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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="anproj_2.html#V7">up-3-dimensional</a> <a href="anproj_2.html#NM1">CollProjectiveSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>









<b>assume </b><a NAME="E1:8"/><i><font color="Green">E6</font></i>: 
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a>  or <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a>  or <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a>  or <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/>

<div><i><font color="Green">E7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><a NAME="E2:8_1"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/><b>hence </b><a NAME="E3:8_1"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:8_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="projdes1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_2"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><a NAME="E2:8_2"/><b>then </b><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:8_2"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/><b>hence </b><a NAME="E4:8_2"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E2:8_2"><i><font color="Green">E9</font></i></a>, <a class="ref" href="projdes1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_3"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><a NAME="E2:8_3"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/><b>hence </b><a NAME="E3:8_3"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:8_3"><i><font color="Green">E10</font></i></a>, <a class="ref" href="projdes1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:8_4"/>
<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/><a NAME="E2:8_4"/><b>then </b><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="projdes1.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:8_4"/>
<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="anproj_2.html#D7">ANPROJ_2:def 7</a></i>;<br/><b>hence </b><a NAME="E4:8_4"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E2:8_4"><i><font color="Green">E10</font></i></a>, <a class="ref" href="projdes1.html#D1" target="_self">Def1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:8"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="projdes1.html#R1" target="_self">are_coplanar</a> 
 <b>by </b><i><a class="txt" href="projdes1.html#E1:8"><i><font color="Green">E6</font></i></a>, <a class="txt" href="projdes1.html#E2:8"><i><font color="Green">E7</font></i></a>, <a class="txt" href="projdes1.html#E3:8"><i><font color="Green">E8</font></i></a>, <a class="txt" href="projdes1.html#E4:8"><i><font color="Green">E9</font></i></a></i>;<br/>


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