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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="incsp_1.html#L1">IncProjStr</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> 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>5</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="E1:18"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> is <a href="projpl_1.html#V1" target="_self">configuration</a> &amp; <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="incproj.html#R3">on</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>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>5</sub></font> &amp; <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="projpl_1.html#R4" target="_self">is_collinear</a>  )
 ;<br/>

<a NAME="E2:18"/><b>then </b><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>5</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="ref" href="incproj.html#D7">INCPROJ:def 7</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</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="E4:18"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="projpl_1.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="ref" href="projpl_1.html#T5" target="_self">Th5</a></i>;<br/>
<b>thus </b><a NAME="E5:18"/>
contradiction
 <b>by </b><i><a class="txt" href="projpl_1.html#E1:18"><i><font color="Green">E16</font></i></a>, <a class="txt" href="projpl_1.html#E2:18"><i><font color="Green">E17</font></i></a>, <a class="txt" href="projpl_1.html#E4:18"><i><font color="Green">E18</font></i></a>, <a class="ref" href="projpl_1.html#D4" target="_self">Def4</a></i>;<br/>


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