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<b>let </b><font color="Maroon">G</font> be   <a href="projpl_1.html#NM1">IncProjectivePlane</a>;<br/><b>let </b><font color="Maroon">e</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>, <font color="Maroon">x1</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>, <font color="Maroon">x2</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>, <font color="Maroon">p1</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>, <font color="Maroon">p2</font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">H</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">G</font>, <font color="Maroon">I</font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">G</font>;<br/>





<b>assume </b><a NAME="E1:47"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">x1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">I</font> &amp; <font color="Maroon">x2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">I</font> &amp; <font color="Maroon">e</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">H</font> &amp; <font color="Maroon">e</font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">I</font> &amp; <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">p1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">p2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">p1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">p2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x2</font> )
 ;<br/>

<b>set </b><font color="Maroon">L1</font> = <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x1</font>;<br/>
<b>set </b><font color="Maroon">L2</font> = <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x2</font>;<br/>
<b>set </b><font color="Maroon">L</font> = <font color="Maroon">p1</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">p2</font>;<br/>
<b>consider </b><font color="Maroon">r</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font><b> such that </b><br/><a NAME="E3:47"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">p1</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">p2</font> &amp; <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">H</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D14">INCPROJ:def 14</a></i>;<br/>
<a NAME="E4:47"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">e</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">e</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">x1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">x2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x2</font> )
 
<b>by </b><i><a class="ref" href="projpl_1.html#D4" target="_self">Def4</a>, </i>;<br/>
<a NAME="E5:47"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x2</font>
 
<b>by </b><i><a class="ref" href="projpl_1.html#D4" target="_self">Def4</a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E6:47"/><b>then </b>
<font color="Maroon">p1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p2</font>
 
<b>by </b><i><a class="ref" href="projpl_1.html#D4" target="_self">Def4</a>, <a class="txt" href="projpl_1.html#E1:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E7:47"/><b>then </b><i><font color="Green">E42</font></i>: 
( <font color="Maroon">p1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">p1</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">p2</font> &amp; <font color="Maroon">p2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">p1</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">p2</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E8:47"/><b>then </b>
<font color="Maroon">p1</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">p2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">x1</font>
 
<b>by </b><i><a class="ref" href="projpl_1.html#D4" target="_self">Def4</a>, <a class="txt" href="projpl_1.html#E1:47"><i><font color="Green">E36</font></i></a>, <a class="txt" href="projpl_1.html#E3:47"><i><font color="Green">E37</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E9:47"/><b>then </b>
<font color="Maroon">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font>
 
<b>by </b><i><a class="ref" href="projpl_1.html#D4" target="_self">Def4</a>, <a class="ref" href="projpl_1.html#T2" target="_self">Th2</a>, <a class="txt" href="projpl_1.html#E1:47"><i><font color="Green">E36</font></i></a>, <a class="ref" href="projpl_1.html#T3" target="_self">Th3</a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E10:47"/>
 ex <font color="Olive">r</font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">G</font> st <br/>( <font color="Olive">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">p1</font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">p2</font> &amp; <font color="Olive">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">H</font> &amp; <font color="Olive">r</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="projpl_1.html#T2" target="_self">Th2</a></i>;<br/>


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