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

<b>let </b><font color="Maroon">IPP</font> be  <a href="incproj.html#V6">2-dimensional</a> <a href="incproj.html#V10">Desarguesian</a> <a href="incproj.html#NM2">IncProjSp</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font>;<br/><b>let </b><font color="Maroon">L</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font>;<br/><b>let </b><font color="Maroon">a1</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>, <font color="Maroon">b1</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>, <font color="Maroon">a2</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>, <font color="Maroon">b2</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>;<br/>









<b>assume </b><a NAME="E1:26"/><i><font color="Green">E33</font></i>: 
( not <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">K</font> &amp; not <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font> &amp; <font color="Maroon">a1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">K</font> &amp; <font color="Maroon">b1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">K</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" target="_self">IncProj</a> <font color="Maroon">K</font>,<font color="Maroon">p</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" target="_self">IncProj</a> <font color="Maroon">K</font>,<font color="Maroon">p</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b2</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">a2</font> = <span class="p1">(<span class="default"><a href="projred1.html#K1" target="_self">IncProj</a> <font color="Maroon">K</font>,<font color="Maroon">p</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a1</font> as   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font> ;<br/>
<a NAME="E3:26"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">a2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<b>then consider </b><font color="Maroon">A</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E5:26"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">a2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> )
 <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">b2</font> = <span class="p1">(<span class="default"><a href="projred1.html#K1" target="_self">IncProj</a> <font color="Maroon">K</font>,<font color="Maroon">p</font>,<font color="Maroon">L</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">b1</font> as    <a href="subset_1.html#M1">Element</a> of the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">IPP</font> <b>by </b><i/>;<br/>
<a NAME="E7:26"/>
<font color="Maroon">b2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font>
 
<b>by </b><i>, </i>;<br/>
<b>then consider </b><font color="Maroon">B</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E9:26"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B</font> &amp; <font color="Maroon">b1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B</font> &amp; <font color="Maroon">b2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B</font> )
 <b>by </b><i>, </i>;<br/>
<a NAME="E10:26"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 
<b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E11:26"/>
<font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b1</font>
 <b>by </b><i>, , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>


</div>
