<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">IPP</font> be  <a href="incproj.html#V9">Fanoian</a> <a href="incproj.html#NM2">IncProjSp</a>;<br/>

<b>consider </b><font color="Maroon">r</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>, <font color="Maroon">A</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E2:15"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="incproj.html#D11">INCPROJ:def 11</a></i>;<br/>
<b>consider </b><font color="Maroon">p</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>, <font color="Maroon">q</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font>, <font color="Maroon">c</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E4:15"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font> &amp; <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D12">INCPROJ:def 12</a></i>;<br/>
<b>consider </b><font color="Maroon">B</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E6:15"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B</font> &amp; <font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">s</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E8:15"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">s</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">r</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">Q</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E10:15"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Q</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">L</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E12:15"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font> &amp; <font color="Maroon">s</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">S</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E14:15"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">S</font> &amp; <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">S</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">R</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E16:15"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">R</font> &amp; <font color="Maroon">s</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">R</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/>
<a NAME="E17:15"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">R</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">Q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1"/>
not <font color="Maroon">R</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">Q</font>
 ;<br/>

<a NAME="E2:15_1"/><b>then </b>
<font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E18:15"/><b>then </b><i><font color="Green">E63</font></i>: 
not <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">R</font>
 
<b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E19:15"/><i><font color="Green">E64</font></i>: 
not <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E20:15"/><i><font color="Green">E65</font></i>: 
not <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">S</font>
 
<b>by </b><i>, , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E21:15"/><i><font color="Green">E66</font></i>: 
not <font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2"/>
<font color="Maroon">q</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:15_2"/><b>then </b>
<font color="Maroon">s</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E3:15_2"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E22:15"/><i><font color="Green">E67</font></i>: 
not <font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_3"/>
<font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">R</font>
 ;<br/>

<a NAME="E2:15_3"/><b>then </b>
<font color="Maroon">s</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E3:15_3"/>
contradiction
 <b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E23:15"/><i><font color="Green">E68</font></i>: 
not <font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E24:15"/>
not <font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_4"/>
<font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:15_4"/><b>then </b>
<font color="Maroon">p</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B</font>
 
<b>by </b><i>, , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>hence </b><a NAME="E3:15_4"/>
contradiction
 <b>by </b><i>, , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon">a</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E26:15"/><i><font color="Green">E69</font></i>: 
( <font color="Maroon">a</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">a</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font> )
 <b>by </b><i>, , , , , , , <a class="ref" href="incproj.html#D13">INCPROJ:def 13</a></i>;<br/>
<a NAME="E27:15"/><i><font color="Green">E70</font></i>: 
not <font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">R</font>
 
<b>by </b><i>, , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E28:15"/><i><font color="Green">E71</font></i>: 
not <font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">S</font>
 
<b>by </b><i>, , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>then consider </b><font color="Maroon">b</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E30:15"/><i><font color="Green">E72</font></i>: 
( <font color="Maroon">b</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">R</font> &amp; <font color="Maroon">b</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">S</font> )
 <b>by </b><i>, , , , , , , <a class="ref" href="incproj.html#D13">INCPROJ:def 13</a></i>;<br/>
<b>consider </b><font color="Maroon">C</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E32:15"/><i><font color="Green">E73</font></i>: 
( <font color="Maroon">a</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C</font> &amp; <font color="Maroon">b</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/>
<a NAME="E33:15"/><i><font color="Green">E74</font></i>: 
not <font color="Maroon">s</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E34:15"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">L</font>
 
<b>by </b><i>, , , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E35:15"/><b>then </b><i><font color="Green">E76</font></i>: 
not <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">L</font>
 
<b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E36:15"/><i><font color="Green">E77</font></i>: 
not <font color="Maroon">s</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">S</font>
 
<b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E37:15"/><i><font color="Green">E78</font></i>: 
( <font color="Maroon">a</font>,<font color="Maroon">p</font>,<font color="Maroon">s</font> <a href="incproj.html#R4">on</a> <font color="Maroon">L</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font> <a href="incproj.html#R4">on</a> <font color="Maroon">Q</font> &amp; <font color="Maroon">b</font>,<font color="Maroon">q</font>,<font color="Maroon">s</font> <a href="incproj.html#R4">on</a> <font color="Maroon">R</font> &amp; <font color="Maroon">b</font>,<font color="Maroon">p</font>,<font color="Maroon">r</font> <a href="incproj.html#R4">on</a> <font color="Maroon">S</font> &amp; <font color="Maroon">c</font>,<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="incproj.html#R4">on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">c</font>,<font color="Maroon">r</font>,<font color="Maroon">s</font> <a href="incproj.html#R4">on</a> <font color="Maroon">B</font> )
 
