<?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">o</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font>;<br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green">E47</font></i>: 
not <font color="Maroon">o</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font>
 ;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="projred1.html#K1">IncProj</a> <font color="Maroon">A</font>,<font color="Maroon">o</font>,<font color="Maroon">A</font>;<br/>
<a NAME="E2:12"/><i><font color="Green">E49</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1">IncProj</a> <font color="Maroon">A</font>,<font color="Maroon">o</font>,<font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="projred2.html#K1" target="_self">CHAIN</a> <font color="Maroon">A</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:12"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="projred2.html#K1" target="_self">CHAIN</a> <font color="Maroon">A</font> holds <br/><span class="p1">(<span class="default"><a href="projred1.html#K1">IncProj</a> <font color="Maroon">A</font>,<font color="Maroon">o</font>,<font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:12_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="projred2.html#K1" target="_self">CHAIN</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:12_1"/><b>then </b>
 ex <font color="Olive">x'</font> being   <a href="subset_1.html#M1">Element</a> of the <a href="incsp_1.html#U1">Points</a> of <font color="Maroon">IPP</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">x'</font> &amp; <font color="Olive">x'</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> )
 
;<br/>
<b>hence </b><a NAME="E3:12_1"/>
<span class="p1">(<span class="default"><a href="projred1.html#K1">IncProj</a> <font color="Maroon">A</font>,<font color="Maroon">o</font>,<font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="projred1.html#T27">PROJRED1:27</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:12"/>
 <a href="projred1.html#K1">IncProj</a> <font color="Maroon">A</font>,<font color="Maroon">o</font>,<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> <span class="p1">(<span class="default"><a href="projred2.html#K1" target="_self">CHAIN</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>


</div>
