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

<b>let </b><font color="Maroon">CPS</font> be   <a href="anproj_2.html#NM1">CollProjectiveSpace</a>;<br/>

<b>assume </b><a NAME="E1:24"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">o</font>, <font color="Olive">p1</font>, <font color="Olive">p2</font>, <font color="Olive">p3</font>, <font color="Olive">q1</font>, <font color="Olive">q2</font>, <font color="Olive">q3</font>, <font color="Olive">r1</font>, <font color="Olive">r2</font>, <font color="Olive">r3</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CPS</font>  st <font color="Olive">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">p2</font> &amp; <font color="Olive">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">p3</font> &amp; <font color="Olive">p2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">p3</font> &amp; <font color="Olive">p1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">p2</font> &amp; <font color="Olive">p1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">p3</font> &amp; <font color="Olive">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">q2</font> &amp; <font color="Olive">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">q3</font> &amp; <font color="Olive">q2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">q3</font> &amp; <font color="Olive">q1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">q2</font> &amp; <font color="Olive">q1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">q3</font> &amp; not <font color="Olive">o</font>,<font color="Olive">p1</font>,<font color="Olive">q1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">o</font>,<font color="Olive">p1</font>,<font color="Olive">p2</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">o</font>,<font color="Olive">p1</font>,<font color="Olive">p3</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">o</font>,<font color="Olive">q1</font>,<font color="Olive">q2</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">o</font>,<font color="Olive">q1</font>,<font color="Olive">q3</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">p1</font>,<font color="Olive">q2</font>,<font color="Olive">r3</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">q1</font>,<font color="Olive">p2</font>,<font color="Olive">r3</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">p1</font>,<font color="Olive">q3</font>,<font color="Olive">r2</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">p3</font>,<font color="Olive">q1</font>,<font color="Olive">r2</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">p2</font>,<font color="Olive">q3</font>,<font color="Olive">r1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">p3</font>,<font color="Olive">q2</font>,<font color="Olive">r1</font> <a href="collsp.html#R1">is_collinear</a>  holds <br/><font color="Olive">r1</font>,<font color="Olive">r2</font>,<font color="Olive">r3</font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/>

<b>let </b><font color="Maroon">o</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">a1</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">a2</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">a3</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">b1</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">b2</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">b3</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">c1</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">c2</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">c3</font> be   <a href="incsp_1.html#NM1">POINT</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>;<br/><b>let </b><font color="Maroon">A1</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">A2</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">A3</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">B1</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">B2</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">B3</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">C1</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">C2</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>, <font color="Maroon">C3</font> be   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E2:24"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">o</font>,<font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a3</font> <a href="incproj.html#R2" target="_self">are_mutually_different</a>  &amp; <font color="Maroon">o</font>,<font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">b3</font> <a href="incproj.html#R2" target="_self">are_mutually_different</a>  )
 <b>and </b><br/><a NAME="E3:24"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">A3</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B3</font>
 <b>and </b><br/><a NAME="E4:24"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">o</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A3</font> &amp; <font color="Maroon">o</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B3</font> )
 <b>and </b><br/><a NAME="E5:24"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">a2</font>,<font color="Maroon">b3</font>,<font color="Maroon">c1</font> <a href="incproj.html#R4" target="_self">on</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b1</font>,<font color="Maroon">c2</font> <a href="incproj.html#R4" target="_self">on</a> <font color="Maroon">B1</font> &amp; <font color="Maroon">a1</font>,<font color="Maroon">b2</font>,<font color="Maroon">c3</font> <a href="incproj.html#R4" target="_self">on</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">a1</font>,<font color="Maroon">b3</font>,<font color="Maroon">c2</font> <a href="incproj.html#R4" target="_self">on</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">a3</font>,<font color="Maroon">b2</font>,<font color="Maroon">c1</font> <a href="incproj.html#R4" target="_self">on</a> <font color="Maroon">B2</font> &amp; <font color="Maroon">a2</font>,<font color="Maroon">b1</font>,<font color="Maroon">c3</font> <a href="incproj.html#R4" target="_self">on</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">b3</font> <a href="incproj.html#R4" target="_self">on</a> <font color="Maroon">A3</font> &amp; <font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a3</font> <a href="incproj.html#R4" target="_self">on</a> <font color="Maroon">B3</font> &amp; <font color="Maroon">c1</font>,<font color="Maroon">c2</font> <a href="incproj.html#R3" target="_self">on</a> <font color="Maroon">C3</font> )
 ;<br/>