<b>by </b><i>, , , , , , , , , <a class="ref" href="incproj.html#D8">INCPROJ:def 8</a></i>;<br/>
<a NAME="E38:15"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="incproj.html#R3">on</a> <font color="Maroon">C</font>
 
<b>by </b><i>, <a class="ref" href="incproj.html#D7">INCPROJ:def 7</a></i>;<br/>
<a NAME="E39:15"/><b>then </b><i><font color="Green">E80</font></i>: 
not <font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , , , , <a class="ref" href="projred1.html#T1" target="_self">Th1</a>, <a class="txt" href="projred1.html#E4:15"><i><font color="Green">E34</font></i></a>, <a class="txt" href="projred1.html#E6:15"><i><font color="Green">E35</font></i></a>, <a class="ref" href="projred1.html#T2" target="_self">Th2</a>, <a class="ref" href="incproj.html#D18">INCPROJ:def 18</a></i>;<br/>
<b>consider </b><font color="Maroon">D</font> being   <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E41:15"/><i><font color="Green">E81</font></i>: 
( <font color="Maroon">b</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">D</font> &amp; <font color="Maroon">c</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">D</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10">INCPROJ:def 10</a></i>;<br/>
<a NAME="E42:15"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">s</font>
 
<b>by </b><i>, , , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E43:15"/><i><font color="Green">E83</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">r</font>
 
<b>by </b><i>, , , , , <a class="txt" href="projred1.html#E2:15"><i><font color="Green">E33</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E44:15"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E45:15"/><i><font color="Green">E85</font></i>: 
not <font color="Maroon">a</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">S</font>
 
<b>by </b><i>, , , , <a class="txt" href="projred1.html#E16:15"><i><font color="Green">E41</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E46:15"/><i><font color="Green">E86</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font>
 
<b>by </b><i>, , , <a class="txt" href="projred1.html#E12:15"><i><font color="Green">E39</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E47:15"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">R</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font>
 
<b>by </b><i>, , , <a class="txt" href="projred1.html#E12:15"><i><font color="Green">E39</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E48:15"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">R</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , , , , <a class="txt" href="projred1.html#E14:15"><i><font color="Green">E40</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E49:15"/><i><font color="Green">E89</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , , , , <a class="txt" href="projred1.html#E16:15"><i><font color="Green">E41</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E50:15"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">C</font>,<font color="Maroon">D</font>,<font color="Maroon">R</font>,<font color="Maroon">S</font> <a href="incproj.html#R2">are_mutually_different</a> 
 
<b>by </b><i>, , , <a class="txt" href="projred1.html#E10:15"><i><font color="Green">E38</font></i></a>, <a class="txt" href="projred1.html#E12:15"><i><font color="Green">E39</font></i></a>, , , , , <a class="ref" href="incproj.html#D6">INCPROJ:def 6</a></i>;<br/>
<a NAME="E51:15"/><i><font color="Green">E91</font></i>: 
not <font color="Maroon">b</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">Q</font>
 
<b>by </b><i>, , , , , <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E52:15"/><b>then </b>
not <font color="Maroon">r</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C</font>
 
<b>by </b><i>, , , <a class="txt" href="projred1.html#E16:15"><i><font color="Green">E41</font></i></a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<b>then consider </b><font color="Maroon">d</font> being   <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font><b> such that </b><br/><a NAME="E54:15"/><i><font color="Green">E92</font></i>: 
( <font color="Maroon">d</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">d</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C</font> )
 <b>by </b><i>, , , , , , , <a class="ref" href="projred1.html#T3" target="_self">Th3</a>, <a class="ref" href="incproj.html#D13">INCPROJ:def 13</a></i>;<br/>
<a NAME="E55:15"/><i><font color="Green">E93</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 
<b>by </b><i>, , , , , <a class="ref" href="projred1.html#T7" target="_self">Th7</a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E56:15"/>
<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font>
 
