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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="projpl_1.html#NM1" title="PROJPL_1:NM.1">IncProjectivePlane</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">e</font>, <font color="Olive" title="b2">x1</font>, <font color="Olive" title="b3">x2</font>, <font color="Olive" title="b4">p1</font>, <font color="Olive" title="b5">p2</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b6">H</font>, <font color="Olive" title="b7">I</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b2">x1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">I</font> &amp; <font color="Olive" title="b3">x2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">I</font> &amp; <font color="Olive" title="b1">e</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b6">H</font> &amp; <font color="Olive" title="b1">e</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Olive" title="b7">I</font> &amp; <font color="Olive" title="b2">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">x2</font> &amp; <font color="Olive" title="b4">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">e</font> &amp; <font color="Olive" title="b5">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">e</font> &amp; <font color="Olive" title="b4">p1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Olive" title="b2">x1</font> &amp; <font color="Olive" title="b5">p2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Olive" title="b3">x2</font> holds <br/> ex <font color="Olive" title="b8">r</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b8">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Olive" title="b5">p2</font> &amp; <font color="Olive" title="b8">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b6">H</font> &amp; <font color="Olive" title="b8">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">e</font> )</span><br/><b>let </b><font color="Maroon" title="c2">e</font>, <font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font>, <font color="Maroon" title="c5">p1</font>, <font color="Maroon" title="c6">p2</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">H</font>, <font color="Olive" title="b2">I</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c3">x1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">I</font> &amp; <font color="Maroon" title="c4">x2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">I</font> &amp; <font color="Maroon" title="c2">e</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">H</font> &amp; <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Olive" title="b2">I</font> &amp; <font color="Maroon" title="c3">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x2</font> &amp; <font color="Maroon" title="c5">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> &amp; <font color="Maroon" title="c5">p1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">x2</font> holds <br/> ex <font color="Olive" title="b3">r</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b3">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font> &amp; <font color="Olive" title="b3">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">H</font> &amp; <font color="Olive" title="b3">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> )</span><br/><b>let </b><font color="Maroon" title="c7">H</font>, <font color="Maroon" title="c8">I</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">x1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">I</font> &amp; <font color="Maroon" title="c4">x2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">I</font> &amp; <font color="Maroon" title="c2">e</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">H</font> &amp; <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c8">I</font> &amp; <font color="Maroon" title="c3">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x2</font> &amp; <font color="Maroon" title="c5">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> &amp; <font color="Maroon" title="c5">p1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">x2</font> implies  ex <font color="Olive" title="b1">r</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font> &amp; <font color="Olive" title="b1">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">H</font> &amp; <font color="Olive" title="b1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> ) )</span><br/>





<b>assume </b><a NAME="E1:47"/><i><font color="Green" title="E34">A1</font></i>: 
( <font color="Maroon" title="c3">x1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">I</font> &amp; <font color="Maroon" title="c4">x2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">I</font> &amp; <font color="Maroon" title="c2">e</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">H</font> &amp; <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c8">I</font> &amp; <font color="Maroon" title="c3">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x2</font> &amp; <font color="Maroon" title="c5">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> &amp; <font color="Maroon" title="c5">p1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">x2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">r</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font> &amp; <font color="Olive" title="b1">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">H</font> &amp; <font color="Olive" title="b1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> )</span><br/>

<b>set </b><font color="Maroon" title="c9">L1</font> = <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c3">x1</font>;<br/>
<b>set </b><font color="Maroon" title="c10">L2</font> = <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">x2</font>;<br/>
<b>set </b><font color="Maroon" title="c11">L</font> = <font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font>;<br/>
<b>consider </b><font color="Maroon" title="c12">r</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:47"/><i><font color="Green" title="E35">A2</font></i>: 
( <font color="Maroon" title="c12">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font> &amp; <font color="Maroon" title="c12">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">H</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D14" title="INCPROJ:def.14">INCPROJ:def 14</a></i>;<br/>
<a NAME="E4:47"/><i><font color="Green" title="E36">A3</font></i>: 
( <font color="Maroon" title="c2">e</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c2">e</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">x2</font> &amp; <font color="Maroon" title="c3">x1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c4">x2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">x2</font> )
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:47"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="projpl_1.html#T16" target="_self" title="PROJPL_1:th.16">Th16</a></i>;<br/>
<a NAME="E5:47"/><b>then </b><i><font color="Green" title="E37">A4</font></i>: 
<font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c4">x2</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:47"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E6:47"/><b>then </b>
<font color="Maroon" title="c5">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">p2</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:47"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="projpl_1.html#E4:47"><i><font color="Green" title="E36">A3</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E7:47"/><b>then </b><i><font color="Green" title="E38">A5</font></i>: 
( <font color="Maroon" title="c5">p1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font> &amp; <font color="Maroon" title="c6">p2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font> )
 
<b>by </b><i><a class="ref" href="projpl_1.html#T16" target="_self" title="PROJPL_1:th.16">Th16</a></i>;<br/>
<a NAME="E8:47"/><b>then </b>
<font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c3">x1</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:47"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="projpl_1.html#E4:47"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="projpl_1.html#E5:47"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E9:47"/><b>then </b>
<font color="Maroon" title="c12">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:47"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="projpl_1.html#E3:47"><i><font color="Green" title="E35">A2</font></i></a>, <a class="txt" href="projpl_1.html#E4:47"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="projpl_1.html#E7:47"><i><font color="Green" title="E38">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E10:47"/>
 ex <font color="Olive" title="b1">r</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b1">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">p1</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c6">p2</font> &amp; <font color="Olive" title="b1">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">H</font> &amp; <font color="Olive" title="b1">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">e</font> )
 <b>by </b><i><a class="txt" href="projpl_1.html#E3:47"><i><font color="Green" title="E35">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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