<a NAME="E6:24"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:24"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">a2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">b3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">c1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A1</font> &amp; <font color="Maroon">a3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B1</font> &amp; <font color="Maroon">b1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B1</font> &amp; <font color="Maroon">c2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B1</font> &amp; <font color="Maroon">a1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">b2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">c3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">a1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">b3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">c2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">a3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B2</font> &amp; <font color="Maroon">b2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B2</font> &amp; <font color="Maroon">c1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B2</font> &amp; <font color="Maroon">a2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">b1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">c3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">b1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A3</font> &amp; <font color="Maroon">b2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A3</font> &amp; <font color="Maroon">b3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A3</font> &amp; <font color="Maroon">a1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B3</font> &amp; <font color="Maroon">a2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B3</font> &amp; <font color="Maroon">a3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B3</font> &amp; <font color="Maroon">c1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C3</font> &amp; <font color="Maroon">c2</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C3</font> )
 
<b>by </b><i><a class="txt" href="incproj.html#E2:24"><i><font color="Green">E28</font></i></a>, , </i>;<br/>
<b>reconsider </b><font color="Maroon">o'</font> = <font color="Maroon">o</font>, <font color="Maroon">a1'</font> = <font color="Maroon">a1</font>, <font color="Maroon">a2'</font> = <font color="Maroon">a2</font>, <font color="Maroon">a3'</font> = <font color="Maroon">a3</font>, <font color="Maroon">b1'</font> = <font color="Maroon">b1</font>, <font color="Maroon">b2'</font> = <font color="Maroon">b2</font>, <font color="Maroon">b3'</font> = <font color="Maroon">b3</font>, <font color="Maroon">c1'</font> = <font color="Maroon">c1</font>, <font color="Maroon">c2'</font> = <font color="Maroon">c2</font>, <font color="Maroon">c3'</font> = <font color="Maroon">c3</font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">CPS</font> ;<br/>
<a NAME="E9:24"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:24_1"/><i><font color="Green">E70</font></i>: 
not <font color="Maroon">c1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c2</font>
 ;<br/>

<a NAME="E2:24_1"/><i><font color="Green">E71</font></i>: 
not <font color="Maroon">a3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">A3</font>
 
<b>by </b><i>, , <a class="txt" href="incproj.html#E3:24"><i><font color="Green">E29</font></i></a>, <a class="ref" href="incproj.html#T6" target="_self">Th6</a>, </i>;<br/>
<a NAME="E3:24_1"/>
not <font color="Maroon">b3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">B3</font>
 
<b>by </b><i>, , <a class="txt" href="incproj.html#E3:24"><i><font color="Green">E29</font></i></a>, <a class="ref" href="incproj.html#T6" target="_self">Th6</a>, </i>;<br/>
<a NAME="E4:24_1"/><b>then </b><i><font color="Green">E72</font></i>: 
<font color="Maroon">A1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">A2</font>
 
<b>by </b><i><a class="txt" href="incproj.html#E3:24"><i><font color="Green">E29</font></i></a>, <a class="ref" href="incproj.html#T6" target="_self">Th6</a>, </i>;<br/>
<a NAME="E5:24_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">B1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B2</font>
 