<b>by </b><i>, , , , , <a class="ref" href="projred1.html#T7" target="_self">Th7</a>, <a class="ref" href="incproj.html#D9">INCPROJ:def 9</a></i>;<br/>
<a NAME="E57:15"/><b>then </b>
<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="incproj.html#R2">are_mutually_different</a> 
 
<b>by </b><i>, <a class="txt" href="projred1.html#E10:15"><i><font color="Green">E38</font></i></a>, <a class="ref" href="projred1.html#T7" target="_self">Th7</a>, <a class="ref" href="projred1.html#T8" target="_self">Th8</a>, <a class="ref" href="incproj.html#D6">INCPROJ:def 6</a></i>;<br/>
<b>hence </b><a NAME="E58:15"/>
 ex <font color="Olive">p</font>, <font color="Olive">q</font>, <font color="Olive">r</font>, <font color="Olive">s</font>, <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font> ex <font color="Olive">A</font>, <font color="Olive">B</font>, <font color="Olive">C</font>, <font color="Olive">Q</font>, <font color="Olive">L</font>, <font color="Olive">R</font>, <font color="Olive">S</font>, <font color="Olive">D</font> being  <a href="incsp_1.html#NM2">LINE</a> of <font color="Maroon">IPP</font> ex <font color="Olive">d</font> being  <a href="incsp_1.html#NM1">POINT</a> of <font color="Maroon">IPP</font> st <br/>( not <font color="Olive">q</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">L</font> &amp; not <font color="Olive">r</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">L</font> &amp; not <font color="Olive">p</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">Q</font> &amp; not <font color="Olive">s</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">Q</font> &amp; not <font color="Olive">p</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">R</font> &amp; not <font color="Olive">r</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">R</font> &amp; not <font color="Olive">q</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">S</font> &amp; not <font color="Olive">s</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">S</font> &amp; <font color="Olive">a</font>,<font color="Olive">p</font>,<font color="Olive">s</font> <a href="incproj.html#R4">on</a> <font color="Olive">L</font> &amp; <font color="Olive">a</font>,<font color="Olive">q</font>,<font color="Olive">r</font> <a href="incproj.html#R4">on</a> <font color="Olive">Q</font> &amp; <font color="Olive">b</font>,<font color="Olive">q</font>,<font color="Olive">s</font> <a href="incproj.html#R4">on</a> <font color="Olive">R</font> &amp; <font color="Olive">b</font>,<font color="Olive">p</font>,<font color="Olive">r</font> <a href="incproj.html#R4">on</a> <font color="Olive">S</font> &amp; <font color="Olive">c</font>,<font color="Olive">p</font>,<font color="Olive">q</font> <a href="incproj.html#R4">on</a> <font color="Olive">A</font> &amp; <font color="Olive">c</font>,<font color="Olive">r</font>,<font color="Olive">s</font> <a href="incproj.html#R4">on</a> <font color="Olive">B</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="incproj.html#R3">on</a> <font color="Olive">C</font> &amp; not <font color="Olive">c</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">C</font> &amp; <font color="Olive">b</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">D</font> &amp; <font color="Olive">c</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">D</font> &amp; <font color="Olive">C</font>,<font color="Olive">D</font>,<font color="Olive">R</font>,<font color="Olive">S</font> <a href="incproj.html#R2">are_mutually_different</a>  &amp; <font color="Olive">d</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">A</font> &amp; <font color="Olive">c</font>,<font color="Olive">d</font>,<font color="Olive">p</font>,<font color="Olive">q</font> <a href="incproj.html#R2">are_mutually_different</a>  )
 <b>by </b><i>, , , , , <a class="ref" href="projred1.html#T1" target="_self">Th1</a>, <a class="txt" href="projred1.html#E4:15"><i><font color="Green">E34</font></i></a>, <a class="txt" href="projred1.html#E6:15"><i><font color="Green">E35</font></i></a>, <a class="ref" href="projred1.html#T2" target="_self">Th2</a>, <a class="txt" href="projred1.html#E8:15"><i><font color="Green">E37</font></i></a>, <a class="txt" href="projred1.html#E10:15"><i><font color="Green">E38</font></i></a>, <a class="txt" href="projred1.html#E12:15"><i><font color="Green">E39</font></i></a>, , <a class="ref" href="projred1.html#T7" target="_self">Th7</a></i>;<br/>


</div>
