sub></font>
 <b>and </b><br/><a NAME="E5:17"/><i><font color="Green">E13</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>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>11</sub></font>,<font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font> <a href="incproj.html#R2">are_mutually_different</a>  )
 <b>and </b><br/><a NAME="E6:17"/>
( <font color="Maroon">c<sub>17</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="incproj.html#R2">are_mutually_different</a>  )
 <b>by </b><i><a class="txt" href="projred1.html#E17"><i><font color="Green">Lemma11</font></i></a></i>;<br/>
<a NAME="E7:17"/>
( <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>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>7</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="projred1.html#E3:17"><i><font color="Green">E12</font></i></a>, <a class="ref" href="incproj.html#D7">INCPROJ:def 7</a>, <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<b>hence </b><a NAME="E8:17"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>4</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>5</sub></font> &amp; <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font> <a href="incproj.html#R2">are_mutually_different</a>  )
 <b>by </b><i><a class="txt" href="projred1.html#E5:17"><i><font color="Green">E13</font></i></a></i>;<br/>


</div>
