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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>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">q</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">G</font>;<br/>









<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E31">A1</font></i>: 
( <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c3">q</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">A</font> <a href="projpl_1.html#K2" title="PROJPL_1:func.2">*</a> <font color="Maroon" title="c5">B</font> )
 ;<br/>

<a NAME="E2:35"/><i><font color="Green" title="E32">A2</font></i>: 
<font color="Maroon" title="c1">G</font> is <a href="projpl_1.html#V1" title="PROJPL_1:attr.1">configuration</a>
 
<b>by </b><i><a class="ref" href="projpl_1.html#T23" target="_self" title="PROJPL_1:th.23">Th23</a></i>;<br/>
<a NAME="E3:35"/><i><font color="Green" title="E33">A3</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="projpl_1.html#NR1" title="PROJPL_1:NR.1">|'</a> <font color="Maroon" title="c5">B</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:35"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="projpl_1.html#T24" target="_self" title="PROJPL_1:th.24">Th24</a></i>;<br/>
<a NAME="E4:35"/><b>then </b><i><font color="Green" title="E34">A4</font></i>: 
<font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">B</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:35"><i><font color="Green" title="E31">A1</font></i></a>, <a class="ref" href="projpl_1.html#T16" target="_self" title="PROJPL_1:th.16">Th16</a></i>;<br/>
<b>hence </b><a NAME="E5:35"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="projpl_1.html#K2" title="PROJPL_1:func.2">*</a> <font color="Maroon" title="c5">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">B</font>
 <b>by </b><i><a class="ref" href="projpl_1.html#T24" target="_self" title="PROJPL_1:th.24">Th24</a></i>;<br/>

<b>set </b><font color="Maroon" title="c6">D</font> = <font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font>;<br/>
<b>set </b><font color="Maroon" title="c7">d</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="projpl_1.html#K2" title="PROJPL_1:func.2">*</a> <font color="Maroon" title="c5">B</font>;<br/>
<b>assume </b><a NAME="E6:35"/><i><font color="Green" title="E35">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="projpl_1.html#K2" title="PROJPL_1:func.2">*</a> <font color="Maroon" title="c5">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font>
 ;<br/>

<a NAME="E7:35"/><i><font color="Green" title="E36">A6</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c3">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:35"><i><font color="Green" title="E31">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="E8:35"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="projpl_1.html#K2" title="PROJPL_1:func.2">*</a> <font color="Maroon" title="c5">B</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E4:35"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="projpl_1.html#T24" target="_self" title="PROJPL_1:th.24">Th24</a></i>;<br/>
<a NAME="E9:35"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">q</font> <a href="projpl_1.html#K1" title="PROJPL_1:func.1">*</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="projpl_1.html#K2" title="PROJPL_1:func.2">*</a> <font color="Maroon" title="c5">B</font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:35"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="projpl_1.html#E2:35"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="projpl_1.html#E6:35"><i><font color="Green" title="E35">A5</font></i></a>, <a class="txt" href="projpl_1.html#E7:35"><i><font color="Green" title="E36">A6</font></i></a>, <a class="ref" href="projpl_1.html#D4" target="_self" title="PROJPL_1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E10:35"/>
contradiction
 <b>by </b><i><a class="txt" href="projpl_1.html#E3:35"><i><font color="Green" title="E33">A3</font></i></a>, <a class="txt" href="projpl_1.html#E4:35"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="projpl_1.html#T24" target="_self" title="PROJPL_1:th.24">Th24</a></i>;<br/>


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