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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="projpl_1.html#NM1">IncProjectivePlane</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><a NAME="E1:35"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="projpl_1.html#K2" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<a NAME="E2:35"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="projpl_1.html#V1" target="_self">configuration</a>
 
<b>by </b><i><a class="ref" href="projpl_1.html#T23" target="_self">Th23</a></i>;<br/>
<a NAME="E3:35"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="projpl_1.html#NR1" target="_self">|'</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:35"><i><font color="Green">E31</font></i></a>, <a class="ref" href="projpl_1.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E4:35"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:35"><i><font color="Green">E31</font></i></a>, <a class="ref" href="projpl_1.html#T16" target="_self">Th16</a></i>;<br/>
<b>hence </b><a NAME="E5:35"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="projpl_1.html#K2" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="projpl_1.html#T24" target="_self">Th24</a></i>;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="projpl_1.html#K2" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>assume </b><a NAME="E6:35"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="projpl_1.html#K2" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E7:35"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:35"><i><font color="Green">E31</font></i></a>, <a class="ref" href="projpl_1.html#T16" target="_self">Th16</a></i>;<br/>
<a NAME="E8:35"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="projpl_1.html#K2" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E4:35"><i><font color="Green">E34</font></i></a>, <a class="ref" href="projpl_1.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E9:35"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="projpl_1.html#K1" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="projpl_1.html#K2" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="projpl_1.html#E1:35"><i><font color="Green">E31</font></i></a>, <a class="txt" href="projpl_1.html#E2:35"><i><font color="Green">E32</font></i></a>, <a class="txt" href="projpl_1.html#E6:35"><i><font color="Green">E35</font></i></a>, <a class="txt" href="projpl_1.html#E7:35"><i><font color="Green">E36</font></i></a>, <a class="ref" href="projpl_1.html#D4" target="_self">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">E33</font></i></a>, <a class="txt" href="projpl_1.html#E4:35"><i><font color="Green">E34</font></i></a>, <a class="ref" href="projpl_1.html#T24" target="_self">Th24</a></i>;<br/>


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