<b>by </b><i><a class="txt" href="incproj.html#E3:24"><i><font color="Green">E29</font></i></a>, <a class="ref" href="incproj.html#T6" target="_self">Th6</a>, , </i>;<br/>
<a NAME="E6:24_1"/><i><font color="Green">E100</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b3</font>
 
<b>by </b><i><a class="ref" href="incproj.html#T6" target="_self">Th6</a>, , , </i>;<br/>
<a NAME="E7:24_1"/>
<font color="Maroon">c1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a3</font>
 
<b>by </b><i><a class="ref" href="incproj.html#T6" target="_self">Th6</a>, , , </i>;<br/>
<b>hence </b><a NAME="E8:24_1"/>
contradiction
 <b>by </b><i>, , <a class="txt" href="incproj.html#E3:24"><i><font color="Green">E29</font></i></a>, <a class="ref" href="incproj.html#T6" target="_self">Th6</a>, , </i>;<br/>


</div><b>end;</b></div>
<a NAME="E10:24"/><i><font color="Green">E101</font></i>: 
( <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3'</font> &amp; <font color="Maroon">a2'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3'</font> &amp; <font color="Maroon">a1'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a2'</font> &amp; <font color="Maroon">a1'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a3'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2'</font> &amp; <font color="Maroon">o'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3'</font> &amp; <font color="Maroon">b2'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3'</font> &amp; <font color="Maroon">b1'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b2'</font> &amp; <font color="Maroon">b1'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b3'</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E11:24"/><i><font color="Green">E138</font></i>: 
not <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b1'</font> <a href="collsp.html#R1">is_collinear</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:24_2"/>
<font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">b1'</font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">K</font> being   <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span><b> such that </b><br/><a NAME="E3:24_2"/><i><font color="Green">E139</font></i>: 
( <font color="Maroon">o</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">K</font> &amp; <font color="Maroon">a1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">K</font> &amp; <font color="Maroon">b1</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">K</font> )
 <b>by </b><i/>;<br/>
<a NAME="E4:24_2"/>
( <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">a1</font> &amp; <font color="Maroon">o</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b1</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:24_2"/><b>then </b>
( <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A3</font> &amp; <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B3</font> )
 
<b>by </b><i>, <a class="ref" href="incproj.html#T6" target="_self">Th6</a>, , </i>;<br/>
<b>hence </b><a NAME="E6:24_2"/>
contradiction
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E12:24"/>
( <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a2'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">o'</font>,<font color="Maroon">a1'</font>,<font color="Maroon">a3'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">b2'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">o'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">b3'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a1'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">c3'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">b1'</font>,<font color="Maroon">a2'</font>,<font color="Maroon">c3'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a1'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">c2'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a3'</font>,<font color="Maroon">b1'</font>,<font color="Maroon">c2'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a2'</font>,<font color="Maroon">b3'</font>,<font color="Maroon">c1'</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">a3'</font>,<font color="Maroon">b2'</font>,<font color="Maroon">c1'</font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i>, <a class="ref" href="incproj.html#T6" target="_self">Th6</a>, </i>;<br/>
<a NAME="E13:24"/><b>then </b>
<font color="Maroon">c1'</font>,<font color="Maroon">c2'</font>,<font color="Maroon">c3'</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E14:24"/><b>then </b>
 ex <font color="Olive">K</font> being  <a href="incsp_1.html#NM2">LINE</a> of <span class="p1">(<span class="default"><a href="incproj.html#K3" target="_self">IncProjSp_of</a> <font color="Maroon">CPS</font></span>)</span> st <br/>( <font color="Maroon">c1</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">K</font> &amp; <font color="Maroon">c2</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">K</font> &amp; <font color="Maroon">c3</font> <a href="incsp_1.html#R1">on</a> <font color="Olive">K</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E15:24"/>
<font color="Maroon">c3</font> <a href="incsp_1.html#R1">on</a> <font color="Maroon">C3</font>
 <b>by </b><i><a class="ref" href="incproj.html#T6" target="_self">Th6</a>, , </i>;<br/>


</div>
