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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="anproj_2.html#NM1">CollProjectiveSpace</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> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/><b>let </b><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> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>



















<b>assume </b><b>that </b><br/><a NAME="E1:16"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E2:16"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>8</sub></font> )
 <b>and </b><br/><a NAME="E3:16"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</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>8</sub></font> )
 <b>and </b><br/><a NAME="E4:16"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>and </b><br/><a NAME="E5:16"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>and </b><br/><a NAME="E6:16"/><i><font color="Green">E19</font></i>: 
( not <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; not <font color="Maroon">c<sub>6</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>and </b><br/><a NAME="E7:16"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E9:16"/>
( <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>11</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="incproj.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="incproj.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="incproj.html#E3:16"><i><font color="Green">E16</font></i></a>, <a class="ref" href="incproj.html#T14" target="_self">Th14</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>16</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E11:16"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font>,<font color="Maroon">c<sub>16</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 <b>by </b><i><a class="ref" href="anproj_2.html#D9">ANPROJ_2:def 9</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>16</sub></font> as   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<a NAME="E13:16"/><i><font color="Green">E22</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>4</sub></font>
 
<b>by </b><i><a class="txt" href="incproj.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="incproj.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="incproj.html#E3:16"><i><font color="Green">E16</font></i></a>, <a class="txt" href="incproj.html#E4:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="incproj.html#E6:16"><i><font color="Green">E19</font></i></a>, <a class="txt" href="incproj.html#E7:16"><i><font color="Green">E20</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E14:16"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="incproj.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="txt" href="incproj.html#E2:16"><i><font color="Green">E15</font></i></a>, <a class="txt" href="incproj.html#E3:16"><i><font color="Green">E16</font></i></a>, <a class="txt" href="incproj.html#E5:16"><i><font color="Green">E18</font></i></a>, <a class="txt" href="incproj.html#E6:16"><i><font color="Green">E19</font></i></a>, <a class="txt" href="incproj.html#E7:16"><i><font color="Green">E20</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E15:16"/><i><font color="Green">E24</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="incproj.html#E11:16"><i><font color="Green">E21</font></i></a>, <a class="ref" href="incproj.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E16:16"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="incproj.html#E11:16"><i><font color="Green">E21</font></i></a>, <a class="ref" href="incproj.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E17:16"/><b>then </b>
( <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>17</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> )
 
<b>by </b><i><a class="txt" href="incproj.html#E4:16"><i><font color="Green">E17</font></i></a>, <a class="txt" href="incproj.html#E5:16"><i><font color="Green">E18</font></i></a>, <a class="txt" href="incproj.html#E13:16"><i><font color="Green">E22</font></i></a>, <a class="txt" href="incproj.html#E14:16"><i><font color="Green">E23</font></i></a>, <a class="txt" href="incproj.html#E15:16"><i><font color="Green">E24</font></i></a>, <a class="ref" href="incproj.html#T12" target="_self">Th12</a></i>;<br/>
<b>hence </b><a NAME="E18:16"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>10</sub></font> )
 ;<br/>


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